POLITECNICO DI MILANO Dipartimento di Fisica Dottorato di Ricerca in Fisica XXV ciclo Ultrafast laser–induced dynamics in ferromagnets: towards the control of the spin order from the femtosecond to the sub–nanosecond time scale Relatore: Prof. Dr. Claudia DALLERA Relatore: Dr. Ettore CARPENE Tutor: Prof. Dr. Giacomo Claudio GHIRINGHELLI Coordinatore: Prof. Dr. Franco CICCACCI Tesi di Dottorato di: Christian PIOVERA Matr. 754139 Anno Accademico 2012–2013
Transcript
POLITECNICO DI MILANO
Dipartimento di Fisica
Dottorato di Ricerca in Fisica
XXV ciclo
Ultrafast laser–induced dynamics in
ferromagnets:
towards the control of the spin order from
the femtosecond to the sub–nanosecond time
scale
Relatore: Prof. Dr. Claudia DALLERA
Relatore: Dr. Ettore CARPENETutor: Prof. Dr. Giacomo Claudio GHIRINGHELLI
4.1 Fermi level distribution . . . . . . . . . . . . . . . . . . . . . . 354.2 Two temperatures model . . . . . . . . . . . . . . . . . . . . . 374.3 Ultrafast demagnetization in nickel films . . . . . . . . . . . . 394.4 Three temperatures model . . . . . . . . . . . . . . . . . . . . 404.5 TR-XMCD measurements of S and L momenta . . . . . . . . 424.6 Ultrafast magnetic dynamics in 4f rare–earth ferromagnets . . 444.7 Ultrafast magnetic dynamics in half–metallic systems . . . . . 454.8 Free-energy in 2D real space . . . . . . . . . . . . . . . . . . . 474.9 Transverse and longitudinal hysteresis loops in iron thin films 484.10 Switching fields vs external field orientation . . . . . . . . . . 504.11 Ultrafast TR-MOKE and transient reflectivity . . . . . . . . . 514.12 Time-resolved reflectivity at various wavelength . . . . . . . . 524.13 Ultrafast demagnetization vs pump intensity . . . . . . . . . . 534.14 Iron DOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554.15 Magnon creation process . . . . . . . . . . . . . . . . . . . . . 58
10 List of figures
4.16 TR-MOKE for different ambient temperatures . . . . . . . . . 594.17 Temperature dependence of the magnetization in iron . . . . . 604.18 Iron specific heat . . . . . . . . . . . . . . . . . . . . . . . . . 604.19 Absorbed energy vs incidence fluence . . . . . . . . . . . . . . 614.20 TR-MOKE vs pump fluence at room temperature . . . . . . . 624.21 Demagnetization vs absorbed energy . . . . . . . . . . . . . . 634.22 Spin temperature vs absorbed energy . . . . . . . . . . . . . . 634.23 Ellitot–Yafet demagnetization vs ambient temperature . . . . 65
5.1 Sketch of electronic superdiffusive process . . . . . . . . . . . . 705.2 Simulation of electronic superdiffusion . . . . . . . . . . . . . 715.3 TMR sample . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.4 TMR characterization . . . . . . . . . . . . . . . . . . . . . . 745.5 Sketch of the optical layout (ii) . . . . . . . . . . . . . . . . . 765.6 TMR conductance vs applied voltage . . . . . . . . . . . . . . 775.7 TMR hysteresis cycles . . . . . . . . . . . . . . . . . . . . . . 785.8 TRM demagnetization vs pump intensity . . . . . . . . . . . . 795.9 TMR demagnetization vs applied current (medium intensity) . 805.10 TMR demagnetization vs applied current (high intensity) . . . 815.11 TMR demagnetization vs applied current (low intensity) . . . 815.12 Photo–induced voltage vs external field and applied voltage (i) 835.13 Photo–induced voltage vs external field and applied voltage (ii) 845.14 Photo–induced voltage vs external field and applied voltage (iii) 85
6.1 Laser induced magnetic precessional motion . . . . . . . . . . 916.2 Inverse Faraday effect . . . . . . . . . . . . . . . . . . . . . . . 926.3 Polarization effects in garnet samples . . . . . . . . . . . . . . 936.4 Magnetic switching via precessional motion . . . . . . . . . . . 946.5 Magnetic pulses generated at the SLAC facility . . . . . . . . 956.6 Sublattices magnetic dynamics in ferrimagnetic FeGdCo . . . 976.7 All–optical switching in GdFeCo . . . . . . . . . . . . . . . . . 986.8 Magnetic switching in (GaMn)As . . . . . . . . . . . . . . . . 996.9 Experimental geometry for magnetic switching . . . . . . . . . 1006.10 Static characterization of iron thin films . . . . . . . . . . . . 1016.11 The effect of multiple pump pulses . . . . . . . . . . . . . . . 1036.12 Magnetic switching dynamics . . . . . . . . . . . . . . . . . . 1046.13 Sketch of the switching process . . . . . . . . . . . . . . . . . 1066.14 Temporal evolution of temperature and effective field . . . . . 108
7.1 Kerr rotation and ellipticity in nickel films . . . . . . . . . . . 1137.2 Sketch of the optical layout (iii) . . . . . . . . . . . . . . . . . 116
List of figures 11
7.3 Kerr rotation and ellipticity . . . . . . . . . . . . . . . . . . . 1217.4 Disentengling optical and magnetic contributions in TR-MOKE124
12 List of figures
Introduction
Time dependent mechanisms in magnetism cover a wide range of phenomena.The corresponding time scales embrace an extremely large window that canrange from tens of years of logical bit lifetimes in data storage devices to thesub–picosecond rate of electronic interactions. From the technological pointof view, the demand for increasing writing speed in memory devices booststhe research towards the investigation of the fastest regime. However such ashort timescale is connected to very fundamental processes at the microscopicand atomic level where our comprehension is still cloudy. The main limitingfactor is the difficulty to experimentally access the correspondent temporalwindow. The study of the so–called ultrafast spin dynamics has been possibleonly recently, thanks to the development of femtosecond laser sources. Theavailability of ultrashort light pulses allows one to probe the evolution of thesystem properties via optical spectroscopies and with femtosecond resolution.
The first pioneering work was performed by Beaurapiere and coworkersin 1996 [1]. They shined a nickel sample with intense femtosecond pulses andobserved a quenching of the spin order occurring in less than a picosecondafter the optical excitation. This process has been called ultrafast demag-netization. Nowadays, it is a well–known laser induced effect in common 3dmagnetic metals, however its comprehension is still under debate after morethan 16 years [2] [3] [4] [5] [6] [7] [8].
The work of Beaurapiere et al. raised interesting opportunities also fortechnological applications. Femtosecond laser pulses revealed to be capableof manipulating the spin order at rates several order of magnitude faster thanmodern magnetic computer components. One of the most intriguing possi-bility is to optically reverse the direction of the magnetization resembling thewriting mechanism of memory devices. From the first experimental demon-strations of nanosecond laser–assisted magnetic inversion in 1997 [9] [10], upto now, picosecond switching has been achieved only in few cases, for in-
2 Introduction
stance, in specific ferrimagnetic samples or in low temperature ferromagneticsemiconductors [11] [12] [13].
In the present work we study laser induced spin dynamics in metallicferromagnets. We exploit the pump–probe technique to detect the transientmodification of the magneto-optical Kerr effect (MOKE) within an extenttime window from few femtoseconds to hundreds of picoseconds. Three arethe main purpose of the investigation: (i) disclosing the mechanisms under-lying the ultrafast demagnetization process, (ii) developing a reliable experi-mental method to achieve the optical spin switching in the picosecond regimeand (iii) studying optical contributions to transient MOKE signals.
First of all, focusing our attention on the femtosecond regime, we charac-terize the ultrafast dynamics of the magnetic order for different laser inten-sities and ambient temperatures in metallic systems. In particular the inves-tigated samples are 8 nm thin iron films expitaxially grown on MgO in ourlaboratory. The observed temperature dependence of the ultrafast demagne-tization and the slower remagnetization allows us to ascribe the former effectto the electron–magnon interaction [2], while the latter to the Elliot–Yafettype electron-phonon scattering. On the other hand, ultrafast spin trans-port phenomena have been investigated during my six months visit at theSpectroscopy of Solids and Interfaces (SSI) group of Professor Dr. T. Rasingat the Radboud University in Nijmegen (Netherlands). According to recenttheories the demagnetization may take place as a consequence of majorityspin draining from the irradiated area [7] [14]. Therefore, we have studiedthe effect of laser excitation in tunneling magnetoresistance microstructureswith the main scope of finding a correlation between spin currents and ultra-fast dynamics. A non negligible possible outcome of such studies, combiningultrafast dynamics and electronic devices, could be the generation of electro-optical devices exploiting femtosecond laser induced spin motion. However,our measurements are still in progress, thus only some preliminary resultsare shown and interpreted in the framework of the electronic superdiffusiontheory.
Secondly, in the picosecond regime, we demonstrate the possibility tochange the magnetization direction in thin iron layers using only ultrashortlaser pulses. The sample heating due to photon absorption, results in co-herent spin waves. With a proper orientation and intensity of the externalfield, we show that it is possible to control the magnetic precessional motion.In this way we could reproducibly and repeatedly commute the magneticvector between preferential directions in less than 100 ps. This rate is morethan ten times higher than the working speed of modern storage magneticdevices. In addition, ferromagnetic iron is characterized by an in–plane bi-axial anisotropy, with the interesting technological followup of allowing one
Introduction 3
to record two bits of information on the same spot.To conclude, we address the problem of optical artifacts in pump-probe
magneto–optical experiments. The measured spin dynamics can contain atransient optical contribution not related to the true magnetic evolution thatmay lead to a wrong interpretation of the experimental data. This issue isof fundamental importance, since our knowledge about ultrafast phenomenais retrieved only via optical spectroscopies. In particular concerning the TR-MOKE technique, many experimental works [15] [16] have already demon-strated that the measured magneto–optical Kerr effect may not follow thetransient spin behavior in the first hundreds of femtoseconds. However in thepicosecond time scale no experimental evidence of optical contribution hasbeen observed up to now. We show that, under particular condition, the Kerrsignal might considerably differ from the genuine magnetic dynamics also fora pump and probe delay longer than 50 ps. We have investigated this issuein two benchmark systems, Fe and CrO2, that allowed us to disentangle themagnetic information from purely optical one after a wide characterization ofthe TR-MOKE dynamics. This last work arises from a collaboration with theexperimental groups of Prof. Dr. M. Munzenberg at the I. PhysikalischesInstitut of Georg–August–Universitat Gottingen (Germany) and Prof Dr.A. Gupta from the department of chemistry of the University of Alabama(USA)
4 Introduction
Chapter 1Time–dependent phenomena in
magnetism
The main subject of the present work is laser induced dynamics in ferromag-netic metallic systems. Exploiting the pump–probe method and femtosecondpulses generated by modern ultrafast laser sources, it is possible to explorethe effects of the optical excitation below the picosecond timescale. For thesake of simplicity, we will identify two different regimes characterized by dis-tinct spin relaxation processes: the femtosecond timescale dominated by theso–called ultrafast demagnetization, and the picosecond one where the maindriving force is the sample heating due to photon absorption. In the lattertemporal window, many processes interesting for technological applicationsmay occur like spin oscillations and magnetic switching.
This section will briefly embrace time-dependent magnetic processes occur-ring from a timescales of few milliseconds to the femtosecond regime. Shrink-ing the temporal dimensions means looking at the very fundamental and stillunclear electronic processes with consequent issues, both experimentally andtheoretically, on the techniques necessary for their comprehension.
6 Time–dependent phenomena in magnetism
Fig. 1.1: Temporal scales of magnetic phenomena.
Generally speaking, a magnetic system at equilibrium is trapped in a sta-ble state and, if the temperature is low enough, it will indefinitely remain inits initial condition. However, raising the temperature, thermal fluctuationscan offer the chance to overcome energy barriers leading the system to newstates. This thermal relaxation dominates the slower temporal scales, theycan last for years till the magnetic arrangement of the specimen reaches itslower energetic state [17]. However, the process can be considerably accel-erated by the presence of an external field. Under such conditions, if theapplied magnetic field is strong enough, the magnetization will change orien-tation in order to minimize its energy. From the microscopic point of view thedynamical process that brings the system to this new state is characterizedby the formation of magnetic domains and the expansion of their boundariescalled domain walls. Magnetic domains are regions in which all the spinsare parallel; these areas grow through domain wall motion till they cover thewhole sample. The fundamental involved mechanisms, nucleation of domainand their propagation, are characterized by different timescales, as sketchedin Fig. 1.1.
Starting from the domain wall motion, its velocity depends on manyfactors, both intrinsic and extrinsic to the studied system. The dipolar mag-netic interaction and the magneto crystalline anisotropy mainly determinesthe propagation. However, also external factors such as temperature, appliedfields, the shape of the sample and the presence of defects may alter the pro-cess. Domain wall velocities can be as fast as ∼ 104 m/s [17]. However,
1.1 Timescales 7
when the magnetization motion is dominated by this kind of process, therate to achieve the rearrangement of the magnetization can widely spreadfrom milliseconds to the nanosecond range [18].
On the other hand the domain nucleation has revealed to be even threeorder of magnitudes faster. It consists in the coherent rotation of the spinsin an uniformly magnetized region of the sample. The energy necessary isof the order of the anisotropy barrier. For thermally activated processes therate is about ∼ 10−9 − 10−8 s while in the presence of a field it can be fasteras 10−12 s [19]. Given the very high speed characterizing the mechanism, i.e.few picoseconds, the magnetic precession in an external field is considered themost effective route to control the magnetization in ferromagnets. Howeverin 2004 Tudosa et al. [20] demonstrated that the magnetization switchingcannot take place below 2 ps: beyond this temporal limit the spin motionbecome non-deterministic and chaotic. This fact puts new constraints to thedevelopment of technological devices, pushing further the research of novelmagnetic phenomena for applications.
With this respect, faster processes have been found at the quantum elec-tronic level. Here, the spin order is established by strong correlations amongelectrons, which are subject to interactions with characteristic rates well be-low 1 ps. As we will see in the next sections, scattering events betweenparticles and quasiparticles can trigger magnetization dynamics in the fem-tosecond regime. For instance, we can mention the creation of Stoner pairsvia Coulomb and exchange interactions or the generation of collective phe-nomena like spin–waves and phonons [21] [22] [23] [24] [25].
However, the knowledge of spin dynamics in this temporal regime is stillvague and debated. One of the main obstacle comes from the difficulty toexperimentally explore the processes in the related time window. Up tonow only optical spectroscopies can probe the femtosecond regime thanksto the recent development of ultrafast laser sources. However, the temporalresolution reveals not high enough in certain circumstances [26] [27] and alsothe use of light to study magnetism has many drawbacks [15] [16] [4]. Oneof the most common technique to perform time–resolved experiments usinglight is the pump–probe method. A laser pulse, called pump, is sent to thesample in order to excite the electronic population and trigger scatteringevents among particles. After a certain delay a probe pulse measures thelaser–induced modifications. In particular, a well-established technique toretrieve the spin evolution is the time-resolved magneto-optical Kerr effect(TR–MOKE) that monitors modification of intensity and polarization of alight beam after the reflection from a magnetic surface.
The study of laser induced spin dynamics through TR-MOKE is the mainsubject of this thesis.
8 Time–dependent phenomena in magnetism
Fig. 1.2: Laser–induced evolution of the magnetization (in particular, theprojection perpendicular to the sample) of a nickel thin film as a functionof the pump–probe delay in picosecond. The pump pulse arrives at ∆t = 0(I). The first picosecond of the dynamics (II) is characterized by a suddendecrease of the magnetization than it starts oscillating with a period of about100 ps for more than half a nanosecond (III). Source [28].
1.2 In this thesis
Time–resolved magneto–optical Kerr effect, the technique employed to mea-sure the magnetic dynamics, is widely described in Chapter 2 together withthe pump–probe method while the optical layout of the experimental setupis presented in Chapter 3.
Spin dynamics triggered by ultrashort laser pulses have been studied fromthe femtosecond timescale, Chapter 4 and 5, to few hundreds of picoseconds,Chapter 6 and 7.
The faster scale is dominated by the so–called ultrafast demagnetizationprocess. In ferromagnetic 3d metals, quenching of the spin order occurswithin 100–200 fs [Fig. 1.2 (II)]. Up to now, many theories have been proposedto explain such effect, see Chapter 4 section 4.1.2. The angular momentumcan be dissipated by different channels, hence the ultrafast demagnetizationcan be regarded as the result of a cooperation among several processes withdistinct contributions. As discussed in Chapter 4, the ultrafast generation ofmagnon may be the main responsible of angular momentum dissipation inIron thin films. On the other hand, laser–induced spin transport phenomenahave been observed capable of influencing the demagnetization in tunnellingmagneto resistance (TMR) systems, as described Chapter 5.
In the picosecond timescale, the sample heating can launch magneticprecessions [Fig. 1.2 (III)]. As explained in Chapter 6 sections 6.1.1 and6.1.2, this is the fastest way to control the magnetization direction with
1.2 In this thesis 9
consequent impacts on technological applications; the magnetic switchingis the mechanism underlaying the writing operations in magnetic memorydevices. We will present a method to achieve all–optical switching in ironthin films within 100 ps.
In the following Chapter 7, we will study the presence of optical contri-bution to the TR-MOKE in the picosecond temporal range. We will showthat time–resolved Kerr rotation and ellipticity can considerably differ forpump–probe delays longer than 50 ps in CrO2 systems. Thus we will pro-pose a method to retrieve the genuine magnetic dynamics from the acquiredcomplex Kerr angle.
The detailed structure of the thesis is reported in the following:
• Chapter 2 describes the magneto–optical Kerr effect with particularattention to the experimental methods used to retrieve the 3D spatialposition of the magnetic vector, section 2.2. In section 2.3 we explainthe pump–probe technique employed to perform time–resolved MOKEexperiments.
• In Chapter 3 we describe the experimental setup. Sections 3.3.1, 3.3.2,3.3.3 and 3.3.4 are devoted to the acquisition methods. Particularattention is focused on 3.3.3 and 3.3.4, presenting the procedure used todetect the optically induced magnetic switching. Section 3.4 is devotedto the sample preparation technique.
• Chapter 4 reports the study of the ultrafast demagnetization process iniron thin films. The introduction, 4.1, is devoted to the state of the artabout laser induced ultrafast spin dynamics. The magnetic propertiesof the sample are described in section 4.2 while, the following part,4.3, reports a detailed description of the electronic and spin dynamicsin iron. The new experimental results are showed and discussed insection 4.4 and 4.5.
• Chapter 5 reports the preliminary results on laser induced spin trans-port phenomena in tunneling magneto resistance (TMR) samples. Thedetails of the TMR systems and the experimental setup are in sec-tions 5.3 and 5.4. The results of our measurements are displayed andcommented in section 5.5.
• In Chapter 6 we present the all–optical magnetic switching in iron thinfilms. The core of this mechanism relies in the laser–excited magneticprecessions, described in section 6.1.1, while the magnetic switching isreported in section 6.1.2. In section 6.2 the experimental geometry that
10 Time–dependent phenomena in magnetism
is of fundamental importance to achieve laser induced spin reorienta-tion is illustrated. After that the experimental data are shown in twoseparate sections: 6.3 describes the effects of multiple pump pulses onthe magnetization position, while 6.4, shows the ultrafast trajectory ofthe picosecond switching. The subsequent discussion is in section 6.5.
• In Chapter 7 we study the presence of optical contribution in TR-MOKE measurements by making a comparison between laser–induceddynamics in Fe and CrO2 films. The presence of optical artifacts is awell–known issue in magneto–optics, as explained in the introductivesection 7.1. The studied samples, i.e. epitaxial Fe and CrO2, are pre-sented in section 7.2. In section 7.3 we discuss the experimental methodwith particular attention to the technicalities exploited to detect kerrrotation and ellipticity for to different polarizations of the probe pulse.In section 7.4 we show the experimental results comparing the opti-cal responses of the two samples. Finally in section 7.5 a method fordisentangling optical and magnetic dynamics is developed.
Chapter 2Experimental methods
In the following we will presented a time-resolved magneto-optical Kerr effect(TR MOKE) experimental configuration capable of entirely characterizingthe magnetization dynamics in thin magnetic films with sub–picosecond res-olution. The magneto–optical Kerr effect can be fully understood in terms ofFresnel scattering matrix formalism: it is essentially based on the variationof the light polarization state reflected from a magnetic surface. This formal-ism is treated in detail for two different experimental geometries. Startingfrom these results, we will show a method to characterize the magnetic vectormeasuring all the real 3D spatial components. The power of the approach re-lies in the possibility to perform vectorial MOKE without modifying neitherthe sample position nor the detection geometry. In addition, the temporalevolution of the magnetization after an optical perturbation can be sampledby the pump–probe technique. It is actually the most common method usedto perform time–resolved experiments via optical spectroscopies.
Light interacting with a magnetic material can undergo modifications of itspolarization state. This effect was first observed in 1845 when Micheal Fara-day, studying the properties of the transmitted light by a glass specimen,showed the possibility to rotate the photon polarization applying an exter-nal magnetic field. More in detail a linearly polarized electromagnetic wavebecomes elliptically polarized with its major axis rotated with respect to theinitial oscillation direction. Later on, in 1877, John Kerr found the sameeffect in reflection.
To clarify these processes we can carry out the following phenomenolog-ical explanation: in a magnetic material circularly right and circularly leftpolarized photons experience different dispersion relations leading to a phaseshift; given that a linearly polarized wave is the superimposition of two circu-larly polarized modes of opposite chirality, we can now explain the rotation.Finally differences in the absorption will introduce the ellipticity.
From a more formal point of view, the effect can be described by the off-diagonal elements of the dielectric tensor: the presence of a magnetic fieldaffects the induced polarization in a direction dependent on its orientation.Therefore an electromagnetic wave along one particular axis will induce anadditional polarization in other directions.
MOKE magnetometry techniques measure changes in the reflected lightdirectly related to the magnetization state of a material. The effect can berelatively small; for example in Fe, Co and Ni, the rotation angle is less thanone degree in the visible range of the spectrum [29] but thanks to modulationmethods, it is possible to be sensitive to even submonolayer magnetic films.[30].
In the following section the MOKE formalism is presented clarifying thepossible detection geometries in order to retrieve the full magnetic informa-tion.
2.2 Vectorial magneto-optical Kerr effect
The knowledge of the magnetization vector is of fundamental importancein the study of magnetic oscillations and anisotropies. In this section wewill show how the magneto-optical Kerr effect can be used to derive thisinformation. The so-called vectorial MOKE technique allows to measure themagnetization orientation in space. It relies on a particular combinationof light polarization and experimental arrangements that can be understoodconsidering the scattering Fresnel matrix formalism combined with the Jones
2.2 Vectorial magneto-optical Kerr effect 13
Fig. 2.1: Experimental geometry. The probing beam impinges on the samplewith an angle θi with respect to the normal to the sample and passes througha Glan-Thompson polarizer rotated of θa from the incidence plane. Theexternal magnetic field Hext is applied along the sample surface and normalto the incidence plane. The M vector represents the sample magnetizationwhile the black axes identify the polar ”p”, the longitudinal ”l” and transverse”t” directions.
calculus method. Within this description the polarized light is expressedin vectorial form while the optical elements and the sample are treated assquared matrices.
First of all, it is necessary to identify a frame of reference. In Fig. 2.1the magnetization vector M is decomposed into projections named accordingto their relative orientation with respect to the light scattering plane: thetransverse and the longitudinal components, Mt and Ml, lie on the samplesurface,respectively perpendicular and parallel to the incidence plane, whilethe polar component Mp is normal to the sample. Concerning the electro-magnetic wave polarization we can identify two axes: the vertical one called”s” that is perpendicular to the incidence plane and the horizontal ”p” whichis parallel. Two other parameters have to be emphasized: the probe beamshines the sample at an angle θi with respect to the surface normal and thereflected light passes trough a Glan-Thompson polarizer rotated by θa fromthe incidence plane. In the Jones formalism, the probe electromagnetic planewave can be expressed as:
(Ep(t)Es(t)
)
= E0
(E0pe
i(kz−ωt+φp)
E0sei(kz−ωt+φs)
)
= E0ei(kz−ωt)
(E0pe
iφp
E0seiφs
)
(2.1)
14 Experimental methods
As depicted in Fig. 2.1, the probe runs into a polarizer after being reflectedby the sample. The resulting light beam is evaluated multiplying eq. 2.1 bythe square matrixes associated to the sample S and the analyzer G:
(Ef
p (t)Ef
s (t)
)
= G ∗ S ∗(Ep(t)Es(t)
)
(2.2)
The square matrix G spatially selects one of the possible orientation for thepolarization of the reflected light:
(cos2(θa) cos(θa) sin(θa)
sin(θa) cos(θa) sin2(θa)
)
(2.3)
On the other hand, S comes from the Fresnel reflection matrix and is respon-sible for the magneto-optical signal. The diagonal components of S deter-mines the reflected intensity while the off–diagonal components are relatedto the magnetic contribution to the optical dielectric tensor. The latter canbe written as function of the transverse, longitudinal and polar projection ofM, allowing to decompose S as the superposition of three terms associatedto their relative contributions to the Kerr effect:
S = m2t T +m2
l L+m2p P (2.4)
with:
T =
(rpp (1 + rt0/mt) 0
0 rss
)
(2.5)
L =
(rpp rlps/ml
−rlps/ml rss
)
(2.6)
P =
(rpp rpps/mp
rpps/mp rss
)
, (2.7)
mt = Mt/Ms, ml = Ml/Ms, mp = Mp/Ms and m2t + m2
l + m2p = 1, with
Ms the saturation magnetization. In the matrix elements rij , the subscriptsdenote the scattering dependence, i.e. rps couples the incident s–polarizedfield component upon reflection into a p–polarized component, while r0 isresponsible for a modulation of the signal intensity that is proportional tothe magnetization thus non altering the light polarization. These terms can
2.2 Vectorial magneto-optical Kerr effect 15
be explicitly written as:
rpp =
(nβ − β ′
nβ + β ′
)
(2.8)
rss =
(β − nβ ′
β + nβ ′
)
(2.9)
rlps =βiQγ
β ′ (nβ + β ′) (β + nβ ′)(2.10)
rpps = − βiQn
(nβ + β ′) (β + nβ ′)(2.11)
rt0 =2βiQγ
n2β2 − β ′2 (2.12)
In the above equations, n is the complex refractive index of the material,
β = cos θi, γ = sin θi and β ′ =√
1− (γn)2. Q is the magneto optical
constant, it is a complex number and we can write it in polar coordinatesQ = Q0e
iq. The magnitude Q0 is proportional to the magnetization M andq is the phase. For example in bulk iron the value at saturation given byVoigt [31] is Q = 0.0215ei0.073
At this point we have all the ingredients to evaluate the electromagneticwave resulting from the interaction with the sample and the polarizer (eq.2.2):
(Ef
p (t)Ef
s (t)
)
=
(cos2(θa) cos(θa) sin(θa)
sin(θa) cos(θa) sin2(θa)
)[m2
t T +m2l L+m2
p P](Ep(t)Es(t)
)
(2.13)
To make an estimation of the results of our experiments, it is necessary topoint out which is the physical quantity of interest. After the analyzer aphotodiode detects the total intensity that, in our formalism, is given by thesquared modulus of the light vector:
I = |Ef , p(t)|2 + |Ef , s(t)|2 (2.14)
These relations represent the backbones to quantitatively determine thereal–space components of the magnetization vector. In the next sections wewill consider two particular experimental cases in which the polarization ofthe probe is either completely vertically or completely horizontal with respectto the scattering plane. We will call the former longitudinal MOKE and thelatter transverse MOKE.
16 Experimental methods
2.2.1 Longitudinal MOKE
In longitudinal MOKE the probe electromagnetic wave oscillates in a planenormal to the incidence one. This assumption considerably simplifies thematrix calculations observing that the probe vector contains only the Es
term. Eq. 2.13 becomes:
Es
(cos(θa)
(rss sin(θa) + cos(θa)
(mlrps
l +mprpps
))
sin(θa)(rss sin(θa) + cos(θa)
(mlr
lps +mpr
pps
))
)
(2.15)
Eq. 2.15 is a two dimensional vector representing a light beam with polariza-tion components both on the horizontal and the vertical axes. As we expectthe reflection from the sample has a different polarization state. The totalintensity is given by the sum of the products of the two terms in eq. 2.15with their complex conjugate (c.c.):
I =|Es|2(cos(θa)
2 + sin(θa)2) [
rssrss ∗ sin(θa)2
+(rss sin(θa) cos(θa)mlr
lps ∗+c.c.
)+(rss sin(θa) cos(θa)mpr
pps ∗+c.c.
)
+ m2l r
lpsr
lps ∗ cos(θ)2 +m2
prppsr
pps ∗ cos(θ)2 +
(mlmpr
lpsr
pps ∗+c.c.
)]
(2.16)
In this expression the last three terms are proportional to |Q|2 and can safelybe neglected once pointed out that the magneto optical constant is in generalvery small, as shown in the previous section. The simplified expression of eq.2.16 is:
I
|Es|2= If = A sin(θa)
2 + (Cml +Dmp) cos(θa) sin(θa) (2.17)
where:
A = |rss|2 (2.18)
C = 2<{
rss(rlps)∗}
(2.19)
D = 2<{rss(rpps)∗}
(2.20)
By a deeper inspection of the three coefficients we notice that A dependsonly on the refractive index and on the incidence angle θi, while C and Dare also function of the magneto-optical constant. Moreover no informationabout the transverse component of the magnetization can be extracted by eq.2.17. With the present experimental geometry it is not possible to measurethe component of M normal to the incidence plane thus another opticalconfiguration should be explored.
2.2 Vectorial magneto-optical Kerr effect 17
2.2.2 Transverse MOKE
Transverse MOKE is characterized by a polarization of the probe beam par-
allel to the scattering plane. Choosing
(Ep
Es
)
=
(Ep
0
)
in eq. 2.13, we obtain:
Ep
(cos(θa)
(rpp cos(θa) + sin(θa)
(−mlrps
l +mprpps
))
sin(θa)(rpp cos(θa) + sin(θa)
(−mlr
lps +mpr
pps
))
)
(2.21)
Having in mind the discussion for longitudinal MOKE, the total measuredintensity can be written as:
I =|Ep|2(cos(θa)
2 + sin(θa)2) {
cos(θa)2rppr
∗pp [1 +mtr0r
∗0 + (mtr0 + c.c.)]
+ sin(θa) cos(θa)rpp[(mpr
p∗ps + cc
)−(mlr
l∗ps + c.c.
)]
+[rpp sin(θa) cos(θa)mtr0
(mpr
p∗ps −mlr
l∗ps
)+ c.c.
]
+ sin(θa)2m2
prppsr
p∗ps − sin(θa)
2m2l r
lpsr
l∗ps
}(2.22)
We can again safely drops the terms proportional to |Q|2, third and fourthlines of eq. 2.22, obtaining:
I
|Ep|2= If = (A′ +B′mt) cos(θa)
2 + (C ′ml +D′mp) cos(θa) sin(θa) (2.23)
where:
A′ = |rpp|2 (2.24)
B′ = 2|rpp|2Re {r∗} (2.25)
C ′ = 2<{rppr
l∗ps
}(2.26)
D′ = 2<{rppr
p∗ps
}(2.27)
The final expression for the intensity closely reminds the one found for thelongitudinal geometry (eq. 2.17). A′, C ′ and D′ coefficients contains rppinstead of rss. In addition also the transverse component of the magnetizationmt, multiplied by B′ depending on the experimental parameters, appears ineq. 2.23. At this point a way to disentangle the three components of themagnetic vector mt, mt andmp from the total measured intensity needs to beworked out. In the next section we will show that the problem can be solvedexploiting simple symmetries in the experimental setup and in the studiedsamples. In this way only two different measurements are enough and neitherthe sample position nor the detection geometry need to be modified.
18 Experimental methods
Fig. 2.2: The coefficients B′, C ′ and D′ calculated as a function of the inci-dence angle θi with Q = 0.025e−0.003 and n = 2.7 + i2.1.
2.2.3 Acquiring the three spatial components of the
magnetic vector
To separate the three component ml, mt and mp we have to enlist somebasic properties of eq. 2.17 and eq. 2.23. Let’s focus on the transverseMOKE intensity 2.23, than the whole discussion can be directly transportedto the longitudinal case. Considering the θa dependence, we can disentanglethe reflectivity and the transverse part (A′ + B′mt), from (C ′ml + D′mp).These terms are multiplied by functions with opposite parity, the first onefor an even function in θa, i.e. cos(θa)
2, while the second one by an odd,i.e.cos(θa) sin(θa).
If = (A′ +B′mt) cos(θa)2
︸ ︷︷ ︸
even
+ (C ′ml +D′mp) cos(θa) sin(θa)︸ ︷︷ ︸
odd
(2.28)
Making two measurements at opposite values of the analyzer angle θa we canevaluate:
Isum = If(θa) + If (−θa) = A′ +B′mt (2.29)
Idiff = If(θa)− If(−θa) = C ′ml +D′mp (2.30)
where Isum contains only the transverse projection mt while Idiff the polarmp and the longitudinal ml. A′ does not affect the magnetic properties ofIsum since it represents only a shift not depending on M. On the otherhand Idiff needs to be further discussed. The C ′ and D′ coefficients arefunction of the incidence angle thetai, the refractive index n and the magneto
2.2 Vectorial magneto-optical Kerr effect 19
Fig. 2.3: Experimental geometry with a biaxial in plane anisotropy system(a) and an uniaxial one (b). For positive external field, the magnetization(pointing upwards) sees the probe beam coming from the right-hand-side.For negative values (dashed vectors) the beam is coming from the oppositeside.
optical index Q. Fixing n and Q we can evaluate their dependence on θifrom eq. 2.26 and 2.27 together with 2.9, 2.11 and 2.12. The results arereported in Fig. 2.2. C ′ is an odd function while D′ is even. This suggestsa way to disentangle the magnetic terms making two measures at oppositeincidence angle and performing again sum and differences. However thismethod requires a modification of the experimental setup and the ability toperfectly align the sample position with respect to the probe beam. Thisis not actually a reliable and easy way to operate, thus another solutionhas been found. Let’s consider two systems with different in plane magneticanisotropies, i.e biaxial and uniaxial anisotropies (see Fig. 2.2) and let’s applyan external field on the sample surface. In Fig. 2.2 (a) we show a biaxial inplane anisotropy system typical for cubic structures like iron bcc (100). If weobserve the relative position of M and the easy axes we note the following:the configuration with the probe coming from the right side (θi > 0) andpositive external field (Hext = 0) is equivalent to the configuration where thebeam comes from the left side ((θi < 0)) and the external field is negative(Hext < 0). This is true also in Fig. 2.2 (b) where a in plane uniaxialanisotropy sample is considered. This means that making two measurementsat two opposite incidence angles corresponds to measuring at two oppositevalues of the external field. From eq 2.30 we obtain:
Idiff (+Hext)− Idiff (−Hext) = 2C ′ml (2.31)
Idiff (+Hext) + Idiff (−Hext) = 2C ′mp (2.32)
At this point, once we know the experimental parameters and the sample
20 Experimental methods
properties (refractive index and magneto opical constant) a numerical esti-mate of A′, B′, C ′ and D′ can be performed. By eq. 2.29, 2.31 and 2.32 wecan finally obtain the real values of ml mp and mt separately.
2.3 TR-MOKE: pump and probe technique
To study the dynamics of a system or the trajectory of simple moving parti-cles, it is necessary to periodically sample their properties during the motion.If we use a camera to freeze frame by frame its evolution we generate a movie.The pump-probe technique is based on a similar approach. A first very shortstimulus, called pump, excite some kind of movement and a likewise fast probelooks at its evolution at different delays (e.g. the cameras). This method isbased on the repeatability of the triggered dynamics. The motion is probedonly once before it stops so it should be launched many times and observedat different delays. The duration of the probe and the pump defines the timeresolution of the retrieved dynamics. To investigated phenomena in the sub-picosecond regime it is thus necessary to operate within this timescale. Thisopportunity is offered by ultrafast laser systems producing few femtosecondslight pulses. Shining a laser pump on a ferromagnetic metal we can locallyexcite the sample bringing the electronic population out of equilibrium. Af-ter a certain delay the probe pulse arrives and undergoes some modificationdue to the transient effect generated by the optical perturbation. Measur-ing these effects, it is possible to extract the laser induced dynamics withfemtosecond resolution.
In this scheme the first laser shot has high intensity and large spot di-mensions on the sample. Typical fluence used on metallic samples are of theorder of few mJ/cm2 that, given a beam diameter of about 100 µm, corre-spond to a pulse energy of about 0.1 µJ. For instance in iron laser intensitieshigher than 14 mJ/cm2 are very close to the sample destruction threshold.Besides, the probe pulse must be very weak, to do not change the systemproperties, and smaller in size, i.e. 10 µm or down to the diffraction limitiwith microscope techniques.
The wavelength of the probe determines the sensitivity of the measure-ments. Infrared, optical, ultraviolet, or x-ray spectral ranges, define verydifferent electronic transitions and consequently provide different informa-tion.
In particular the data shown in this thesis have been acquired employingthe magneto–optical Kerr effect. As demonstrated in the previous section2.2, the detected MOKE signal is proportional to the real magnetic vector,therefore the pump–pump method allows one to retrieve the magnetic spatial
2.3 TR-MOKE: pump and probe technique 21
3D trajectory triggered by optical excitation in the femtosecond time scale.The laser pulses have a wavelength of 800 nm, equal to 1.55 eV, with a full-width-half-maximum of ∼ 50 fs and a corresponding temporal resolution ofabout 75 fs (given by the cross correlation of the pulses).
22 Experimental methods
Chapter 3Experimental set-up
In this chapter the experimental set-up exploited for time-resolved magneto-optical Kerr effect measurements is described. Starting from the light gen-eration and then passing to the beamline, we will follow the ultrafast laserpulse until it reaches the sample where the TR-MOKE signal is detected.The first section 3.1 deals with the laser source used for pump and probeexperiments. Thus the beam line for magneto-optical Kerr effect measure-ments is presented in section 3.2 with special attention to the data aquisitionmethod 3.3. Here it is important to stress that different requirements has tobe taken into account when we want to deal with light induced modificationof the sample ground state.
The laser source is a Coherent Inc. commercial system capable of light pulseswith a Gaussian temporal profile of 50 fs full width half maximum. Thephoton energy is about 1.55 eV corresponding to a wavelenght of 800 nmand the total power reaches 2 W at a repetition rate of 1 kHz.
It is a mode-locked amplified Titanium:sapphire laser composed by 2stages:
• a mode-locked MIRA Ti:sapphire oscillator;
• a LEGEND Ti:sapphire regenerative amplifier.
The pulse is firstly generated by the MIRA and then it is amplified by theLEGEND. The MIRA is pumped by a continuous wave frequency doubledNd:YVO (the VERDI module) and produces pulses with a power of 400 mWand a repetition rate of 78 MHz. After that the LEGEND is pumped by 1kHz, Q-switched, frequency doubled Nd:YLF (the EVOLUTION module).The amplification is controlled by two Pockels cells that release the pulses.The active media operate at 800 nm that is the optimal value to obtainmaximum efficiency and gain from Titanium:sapphire crystals.
In the following the line dedicated to the time-resolved magneto opticalmeasurements is discussed.
3.2 Optical layout
The time-resolved magneto-optical Kerr effect setup has been especially de-signed to achieve high sensitivity with the best temporal resolution. Thanksto its versatility, three dimensional vectorial MOKE can be performed atdifferent temperatures and different pump and probe wavelengths.
In fig Fig. 3.1 a sketch of the setup is shown. The pump beam (dashedline) is focused on the sample after being retarded by a mechanical delay linecapable of a spatial resolution of 0.1 µ m. The final dimension of the laserspot is of the order of hundreds of microns and the fluence can be tuned up to50 mJ/cm2. The other beam, the probe, is split into two parts. The first oneimpinges the sample with an angle of about 45◦, here the intensity is less than0.1 mJ/cm2 and the beam size about 10 µm. After that the reflected lightpasses through a Glan-Thompson polarizer and reaches a photodiode. Thesecond part is attenuated and detected by another photodiode. To operate at
3.3 Data acquisition methods 25
Fig. 3.1: Sketch of the optical layout for time-resolved MOKE measurements.We used a two-detector scheme and a lock-in amplifier in order to improvethe sensitivity.
very high sensitivity these two signals are made equal and sent to a differentialinput of a lock-in amplifier. In this way it is possible to acquire at the laserfrequency (1 kHz) without any additional modulation [2]. An external fieldis applied vertically (or horizontally) by two Helmholtz coils, allowing toacquire hysteresis loops at high repetition rates (up to 2 Hz). The maximumfield is about 300 Oe. The possibility to work at different temperature isalso available. The sample can be mounted in a continuous-flow cryostatoperating between 4 K and 500 K. The focusing lenses of pump and probeare mounted over a micrometer stage in order to preferentially modify thespot dimensions. Moreover using half-wave plates and Beta Barium Borate(BBO) non-linear crystals it is possible to rotate the polarization of the lightand generate double frequency pulses. The incidence angle can be changedeasily moving the sample holder. In such experiment the shortest time lapsethat can be measured is given by the cross correlation of the two pulses: inour case it is about 75 fs with a temporal length of 50 fs for the two beams.
3.3 Data acquisition methods
The experimental setup can operate in different modes according to the re-quired data. Once the pump and probe delay is fixed, it is possible to measureeither the whole hysteresis loop (section 3.3.1) or only the magnetic signal atthe saturation field (section 3.3.2). While the former allows one to retrieve
26 Experimental set-up
thorough information on the magnetic state, the latter is used to performvery fast scans in a temporal window of about 700 ps. In addition, to chal-lenge the issue of optical magnetic switching, two other distinct acquisitionmethods have been designed. In section 3.3.3 we will show how measuringthe effect on the magnetization of multiple pump pulses and in section 3.3.4how the ultrafast spin dynamics is acquired.
3.3.1 Hysteresis loops and transient reflectivity
For the first method an external field Hext slowly sweeps between two op-posite values following a triangular shape with a rate of about 2 − 1 Hz, asshown in Fig. 3.4 (a), left panel. At the same time probe pulses reach thesample and record the magnetization value (or its projections, see chapter2.2) for all the generated Hext intensities. The magnetic hysteresis loop isthereby reconstructed.
In a time-resolved experiment the pump pulses precedes the probe onesand modify the magnetization in the irradiated area. Fixing the pump andprobe delay and measuring the whole hysteresis loops allow one to collect thespin evolution for all the desired external fields. Then the whole dynamics isacquired by changing the pump–probe delay.
The strength of this method relies in the completeness of the magneticinformation. As described in chapter 2.2, to retrieve the orientation of themagnetic vector, e.g. distinguishing the polar and the longitudinal projec-tions, it is necessary to collect the MOKE signal at opposite values of Hext.By a closer inspection of eqs. 2.23 and 2.17, we observe also that the transientreflectivity can be extracted. The terms A and A′ do not carry any magneticpiece of information but describe the reflectivity of the sample. Consequentlythe centers of the loops shift following the induced reflectivity dynamics thatis simultaneously acquired, as shown in Fig. 3.2.
The main drawback of the technique is the time necessary to acquirean entire hysteresis loop. To reasonably reduce the signal to noise ratio,many complete cycles are needed, thus the procedure can be quiet time–consuming. When only one component of the magnetization is present andwe are interested at the dynamics at a certain value of the external field, i.e.saturation, a faster method has been designed, as described in the followingsection.
3.3.2 Acquisition with pulsed external field
In this section we will develop a method that allows us to measure the time-resolved magnetic signal with a fast rate at the saturating external field Hsat.
3.3 Data acquisition methods 27
Fig. 3.2: The reflectivity transient (black curve)is reported as a functionof the pump and probe delays with the corresponding hysteresis loops foran iron thin film. ∆R/R is described by the centre of the loops while themagnetic dynamics can be extrapolated by the variation of the remanence.Source ref. [2].
A very strong and pulsed current is injected within a couple of Helmholtzcoils concentric to the ones devoted to the generation of the external mag-netic field called Hext. These coils produce a field Hpulsed of 500 Oe, witha temporal width of about 0.4 ms and a repetition rate of 500 Hz. WhenHpulsed is coupled to Hext which, in this case, is set constant and in theopposite direction, we obtain a square magnetic wave ranging between -250Oe and + 250 Oe, as shown in Fig. 3.3. Finally this field is properly syn-chronized with respect to the laser pulses, dropping each pump–probe eventto opposite values of (Hpulsed +Hext). If the maximum and lower magneticfield intensities are strong enough to drive the magnetization to differentsaturation states, i.e. M(+Hsat) and M(−Hsat), we can directly extract∆M = M(+Hsat)−M(Hsat) by triggering the lock-in amplifier at the wavefrequency, i.e. 500 Hz.
To conclude we observe that the transient reflectivity cannot be acquiredin parallel with this procedure.
3.3.3 Magnetic switching: the effect of multiple pump
pulses
Usually in pump and probe experiments after one intense light perturbationand the other, the system recoveries its initial non-irradiated state. All the
28 Experimental set-up
Fig. 3.3: The external magnetic field, in green, is modulated at 500Hz resem-bling a squared wave shape between -250 Oe and + 250 Oe. Meanwhile thepump (red) and the probe pulses (blue) reach the sample with 1kHz repeti-tion rate. In such a way thanks to lock-in amplifier in phase with the field,it is possible to measure the laser induced variation of the magnetizationperforming only one scan.
induced ultrafast processes ceases in few nanoseconds that is the time for theabsorbed energy to dissipate out. However when we come to a permanentmodification of the sample, e.g. magnetic switching, this doesn’t hold anylonger. One pump is enough to drive the magnetization to a new equilibriumposition, the subsequent pulse finds an altered situation and generates adifferent dynamics bringing the system in a further different state. As aresult we cannot average out multiple pump and probe events using thepreviously described acquisition methods. Here we present an experimentalapproach that allows us to measure the effect of multiple pump pulses on thewhole magnetic hysteresis loop for very long pump-probe delays (at least 1ms).
The repetition rate of the probe beam is reduced to 250 Hz while the pumpremains unaltered at 1 kHz. Between subsequent probes, an additional pulsedmagnetic field Hpulsed is applied parallel to the external one as described inthe previous section. In this case the field pulses are synchronized with theprobe ones (thus, at a repetition rate of 250 Hz) and are properly delayedin order to fall between two pump pulses. The external field Hext sweepsfollowing a triangular shape with a rate of ∼ 1 kOe/s (Fig. 3.4 (a)), thusthe magnetization is sampled at field intervals of about 4 Oe. The scopeof the pulsed magnetic field is to cancel the effect induced by all preceding
3.3 Data acquisition methods 29
Fig. 3.4: a) The external magnetic field Hext sweeps continuously betweentwo opposite values (±300 Oe), with a rate of about 1 kOe/s. Additionally(see inset), short (0.4 ms) and intense (about 0.5 kOe) magnetic field pulsesare applied parallel to Hext at the frequency of the probe, i.e., 250 Hz. Themagnetic pulses can be either positive (as in the inset) or negative. (b) Thetemporal sequence of pump, probe, and magnetic field pulses can be modifiedin order to study the effects of zero, one, two, and three pump irradiationson the magnetization (see text). Source [32].
pumps by rapidly bringing the magnetization to saturation and back. Witha proper temporal sequence of the pump, probe, and magnetic field pulses,the modification induced by zero, one, two, and three pump irradiationscan be investigated. The procedure is sketched in Fig. 3.4 (b). Notice thatthe probe shortly precedes the nearest pump pulse by a fixed delay (a fewpicoseconds). When the pulsed magnetic field falls right before the probe(zero–pulse case), the effects of all previous pumps are canceled. In thiscase, the hysteresis loop can be measured with the sweeping external field asif no optical excitation was present. When one pump falls between the probeand the pulsed magnetic field (one–pulse case), each probe will detect themodification induced by a single pumping. With the sweeping field running,it is possible to study the effect of a single pump as a function of the intensity
30 Experimental set-up
Fig. 3.5: Short (0.4 ms) and intense (about 0.5 kOe) magnetic field pulsesare applied parallel to H at the frequency of the probe, i.e. 500 Hz. Themagnetic pulses can be either positive or negative. The temporal sequenceof pump, probe, and magnetic field pulses is shown to better understand therole of the field to renew the starting magnetic condition.
of the external field. Similarly, when two or three laser pumps fall between themagnetic pulse and the probe (two–pulse and three–pulse cases, respectively),each probe samples the changes produced by two or three subsequent laserirradiations on the magnetic state of the film. It should be mentioned thatonly one branch of the hysteresis loop can be measured. An example willclarify this point. Lets assume that the sweeping external field is startingfrom negative intensity (about -250 Oe) and the pulsed magnetic field ispositive but intense enough (about +500 Oe) to saturate the magnetization inthe opposite direction. Each magnetic pulse will rapidly guide the magneticvector to saturation through one branch (the up branch) of the hysteresisloop. When the pulsed field ends (within 0.4 ms), only the negative externalfield is present, and the magnetization will return to its initial magnitude andorientation through the other branch (the down branch) of the loop. As theintensity of the external field increases, the process will repeat in the sameway. Therefore, with positive pulsed field we can only measure the branch ofthe hysteresis loop that would be obtained without pulses and sweeping theexternal field from positive to negative intensity (down branch). To measurethe opposite branch of the loop, the pulsed field has to be inverted.
3.4 Sample preparation 31
3.3.4 Magnetic switching: the ultrafast dynamics
To study the ultrafast dynamics of a laser-induced spin switching we canexploit the afore described method with only slight modifications. Start-ing from the zero-pump case (Fig. 3.4 b) the temporal order of pump andprobe should be inverted. The field pulse (in green) is followed by the pumpone (brown stick) and after that the probe beam (orange stick) detects thelaser induced dynamics. The available temporal range is about 0 − 500 ps.The effect of all subsequent pumps are canceled by Hpulsed. For the sake ofcompleteness we mention that this measurements can be performed also athigher probe repetition rates. The mechanism is sketched in Fig. 3.5 with achopped beam at 500 Hz and a pulsed field at the same frequency.
3.4 Sample preparation
The iron samples studied in this thesis have been expitaxially grown andcharacterized in our lab. The vacuum system used for this purpose oper-ates in ultra-high vacuum conditions with a base pressure of 10−10 mbar. Itis schematically shown in Fig. 3.6. The system consists of three chamberspumped independently by turbomolecular pumps: load lock, preparation andmeasurement chambers. The latter is devoted to time-resolved photoemis-sione experiments and it won’t be discussed here. The load-lock chamber isequipped with a fast entry port and a transfer arm which allows mountingand transferring the samples in vacuum. In the preparation chamber twoKnudsen-type evaporation cells for thin film deposition and a conventionalAr+ sputter gun are installed. The sample holder can be heated up to 1000K in order to perform sputtering-annealing cycles. Additionally, a low energyelectron diffraction (LEED) system and an Auger spectrometer are mounted,allowing to check in situ the chemical and crystallographic conditions of thespecimens.
The thin Fe(001) films (about 8 nm thick) have been epitaxially grownon MgO(001) substrates. Fe grows with the (100) axis parallel to the (110)axis of the MgO. The magnesium oxide substrate is a one side epipolishedsingle crystal manufactured by MaTeck with orientation (100), dimensionsof 10 mm x 10 mm x 0.5 mm, purity > 99− 95% and surface roughness < 5A. Prior to the deposition, the substrates are cleaned by repeated cycles ofsputtering and annealing. During the sputtering the sample is bombardedby Ar+ ions, with kinetic energy of 1 keV and with a mean current of 2.8µ A. For the annealing, the sample is heated up to 800 K and kept at thistemperature for 20 min. The Fe deposition is performed with an electron-
32 Experimental set-up
Fig. 3.6: The UHV system is composed by three independent chambers:the fast-entry load-lock chamber with the transfer arm (right), the samplepreparation chamber equipped with evaporators, sputter-gun, LEED, andAuger analyzers (center), and the photoemission chamber (left).
beam evaporator at a rate of about 0.2 nm/min to the substrates held atroom temperature. After the deposition, the samples is annealed to about750K, in order to reduce the possible defects formed during the epitaxialgrowth, and characterized through LEED.
Chapter 4Ultrafast demagnetization in thin iron
films
In this chapter we describe the laser induced ultrafast spin dynamics in thiniron films by means of time-resolved magneto-optical Kerr effect. We ex-plored the magnetic dynamics in the first picoseconds after the optical exci-tation, analysing its dependence on the laser intensity and the ambient tem-perature. Measurements in a large range of these external parameters allowedto clarify the role of electron-phonon and electron-magnon interactions. Therapid (< 100 fs) demagnetization has been ascribed to electron-magnon exci-tations while the subsequent recovery (on a time scale slightly shorter than apicosecond) has been attributed to the Elliott-Yafet spin-flip scattering pro-cess mediated by electron–phonon scattering. In particular we demonstratethat the ultrafast loss of the spin order does not show any dependence onthe starting sample temperature as instead expected for processes mediatedby electron-phonon interactions. This behaviour is in good agreement withthe magnon creation scenario proposed by Carpene et al.[2].
To give an insight to the ultrafast demagnetization process we will start,in section 4.1.1, from the description of the electronic relaxation after thephoton absorption and the subsequent energy transfer to the lattice in asimple non magnetic metal. In the following section 4.1.2, the spin degree offreedom is added and a wide presentation of the state of the art about theultrafast demagnetization is carried on.
In section 4.2 we will present the magnetic properties of the studied sam-ple, i.e. thin iron films. We take this opportunity to make a wide analysissince it will be useful also for the description of the spin oscillation and themagnetic switching treated in Chapter 6.
After that, we will describe the ultrafast laser–induced dynamics in iron,section 4.3. In particular we will focus on the work by Carpene et al. pub-lished in Physical Review B in 2008 [2] as well as the demagnetization modelproposed therein. Accordingly to the authors the loss of the spin order canbe explained by magnons generated by hot electrons in the first hundredfemtoseconds. The model is furthermore discussed in the light of the mostrecent experimental findings present in literature.
In the subsequent sections 4.4 and 4.6, we will show our new experimen-tal results supporting the aforementioned scenario in which the magneticdynamics is mainly driven by electron-magnon interactions. A phenomeno-logical method allows us to disentangle the ultrafast demagnetization fromthe whole transient signal. In this way we observe that the ultrafast pro-cess is not affected by the ambient temperature contradicting other modelsthat predict that the main role is played by spin-flip events mediated by theelectron-phonon scattering.
4.1.1 Laser induced dynamics in a simple metal
We will study the laser excitation first considering a simple non magneticmetal and then focusing on the particular case of a ferromagnet in which thespin order needs to be considered as an additional energy reservoir.
4.1 Introduction 35
Fig. 4.1: Normalized electronic distribution at the Fermi level of a metal-lic system. a) At the equilibrium electronic density is well described bythe Fermi-Dirach distribution. b) Absorbed photons with energy hν excitesome electrons to empty states above the Fermi level establishing an out–of–equilibrium distribution. c) Scattering events restore the Fermi-Dirachdistribution. Here the temperature is higher than at t < 0, i.e. the slope ofthe Fermi edge decreases.
36 Ultrafast demagnetization in thin iron films
In metallic systems the equilibrium electronic density is well described bythe Fermi-Dirach distribution, see Fig. 4.1 panel a):
1
e(εi−µ)/kTe(t<0) + 1(4.1)
where µ is the chemical potential, Te (t < 0) is the electronic temperatureand t < 0 denotes the times before the pump arrival. In this condition Te
is equal to the sample temperature called Tl. When the first pulse (t = 0)arrives it deposits energy in the system breaking the thermal equilibrium.The absorption of photons in the near infrared spectral region, i.e. 1.55 eV,modifies the electronic population across the fermi level creating highly en-ergetic electron-hole pairs. A non-equilibrium distribution, as depicted inFig. 4.1 panel b), is established instantaneously. In this condition the par-ticle and quasiparticle scattering is highly enhanced according to the Fermiliquid theory of Landau [33]. Thus electron-electron, hole-hole and electron-hole interactions lead the electrons towards thermalization with typical timeconstants of about τee ∼ 10 fs . It has been experimentally shown thatalso electron-phonon scattering events [34] and Auger processes [35] [36] canweakly contribute. The achieved Fermi–Dirach distribution is characterizedby an higher temperature Te(τee) > Te (t < 0), Fig. 4.1 panel c), that de-pends on the absorbed energy density N and the electronic specific heat ceaccording to:
N =
∫ Te(t<0)
Te(τee)
cedT (4.2)
Te(τee) definitely deviates from the lattice temperature Tl(τee) ∼= Te (t < 0),as depicted in Fig. 4.2 displaying temperatures as a function of pump–probedelays. For this reasons, the energy starts to flow from the electronic systemto the lattice via phonon cascades. The mechanism leads to a cooling of theelectronic distribution and to an increase of Tl that ultimately depends on thetemperature dependent lattice specific heat. The corresponding timescale isdetermined by the electron-phonon coupling that can be evaluated by thetheory developed by Allen [37] in about τel ∼ 100 fs – 1 ps. After thisprocess the lattice and the electronic temperatures finally match Tl
∼= Te.The last step is the heat diffusion outside the irradiated area. It depends onthe thermal conductivities of the material and the surrounding media, e.g.sample substrate and air. It takes place on a timescale longer than τth > 1 nsand brings the system back to its initial non–irradiated condition, i.e. t < 0in Fig. 4.2 .
To quantitative describe this process, a detailed many body theory ofthe the relaxation mechanism should be employed. However this issue goes
4.1 Introduction 37
Fig. 4.2: Time evolution of the electron and lattice temperatures in Ni esti-mated by the two temperature model. Source [38].
far beyond the scope of this thesis and many simplified descriptions havebeen used with nevertheless very successful results. In particular we willbriefly describe an extended version of the so called two temperatures model[39]. Sun et al. [40] proposed a scenario in which the electronic and latticedynamics are described by three coupled rate equations accounting for thenon-thermalized, eq. 4.3, the thermalized electronic distributions, eq. 4.4and the phonon subsystem, eq. 4.5:
∂N(t)
∂t= −αN(t)− βN(t) (4.3)
∂CeTe)t =
∂t= −Gel(Te(t)− Tl(t)) + αN(t) (4.4)
∂ClTl(t)
∂t= −Gel(Tl(t)− Te(t)) + βN(t) (4.5)
N stands for the energy density stored in non-thermal part, Gel represent theelectron-phonon interaction and Ce (respectively Cl) the electronic (respec-tively lattice) specific heat. The coupling constant α and β are proportionalto the inverse of the electron thermalization time. In particular α is the en-ergy loss rate from non-thermal part to the thermalized part of the electronicreservoir and β represents the loss rate to the phonon bath.
Fig. 4.2 reports an example of the evaluated process from Ref. [38].Here the different timescales are clear. The electrons first respond to theoptical stimulus, Te rises with time constant, τee, and then decays with τepbecause of electron-phonon interactions, i.e ∆Te ∝ (1 − e−t/τee)e−t/τep. Thelattice temperature slowly grows following the same exponential law ∆Te ∝
38 Ultrafast demagnetization in thin iron films
(1−e−t/τep) (for the sake of semplicity, we neglected the energy flow from theout of equilibrium population to the lattice that is in any case very small,i.e. β ∼ 0) As we will see in the next sections, typical time constants for athin iron films are τee < 30 fs and τep ∼ 200− 300 fs. Moreover, the effectivetemperature differences between Te and Tl can be very large. Since theelectron heat capacity is typically one to two orders of magnitude smaller thanthat of the lattice, Te may reach several thousand Kelvin while the maximumlattice temperature remains relative cold. In iron we extracted electronictemperatures of the order of 1000 – 2000 K while the lattice hardly achieve900–1000 K for very high laser fluences (close to the sample destructionthreshold).
4.1.2 Laser induced ultrafast demagnetization
Moving to the description of laser induced dynamics in ferromagnetic metals,the spin order is an additional degree of freedom that needs to be consid-ered. Scattering events involving excited particles can modify their angularmomentum leading to a time-dependent transient magnetization. In partic-ular, we can first point out that on a very long time scale when the thermalequilibrium is reached, we expect a reduced magnetization being the sampletemperature closer to the Curie point. This is what Vaterlaus and coworkers[41] [42] observed in 1990 and 1991 measuring a very slow magnetic relaxationof about 100 – 200 ps in ferromagnetic Gd by time and spin–resolved photoe-mission. This process was ascribed to spin–lattice interactions, responsiblefor the slow spin thermalization with electrons and the lattice. However theauthors exploited laser pulses with a temporal duration of about 60 ps, as wewill see, far bigger than the relevant spin time scales. In fact, one year laterin 1996, Beaurepaire [1] et al. performed the first experiment capable to re-trieve the magnetization dynamics with femtosecond resolution and found anunexpected faster quenching of the magnetic order. Using 60 fs laser pulses tomeasure both the transient transmissivity and the magneto-optical Kerr ef-fect of 22 nm Ni thin films, they observed a demagnetization occurring within2 ps, one order of magnitude slower than the electronic thermalization timeof about 260 fs, Fig. 4.3. After that the transient magnetization recoveredtowards a long living equilibrium value till the nanosecond heat dissipation.The dynamics showed a temporal profile that couldn’t be explained on thebasis of simple spin-lattice relaxation. This work was the first demonstrationof the so called, ultrafast demagnetization process, and also the first proofthat electrons, lattice and spins follow distinct paths towards thermal equi-librium. A first phenomenological approach to describe the mechanism wasproposed by the same authors modifying the two temperature model with a
4.1 Introduction 39
Fig. 4.3: Panel a): the first laser-induced magnetic dynamics measured withfemtosecond resolution by Beaurepaire et al. [1]. They measured the time–resolved magneto–optical Kerr effect in Ni(20 nm)/MgF2 (100 nm) film for7 mJ/cm2 pump fluence. Panel b): recent measurements on Ni (10 nm) thinfilms by Koopmans et al. [43]. Improvements in the experimental techniquesallowed to unveil the sub–picosecond nature of the ultrafast demagnetizationprocess.
third energy reservoir: the spin order, with a temperature Ts, a specific heatCs and coupled to electrons and phonons by Ges and Gsl:
∂CeTe)t =
∂t= −Gel(Te(t)− Tl(t))−Ges(Te(t)− Ts(t)) + P (t) (4.6)
∂CpTl(t)
∂t= −Gel(Tl(t)− Te(t))−Gsl(Tl(t)− Ts(t)) (4.7)
∂CsTs(t)
∂t= −Ges(Ts(t)− Te(t))−Gsl(Ts(t)− Tl(t)) (4.8)
(4.9)
where P (t) is the laser source term applied only to the electronic term (theinitial heating process occurs mainly in the electronic bath).An example ofevaluated Ts, Te and Tl is reported in Fig. 4.4. The transient spin evolu-tion differs from the electronic and the lattice ones meaning that distinctinteractions are taking place. The surprising experimental results triggeredresearchers to further investigate the ultrafast mangetic dynamics and al-ready in 1997, using pump-probe second-harmonic generation, Hohlfeld etal. [10], obtained a demagnetization rate of few hundreds femtosecond (in ananalogous nickel film). Afterwards, the improvement of both laser sourcesand experimental techniques made possible to explore the dynamics with
40 Ultrafast demagnetization in thin iron films
Fig. 4.4: Calculated spin Ts, electron Te, and lattice Tl temperatures as afunction of time using the three temperature model to explain the ultrafastdemagnetization nickel reported by Beaurepaire et al. [1].
better resolution confirming the sub-picosecond nature of the ultrafast de-magnetization process.
By now, the mechanism has been observed for all elementary ferromag-netic transition metals (Co, Ni, Fe) and several alloys. A wide range of al-ternative techniques has been used, like for example time and spin–resolvedphotoemission [44], terahertz generation [45] and X-ray magnetic circulardichroism [26]. In the last 16 years a lot of effort has been devoted in theunderstanding the underlying mechanism, however a unique comprehensivepicture is still missing up to now.
Generally speaking, the demagnetization process requires a certain amountof spin angular momentum being transferred from the spin sub–system toother degrees of freedom. Therefore, it is of crucial importance to identifythe transfer channels together with the corresponding rates. Both the latticeand the electronic system should be able to accomodate angular momentumhowever none of them seems to be able of fully explaining the experimentalfindings.
The direct transfer of angular momentum to the lattice is provided by thecoupling between spin and phonons, but it has been demonstrated to be verysmall in ferromagnets. In fact the energy of the process is usually consideredto be of the same order of magnitude as the magnetocrystalline anisotropy,i.e. 100 µeV for 3d metals. Hubner and Zhang [46] showed that in nickel theinteraction time can be quite long, e.g., 300 ps.
On the other hand, the stronger spin–orbit interaction, i.e. 100–50 meV,
4.1 Introduction 41
can be responsible for the angular momentum flow into the electron orbitsor the lattice. This energy range would correspond to a minimum relaxationtime of ∼ 40–20 fs, i.e., fast enough to explain the ultrafast effects. In thepresence of spin–orbit coupling, in a solid, Bloch eigenstates are mixturesof spin ”up” and ”down” states, although usually one state dominates andelectrons can still be called ”up” and ”down”. As a result, electron scatteringevents can cause spins to flip exchanging momentum with the lattice or withthe orbital reservoir, although strongly quenched. In ferromagnets there aremainly three electronic interactions that can induce spin–flips events, i.e.Stoner excitations (i), electron-magnon interactions (ii), and Elliott–Yafetelectronic scattering with phonons, electrons or impurities (iii).
Stoner excitations (i) consist in single particle spin flip events throughCoulomb interaction. A majority electrons undergo spin reversal and decaysto a lower unoccupied minority state. The energy required by this process isof the order of∼ 1 eV that is the characteristic value of the exchange splitting.However common pump-probe experiment are performed with near-infraredwavelengths around 800 nm, i.e. 1.55 eV, and excited particles, after thethermalization, do not possess enough energy to create Stoner pairs. In thelow-energy range another kind of spin excitation, called magnon, dominates(ii). A magnon is a quantized spin waves, i.e. a collective excitation, carryinga fixed amount of energy, linear and angular momentum. In particular themagnetic momentum is of two Bohr magnetons S=1. An electronic spin-flip is characterized by ∆S = ±1, therefore this event can be assisted by thegeneration or annihilation of a magnon. To conclude we have to consider alsopossible scattering mechanisms of excited particles with phonons, electronsor impurities (iii). As demonstrated by Elliot and Yafet [24] [25], theseinteractions, with energy well below 1.55 eV, can change the probability tofind the electron in one of the spin states transferring angular momentumfrom the spin system to the lattice without the orbital momentum beingaffected.
Due to the involved energy scale, Stoner excitation have been generallynot included in the possible alternatives of ultrafast demagnetization chan-nels. On the other hand both magnon generation (ii) and the Elliot–Yafetscattering (iii) has been investigated even if both the mechanisms are char-acterized by non-negligible drawbacks. The main difference between the twomechanism relies in the channel that accomodates the magnetic angular mo-mentum. Through an electron-magnon scattering event the momentum istransferred to the orbital degree of freedom while Ellitot–Yafet spin–flips aresustained by the lattice. Up to now, considering magnons, the transferringtowards the orbital degree of freedom has not been observed in a temporalwindow between 100 fs and 1 ps [47] [27]. In particular, in 2007, Stamm and
42 Ultrafast demagnetization in thin iron films
coworkers [26] made the first time-resolve x-ray magnetic circular dichroismexperiment with femtosecond resolution capable of retrieving the dynamics ofL and S separately. Exploiting the slicing source of synchrotron radiation ofthe electron storage ring BESSY II [48], in Berlin, they studied the ultrafastdemagnetization in nickel films and observed a different behaviour betweenthe spin and the orbital momenta. The same phenomenon was later observedalso in cobalt samples [27], however, as shown in Fig. 4.5 panel a) and b),the decrease of both angular momenta cannot be explained by a transferringfrom one reservoir to the other. As pointed out by the authors the observeddynamics could demonstrate a transient change in the magneto-crystallineanisotropy and in the spin orbit–interaction. However, since these processescan be faster than 20–40 fs, further improvements in the temporal resolvingpower are still necessary.
Fig. 4.5: Time–resolved spin S and orbital angular momentum L, obtainedfrom XMCD data. Panel a) reports the dynamics for 17 nm thick Ni filmsas measured by Stamm et al. [47]. Panel b) contains data for a 15 nm thickCo0.5Pd0.5 film by Boeglin et al. [27]
On the other hand, the flipping probability in Elliot–Yafet scatteringhas been estimated to be too low in the femtosecond regime [49]. Since anexperimental proof is still missing, a definitive statement about this processcannot be done yet.
The magnon creation channel has been proposed for the first time byCarpene et al. in 2008 [2] studying the magnetic dynamics in iron thin films.A deeper presentation of the model for simple 3d ferromagnets is developedin section 4.3.3 and in section 4.4 where we will show our new measurementsthat, according to our interpretation, should sustain the electron–magnon
4.1 Introduction 43
interaction as main channel for spin momentum dissipation.On the other hand, Elliot–Yafet scattering mechanism has been widely
used since 2005 when Koopmans and coworkers [3] developed a model inwhich the whole complexity of the magnetic behaviour in the first picosec-onds (both demagnetizzation and remagnetization), could be explained byconsidering only electron-phonon interactions. In 2010 Koopmans et al. [43]improved their model capable to explain the magnetic dynamics of both 3dand 4f metals. Treating 4f metals is not a purpose of this thesis, however itis interesting to notice that, in general, in rare–earth ferromagnets very slowdemagnetization times, i.e. ∼ 30−−100 ps, have been measured. Since mostof the magnetic moment is localized in the 4f inner shell while the photonabsorption involves only the 5d electrons at the Fermi level, the transfer ofenergy from the excited electron bath to the 4f spin is slower. However,some rare–earth ferromagnets, like Gd and Tb, shows a so–called two–stepdemagnetization (Fig. 4.6): the slow quenching of the magnetization is pre-ceded by a sub-picosecond one (∼ 0.7 ps) active in the electronically excitedstate [50].
Another model, among the ones exploiting the Elliot-Yafett mechanism,needs to be mentioned. According to Krauss et al. [8] also the electron–electron interaction can flip the particles spin with very high rates in thefirst femtoseconds. Starting from the three temperature approach they im-plemented the electronic coulomb interaction to finally identified the drivingforce as the equilibration of temperatures and chemical potentials betweenthe electron and spin subsystems, i.e. the phonon presence is not required.
Before concluding the overview about the scattering processes mediatedby spin–orbit interactions, we have to cite a particular variety of ferromag-netic materials, the so–called half metals. They are undoubtedly a studycase for ultrafast demagnetization processes as demonstrated by Muller etal. [6]. In these systems the conduction electrons are characterized by ahigh degree of spin polarization, i.e above 80% while for common iron it isaround ∼ 50%. The minority spin energy states are mainly shifted abovethe Fermi level and quiet empty, consequently conduction electrons are inalmost ”pure” one spin states. Therefore, considering laser induced ultra-fast dynamics, spin-flip events towards spin–orbit interaction are stronglyhindered, hence the energy has to be transferred to the spin system mainlythrough the weaker lattice excitations. The measured dynamics for halfmetallic systems can be slower than 1 ns for Fe3O4, as show in Fig. 4.7, andeven more interesting, a dependence of the demagnetization time on the spinpolarization has been found. It is a further proof that spin–orbit interactionplays a dominant role in the process. In particular the authors propose amodel based on Elliot–Yafer–type electron–spin interactions that explicitly
44 Ultrafast demagnetization in thin iron films
Fig. 4.6: Time-dependent XMCD signals for Gd (top) and Tb (bottom)measured with fs x-ray pulses by Wietstuck et al. [50]. The demagnetiza-tion progresses by a two step process. For positive delays, the dashed areasenlighten the first sub-picosecond front and the white ones contain the slowdemagnetization with time constant of about 40 ps for Gd and 8 ps for Tb.
4.1 Introduction 45
unveil the ultrafast demagnetization time as a function of the electronic spinpolarization. Further insights into the model have been recently developedby Mann et al. [51].
Fig. 4.7: Laser induced magnetic dynamics in half metallic systems measuredby Muller et al. [6].
The loss of angular momentum on the femtosecond regime can be ex-plained not only by the occurrence of scattering events among excited parti-cles. Zhang and Hubner in 2000 [52] were the first to consider the relativisticcoupling of spins and electrons to the laser electromagnetic field. Accordingto their theoretical description a cooperative process between the light fieldand the spin-orbit interaction takes places on the femtosecond time scale,driving the loss of magnetic order. Bigot et al. in 2009 [5] experimentallydemonstrated that the transient material polarization induced by the pho-ton field interacts coherently with the magnetization. That could affect thesubsequent dynamics, modifying the total angular momentum and being thecause of the delayed response of the spin temperature with respect to theelectronic one. However the real consequences of these effects are not clearyet.
Another mechanism that is catching more and more attention in the lastyears and do not require the presence of controversial debated scatteringevents, is the so called electronic superdiffusion. This theory, developedby Battiato et al. in 2010 [7], explains the loss of angular momentum by
46 Ultrafast demagnetization in thin iron films
a drain of majority electrons out of the irradiated area. In particular theexcite particles move into the material with different velocities, and, sincethe majority spin have a longer lifetime, they could abandon the probedregion moving elsewhere in the sample, e.g. the substrate [14]. This theoryis widely explained in Chapter 5, that is entirely devoted to the, still inprogress, experimental demonstration of the phenomenon.
To complete our overview other the ultrafast magnetic dynamics also thepicosecond recovery after the demagnetization needs to be treated. As al-ready mentioned, in Fig. 4.3, a remagnetization take place after the suddenjump. It is commonly believed that this part of the dynamics can be as-cribed to Elliott-Yafet spin-flips mediated by electron-phonon scattering [43][49]. Although the interactions has very low probability immediately afterthe femtosecond pump pulse, in the picosecond timescale it is the dominantmechanism that brings the spin bath to thermal equilibrium with lattice andelectrons.
4.2 Iron thin film: magnetic properties
The studied samples of the present work are 8 nm thick Iron thin films. Theyhave been grown in our lab by electron beam evaporation with the prepa-ration procedure described in section 3.4. The as-grown magnetic layer ischaracterized by a biaxial in-plane anisotropy with the easy axes along the[100] and [010] directions. A strong shape anisotropy, due to the samplethickness, further forces the magnetization M to lie on the film plane. Ulti-mately, without any applied field, M is located on one of the four preferentialdirections of the surface plane as shown in Fig. 4.8 a). In addition we haveto remark that iron has its [100] axis parallel to the [110] one of the MgOsubstrate because of the relative lattice parameters.
These anisotropies are described in a phenomenological formalism whichis carried out considering the free–energy G as a function of the mutualdirection of the magnetic vector M and the external field Hext. For a planarbiaxial system we have [17]:
G =K1
4sin2 2ϕ− µ0MHext cos(ϕ− θ) (4.10)
where ϕ (respectively θ) is the angle on the film plane formed by M (theexternal field Hext) with the [100] axis, see Fig. 4.8. The anisotropy constantK1 usually depends on the sample thickness d and is given by a bulk term,Kb, and a surface/interface contribution, Ks, as K1 = Kb −Ks/d [53]. Thesurface/interface term is very important especially for ultrathin films of a few
4.2 Iron thin film: magnetic properties 47
Fig. 4.8: a) In a pictoresque view, the black line represents the four minimaof the free-energy density as a function of the magnetization direction in thereal space: [100] and [010] are the easy axes separated by energy barriers (thehard axes). (b) The external field Hext and the magnetization M form theangles θ and ϕ, respectively, with the [100] easy axis of the epitaxial Fe(001)film. For small angle ϕ the magnetization vector aligns with the vectorialsum of the anisotropy and external field.
monolayers. Eq. 4.10 can be solved numerically to determine the position ofthe magnetization in the real 2D space. The free energy G has several localminima, e.g when Hext is zero, M lies exactly on one of the two easy axes[100], [010], [100] and [010] of Fig. 4.8 a), i.e. ϕ = 0, 90◦, 180◦, 270◦. On thecontrary, if we apply a field the local minima will change accordingly to themodulus and the orientation of Hext.
A more useful way to write equation 4.10 is:
g = G/µ0M =Han
8sin2 2ϕ−Hext cos(ϕ− θ) (4.11)
which has the dimension of a magnetic field. Han is the intensity of theso-called anisotropy field lying along the easy axes and equal to Han =2K1/µ0Ms [17]. The value of Han amounts to about 550 Oe for iron withM = 2.1 T and K1 = 4.8 · 104 J/m3. Minimizing the free energy as a func-tion of ϕ (the angle between the magnetization and one of the easy axis) isequivalent to evaluate the following equilibrium conditions:
∂g
∂ϕ=
Han
4sin 4ϕ−Hext sin(ϕ− θ) (4.12)
∂2g
∂ϕ2= Han cos 4ϕ−Hext cos(ϕ− θ) = A > 0 (4.13)
Eq. 4.13, completely identifies the effective field Heff determined bythe interplay between external field and magnetocrystalline anisotropy. It
48 Ultrafast demagnetization in thin iron films
Fig. 4.9: Normalized longitudinal (a) and transverse (b) projections of thehysteresis loop for the external field applied at θ = 30◦ from the [100] easyaxis. (c) 2D-graph of the transverse vs. longitudinal projections depicting thetrajectory of the magnetization vector on the film plane. In all three graphs,the numbered arrows help relate the different positions of the trajectory withthe corresponding points on the hysteresis loops. Source ref. [54].
is parallel to the magnetization M and equal to the vectorial sum Heff =Hext+Han−Hdem. Hdem is the demagnetizing field that, in our specific caseof a thin epitaxial Fe layer with the magnetization lying on the film plane,acts only on the out-of-plane component of M and is equal to |Hdem| = |M|.
Sweeping the external field the local minima will change causing M tomove on the film plane. In particular it describes a squared trajectory asreported in Fig. 4.9 panel c) that also shows the measured hysteresis loopsfor an angle θ = 30◦ and −125 Oe < Hext < 125 Oe panel a) and b).The longitudinal ml [Fig. 4.9 a] and transverse mt [Fig. 4.9 b] cycles havebeen acquired exploiting the experimental techniques described in section2.2. Plotting mt as a function of ml, we obtain the position of M in thereal space for each values of Hext [Fig. 4.9 c]. The small arrows help relatingthe positions to the ml(Hext) and mt(Hext) loops. Focusing on the branchcorresponding to the increasing applied field (from negative to positive values,solid lines) interesting features can be unveiled:
1. For high external fields (arrows 1 and 6) the magnetization is saturated(its modulus is Ms). The sample is in the single magnetic domainstate and under the effect of the field M changes direction keeping itsmodulus constant. This behavior represents the well-known coherentrotation regime [55] in which the trajectory is tangent to the dashedcircle of unitary radius in Fig. 4.9 c), i.e. m2
t +m2l = M2
s .
2. At remanence (Hext = 0, arrow 2), the magnetization vector is alignedto the [100] easy axis.
4.2 Iron thin film: magnetic properties 49
3. The steep changes marked by arrows 3 and 5 correspond to the mag-netization switching between easy axes. Increasing the applied fieldfrom negative to positive values, M moves from the [100] to the [010]direction (arrow 4) and then to the [100] axis with two separate steps.These transitions are characterized by straight paths where the mod-ulus of the magnetization is clearly not conserved
√
m2t +m2
l 6= Ms
although the total magnetization is still equal to mt+ml = Ms. Here adifferent process is taking place: it involves the nucleation of domainsand the motion of domain walls. In particular the switching betweeneasy axis cannot occur by coherent rotation because of the presence ofa maximum in the free energy, i.e. hard axis. To overcome this energybarrier a magnetic field of the order of the anisotropy field Han = 550Oe should be necessary. However, very small Hext values have beenobserved, i.e. 10 − 25 Oe. Considering the step number 5, while Hext
is decreasing, the crystallographic direction [100] becomes less energet-ically favorable with respect to the easy axis [010]. Some spins switchalong this direction organized into small regions. These areas are calleddomains while their boundaries domain walls. After that they growthrough domain wall motion till the covering of all the sample. Theobserved energetic barrier is associated to the pinning of the domainwalls due to the presence of defects in the sample that hinders the do-main expansion. In addition we observe that in order to conserve thetotal microscopic magnetic moments, the relation M[100] +M[010] = Ms
must be satisfied. This is exactly the analytical form of the linear pathexperimentally observed.
To account for the difference in the coercivity of the longitudinal andthe transverse hysteresis loops it is necessary to consider the position of theexternal field with respect to the easy axis. Cowburn et al. [56] developeda simple model in which the switching field is evaluated starting from thefree energy density G of a single magnetic domain and the energy requiredto unpin a domain wall ∆ε. Considering the possible magnetization jumps,they estimated:
H1 = H0 +∆ε
µ0| (| cos θ|+ | sin θ|) | (4.14)
H2 = H0 +∆ε
µ0| (| cos θ| − | sin θ|) | (4.15)
For 45◦ < θ < 45◦, H1 refers to the [100] → [010] jump and H2 to the[010] → [100]. For 45◦ < θ < 135◦, H1 refers to the [010] → [100] jump andH2 to [100] → [010].
50 Ultrafast demagnetization in thin iron films
Fig. 4.10: Switching fields vs Hext orientation, i.e. ϕ. For 45◦ < ϕ < 45◦,H1 refers to the [100] → [010] jump and H2 to the [010] → [100] jump.For 45◦ < θ < 135◦, H1 refers to the [010] → [100] jump and H2 to the[100] → [010]. The dots are the experimental data, the lines are the fitsaccording to eqs. 4.14 and 4.15. Source [57].
The termH0 is a fitting parameter accounting for the magnetic aftereffect,[18] i.e., the dependence of the coercivity on the external field sweep-rate. InFig. 4.10 the dependency on the angle is reported together with the theoret-ical fit.
4.3 Ultrafast dynamics
In this section we will give an overview on the laser induced ultrafast dy-namics in metallic iron films. The first studies date back to 2002 when T.Kampfrath and coworkers measured TR-MOKE signal in a 200 nm thickpolycrystalline film on a silicon substrate [58]. After that few works facedthe problem with magneto-optical technique [59] [60] [2] and only recentlyalso time-resolved photoemission experiments have been carried out [61] [62].
The biggest contribution comes from the work of Carpene et al. in 2008[2]. They studied the femtosecond MOKE dynamics together with the time-resolved reflectivity signal. In this way it is possible to explore all the ultrafastscattering events involving electrons, phonons and spins and ensure thatpurely optical effects are disentangled from magnetic ones.
The system is a 8 nm Iron thin film (described in the previous section),and the experimental magneto-optical setup has already been presented inchapter 3.2. The laser wavelength is 800 nm, the probe beam is p-polarized
4.3 Ultrafast dynamics 51
Fig. 4.11: Comparison between the initial reflectivity (open symbols) andmagnetization (solid symbols) curves induced by the 3 mJ/cm2 pump pulse.The delay ∼150 fs between reflectivity and magnetization responses is em-phasized. The inset reports the hysteresis loops measured with no pump(solid line) and 160 fs after the 6 mJ/cm2 pump pulse (dashed line).
and hits the sample with an incidence angle of about 45◦. For each delaybetween pump and probe the hysteresis loop has been measured. The tem-poral evolution of the magnetization has been deduced from the variationof the remanence while the center of the loops follows the transient reflec-tivity signal. This technique allows to simultaneously extract time-resolvedreflectivity and magnetization under the same experimental conditions (seesection 3.3.1). Another separate experiment was performed to better disclosethe transient optical properties. The probe wavelengths have been selectedfrom the supercontinuum beam generated by 800 nm photons through a 2mm thick sapphire crystal. The white light has been focused on the sampleinside the spot irradiated by the pump and after reflection, interferometricfilters discriminate the desired energy from 2.48 eV (500 nm) to 1.75 eV (710nm).
4.3.1 Time-resolved Reflectivity
Fig. 4.11 shows the evolution of the magnetization M (solid symbols) andthe reflectivity R (open symbols) after a laser excitation of about 3 mJ/cm2.The remanence is reduced by about 15% while the reflectivity by less than1%. The amplitude of the hysteresis loop decreases without the coercive force
52 Ultrafast demagnetization in thin iron films
Fig. 4.12: Time-resolved reflectivity curves (symbols), with correspondingfittings (lines) according to eq. 4.16 , obtained with 1.55 eV pump photons(800 nm) and various probe photon energies. The upper inset shows theelectronic (solid line) and lattice (dashed line) contributions to the reflectivitycurve measured with 2.14 eV probe. The lower inset reports their spectralweights vs the probe wavelengths.
being affected, see inset (M/M0 reduced up to 30% with a pump fluence of6 mJ/cm2). Regarding the transient reflectivity, the signal shows a delayedresponse of about ∼ 150 fs. This feature is not due to a real slower responsebut relates to the optical properties of iron, as shown by Fig. 4.12reportingthe measurements acquired with probe wavelengths in the visible range: re-ducing the laser energy to 1.77 eV the signal at larger pump-probe delaysincreases enough to hide the fast part close to 0 fs.
The reflectivity data have been reproduced (see inset of Fig. 4.12) accord-ing to the phenomenological model:
∆R/R = {α[1− e−t/τee
]e−t/τep + β
[1− e−t/τep
]}e−t/τth (4.16)
where only the parameters α and β, i.e. the spectral weights, have beenallowed to vary with the probe wavelength. The first term proportionalto α represents the electronic response, initially determined by the electron-electron thermalization (with time constant τee) and then decaying by energytransfer to the lattice with the characteristic electron-phonon relaxation timeτep. The second term, proportional to β, accounts for the lattice heatingand thus rises with the same time constant τep; the additional relaxationparameter is due to heat diffusion outside the irradiated area τth. In the upper
4.3 Ultrafast dynamics 53
Fig. 4.13: Magnetization curves at three different pump fluences (symbols)and corresponding fittings (lines) using eq. 4.16. The inset reports a zoomof the normalized demagnetization fronts in the first 200 fs, with the cor-responding values of the time constant τem. For comparison, the electroniccomponent of the transient reflectivity, as extracted from the curves of fig-urename 4.12, is shown as well (dashed line).
inset of Fig. 4.12 fitting for the 2.14 eV case is reported with electronic andlattice components explicitly shown. In the lower inset the spectral weightsas a function of the probe energy are plotted. Moving towards 1.77 eV thefast contribution coming from the electronic response tends to zero while thelattice one rises up. The extrapolated time constant are τee < 30 fs andτep = 240± 10 fs. The electron thermalization time cannot be unequivocallydetermined being shorter than the pulse duration (50 fs).
4.3.2 Time-resolve MOKE
Fig. 4.13 shows the time evolution of the magnetization M normalized tothe value at positive delays M0 for different pump fluences. M promptlyfollows the electronic response, thus the loss of spin order is connected to thenon-equilibrium electron distribution and its thermalization. The minimumM/M0 scales proportionally to the fluence and three distinct regimes can beidentified for all the curves:
1. an ultrafast demagnetization in roughly 160 fs;
2. a subsequent, partial recovery within about 3 ps;
3. a very slow restoring that is longer than the investigated time window.
54 Ultrafast demagnetization in thin iron films
Therefore, by fitting the experimental results by a model similar to eq. 4.16,three time constants can be retrieved. The ultrafast demagnetization time(1) ranges within τem = 50 − 75 fs, increasing with the pump fluence (insetof Fig. 4.13). The spin relaxation (2) is τs = 800± 130 fs, weakly dependenton the pump intensity, and τth, larger than 100 ps, accounts for the heatdiffusion outside the irradiated area (3).
These time scales are definitely different from the one measured for electron-electron interaction and electron-phonon coupling establishing that electronsand spins follow diverse relaxation paths after optical excitation. In particu-lar the ultrafast demagnetization is achieved after the thermalization of outof equilibrium electrons (τee < 30fs) and before the emergency of electro-phonon scattering events (τep = 240± 10fs). For comparison, the electronicresponse extrapolated from the reflectivity data is reported in the inset ofFig. 4.13.
To explain the ultrafast magnetic dynamics the authors proposed a sce-nario in which the demagnetization is solely determined by the electron-magnon interaction. The unbalanced population of majority and minorityelectrons favours spin-flip processes that decrease the total spin leading toa lower magnetization. The angular momentum is transferred to the orbitaldegree of freedom, rapidly quenched because of the crystal field. Electron–magnon interaction has been quantitative estimated considering the closeanalogy between phonons and spin waves and adapting the theory of electron-phonon interaction of Allen [37] [63]. The authors evaluated a coupling ratethat is in very good agreement with the experimental data. In the next sec-tion the model is described and further discussed in the light of very recentexperimental results.
4.3.3 Electron-magnon interaction and ultrafast demag-
netization
The starting point of the model is the spin-orbit LS coupling. This interac-tion allows exchange between electron spin S and orbital angular momentumL. Both are not constants of motion and only their sum should conserve insolids. In addition L is constrained by crystal field thus changes in the spinangular momentum should be quenched by the lattice.
More in detail, considering the projections Lz along the quantization axisz, we can write the following relationship involving U , the electron potentialenergy:
dLz/dt = Tz = −δU/δφ (4.17)
where Tz is the torque and φ is the azimuthal angle about z. The right–
4.3 Ultrafast dynamics 55
Fig. 4.14: Calculated spin-resolved density of states for ferromagnetic iron.The majority bands are depicted in green while the minority in red. Theenergy is in Rydberg, 1 Ry = ∼ 13.6 eV. Source [64].
hand part of 4.17, is not zero since U has the symmetry of the crystallineenvironment. Therefore Lz is not a constant of motion and any variation ofthe orbital angular momentum dLz/dt is quenched as the result of the torqueexerted on the electron by the crystal field. Tz can be regarded as the rateof momentum transferred between the electronic system and the lattice thatultimately acts as a reservoir.
Under equilibrium conditions and for temperature T << TC , the magne-tization deviates from its saturation value because of low-energy spin exci-tations (magnons), the number of which follows the Bose-Einstein distribu-tion. Scattering events can modify this condition, but electronic collisionsare hindered by the exclusion principle and limited to a small volume inthe momentum space within an energy of kBT across the Fermi level. Fem-tosecond laser pulse, however, induces drastic changes promoting electronsto unoccupied levels and opening new scattering channels. Electron-electroninteraction rapidly leads to a hot electronic distribution where electrons ex-change energy, linear and angular momentum as well. In 3d ferromagneticmetals, the number of unoccupied levels for minority spin electrons is large,while majority bands are almost filled (see Fig. 4.14). Therefore, spin-flipprocesses should preferentially transform a majority electron into a minorityone. A decrease in the spin momentum leads to an increase in orbital one,but the latter is rapidly quenched by the crystal field, see eq. 4.17. The neteffect is a reduced magnetization.
56 Ultrafast demagnetization in thin iron films
The electron–magnon scattering rate has been estimated adapting thetheory of electron-phonon interaction of Allen [37] to the electron-magnoncoupling [63] with the following results:
τem = (5πkBTe) /(3~λmω
2m
)(4.18)
where Te is the electronic temperature, λm the electron–magnon coupling andωm the cut–off frequency of the magnonic dispersion. Te can be evaluatedconsidering the absorbed pump intensity by the relation:
Ea = γT 2e − T 2
0
2(4.19)
T0 is the initial electronic temperature (at equilibrium it is equal to the sam-ple temperature ∼ 300 K) and γ = (0.7 mJ cm2 K−2) is the electronic specificheat of iron [65]. Ea has been estimated according to optical parameters as:
Ea =[1− e−d/λ
]F (1− R)/d (4.20)
where F is the incident laser fluence, R = 0.5 is the reflectivity at the pumpwavelength, λ = 17 nm is the absorption length, and d = 7 nm is the filmthickness. Depending on the laser fluence the found electronic temperature isTe = 1000− 2000 K. Introducing these values in 4.18, the authors estimate atime constant τem ∼ 40−80 fs that nicely agrees with the experimental valuesof 50− 75 fs. Furthermore, its dependence on the electronic temperature Te
is compatible with the measured behaviour at increasing pump fluences (seeinset of Fig. 4.13).
To conclude the section we will discuss very recent experimental resultsthat could reinforce the magnon creation model. First of all it is necessaryto stress that magnon emission by excited electrons has been typically con-sidered a slow process, occurring within picoseconds [21], even in iron wheremagnons are predict to play an important role [66] [67]. In 2010 Schmidt andcoworkers [61] demonstrated by spin, angular and time-resolved two photonphotoemission that this scattering process can take place on the femtosec-ond timescale. In particular they studied the decay time of potential imagestates in thin iron films (3 monolayer) grown on Cu(001). Here they observedelectronic relaxation rate of the order of ten femtosecond with a strong spindependence. This result could be explained by many-body theories only ifmagnon generation is taken into account. Neither Elliot–Yafet scatteringevents nor single particle spin-fips (Stoner excitations) could account for themeasured effects. The former is prominent on the picosecond timescale whilethe latter only on higher energies. The magnon creation process is sketchedin Fig. 4.15. An excited minority electron scatters exchanging energy with
4.4 Ultrafast dynamics: pump fluence and ambient temperaturedependencies 57
a spin up particle that jumps above the Fermi level. The hole left in themajority band is filled through magnon generation, thus the final state has ahot electron in the energy band of opposite spin. In the depicted frameworkthe demagnetization takes place through the transfer of angular momentumfrom the spin S to the orbital degree of freedom L. In 2010 Boeglin et al.[27] measured separately the two transient angular momenta in thin cobaltfilms by time-resolved XMCD technique. As already discussed in chapter1, they observed different dynamics. In particular both S and L quench inabout 200 − 300 fs, during the thermalization of charges and spins. Dueto the experimental resolution, faster processes couldn’t be detected evenif, considering extended spin-orbit phenomena, other effects are expected inthe first tens of femtosecond. Altough these results are not a proof of theelectron–magnon creation model, they enlighten the important role playedby the spin-orbit interaction supporting the necessity to consider an angularmomentum dissipation channel that involves LS coupling.
To conclude a comparison with other processes, like the most popularElliot–Yafet type electron–phonon scattering is necessary. Our picture issubstantially in agreement with the conclusions drawn by Koopmans et al.[43], but it involves the mediation of electrons orbital angular momentumrather than the lattice. According to the description of Elliot and Yafet,the angular momentum from the electronic system can be delivered to thelattice by electron-phonon interaction. However there is not yet an experi-mental evidence of Elliot-Yafet spin-flip processes on the femtosecond regime.Only theoretical works attempted to evaluate this probability with oppositeresults. In a recent paper Carva and coworkers [49] computed the demagne-tization rate mediated by the Elliot-Yafet mechanism for laser-created non–equilibrium as well as thermalized electron distributions. Increased spin-flipprobabilities have been found but with an induced effect on the total angularmomentum too small to account for femtosecond demagnetization rate of theorder of tens per cent.
For all these reasons the emission of magnons should be considered in thefemtosecond time scale as significant source for ultrafast spin-flip process, i.e.demagnetization.
4.4 Ultrafast dynamics: pump fluence and
ambient temperature dependencies
In order to sustain the electron-magnon creation model we have exploredthe ultrafast demagnetization in iron thin films for different pump fluences
58 Ultrafast demagnetization in thin iron films
Fig. 4.15: Schematic illustration of an exchange spin-flip process mediatedby a magnon creation (wavy line). An excited minority electron scatters ex-changing energy with a spin up particle that jumps above the Fermi level.After that, the hole left in the majority band is filled through magnon gener-ation. The final state has now a hot electron in the energy band of oppositespin.
and sample temperatures. The laser intensity affects the number of excitedcharges while the ambient temperature is related to the phonon and themagnon populations. The validity of such analysis relies in the possibility towork over the three degrees of freedom involved in the ultrafast magnetic dy-namics, i.e. electrons, phonons and spins by simply modifying experimentalparameters.
We have performed TR-MOKE measurements for four different fluences1.5, 3, 4.4, 6 mJ/cm2 and three temperatures 80 K, 300 K and 500 K. Theexperimental setup is shown in Chapter 3.2. The probe pulse is p-polarizedin order to detect the transverse magnetic component, as explained in 2.2.The sample is aligned with one easy axis perpendicular to the scatteringplane and parallel to the external field Hext i.e. φ = 0 and θ = 0 in Fig. 4.8.In such a way sweeping Hext, no longitudinal component can be observedand the magnetization only switches on the vertical easy axis. The fastacquisition scheme described in section 3.3.2 is exploited in order to performmany averages increasing the signal to noise ratio.
The evolution of the transient magnetization M, as normalized to thesaturation value M0 before the arrival of the pump pulse, is displayed inFig. 4.16 for the higher fluence case. The blue line depict data taken at 80K, black at room temperature and red at 500 K. A trend is evident, increas-ing the temperature the effect on the magnetization increases. However the
4.4 Ultrafast dynamics: pump fluence and ambient temperaturedependencies 59
Fig. 4.16: Transient magnetization measured at 80 K (blue line), 300 K (blackline) and 500 K (red line) normalized to the saturation value M0 before thearrival of the pump pulse (fluence 6 mJ/cm2).
energy deposited on the sample is different for all the free cases. To analysethe whole set of data it is necessary to get rid of the temperature dependentabsorption that has been evaluated in the following manner. It is well es-tablished that after sufficiently long delays, i.e. a few picoseconds after thepump, electrons, spins, and lattice have reached thermal equilibrium and thesaturation magnetization is uniquely determined by the local temperature.In iron, the temperature dependence of M(T ), Fig. 4.17, is known [68] andcan be analytically expressed as:
being η = T/TC with TC = 1044 K is the Curie temperature of Fe, a =0.1098, b = 0.368, and c = 0.129. Knowing the starting temperature T0 andthe pump induced ∆M/M (taken after the first spin recovery, see arrows inFig. 4.16) it is possible to extract the maximum sample temperature Tmax.At this point the energy stored in the irradiated volume can be computed as:
E/V =
∫ Tmax
T0
cpdT (4.22)
where cp is the specific heat of Iron, reported in Fig. 4.17 as a function oftemperature. We have numerically evaluated eq. 4.22 for every measureddynamics in order to extract the real absorbed energy E/V . Fig. 4.19 showsthe results as a function of the incident laser fluence. Red, black and bluepoint represents data acquired respectively at 80K, 300 K and 500 K.
60 Ultrafast demagnetization in thin iron films
Fig. 4.17: Normalized M(T )/M(0) of Iron as a function of temperature. TheCurie point is at about 1043 K.
Fig. 4.18: Specific heat of iron as a function of the temperature (from Ref.[69]).
4.4 Ultrafast dynamics: pump fluence and ambient temperaturedependencies 61
Fig. 4.19: Absorbed energy as a function of the incident laser fluence. In-creasing the temperature the optical properties of the sample change andconsequently the amount of absorbed photons. The lines are a guide to theeye.
The measured transient magnetization curves have been fitted accordinglyto the phenomenological model:
M/M0 = {A[1− e−t/τem
]e−t/τs +B
(1− e−t/τs
)}(−e−t/τth
)+ 1 (4.23)
where, consistently with the previous annotation, the ultrafast demagnetiza-tion is described by τem, the subsequent spin recovery is τs and τth accountsfor the heat diffusion outside the irradiated area. A and B are fitting param-eters.
Room temperature data, for all the four measured pump intensities arereported together with the fitting curves in Fig. 4.20. From eq. 4.23 twodynamics can be naively distinguished, as shown in the inset. The fastpart, in violet, resembles the ultrafast demagnetization whose maximum rate∆M/M0 is quantified by the parameter A; the curve drops with a rate τemand restores with a time constant τs. The slow part, in violet, describesthe thermalization of spins with electrons and phonons to a value ∆M/M0
equal to B; this dynamics rises with a rate τm and vanishes because of energydissipation described by τth.
Fig. 4.21 shows the two parameters A and B as a function of the adsorbedenergy E/V for the three sample temperatures T0. In panel i), reporting∆M/M0 for the slow dynamics (B), two features are evident: the non linearevolution and a trend driven by T0. The effect on the magnetization increasesboth with the adsorbed energy and with the starting sample temperature.On the other hand the ultrafast demagnetization described by A in panel
62 Ultrafast demagnetization in thin iron films
Fig. 4.20: Room temperature transient magnetization data together with thefit. Accordingly to eq. 4.23 two dynamics can be disentangled as shown inthe inset (in orange the fast dynamics and in violet the slow one).
ii) shows a significant different behaviour. First of all the demagnetization∆M/M0 is linear with the adsorbed energy and no temperature dependenceis present, i.e. the slope is the same for all the considered T0.
4.5 Discussion
The behaviour of M/M0 in Fig. 4.21 panel i) is explained considering thetemperature dependence of M(T ). Referring to the curve M(T ) of Fig. 4.17,we can translate a variation in the magnetization in a jump in temperature bythe inversion of Eq. 4.21. The result of the conversion is reported in Fig. 4.22panel i). The spin temperature Tspin scales linearly with the adsorbed energy.This result should not be surprising. The slow part of the dynamics is domi-nated by the thermal equilibration of the spin with the lattice bath. The spintemperature thus resembles the sample one Tlattice = Tspin that ultimatelydepends on the absorbed energy, the starting T0 and the specific heat of thesystem cp by E/V =
∫ Tlattice
T0
cpdT . In the considered time window cp is aboutconstant leading to a linear variation of Tspin as a function of the absorbedenergy. The non linearity of B [Fig. 4.21 i] comes from the behaviour ofM(T ); moving to the curie temperature, a small ∆T means an increasinglylarge ∆M .
The demagnetizing regime shows a large dependance on the starting tem-perature T0 that can be explained via Elliot–Yafet electron–phonon interac-tions. As theorized firstly by Elliot for paramagnetic systems and later by
4.5 Discussion 63
Fig. 4.21: Fitting parameters B (panel i) and A (panel ii) of eq. 4.23 as afunction of the absorbed energy E/V for the three sample temperatures. Baccounts for the minimum M/M0 during the so called slow dynamics, whileA during the fast part.
Fig. 4.22: Panels i) and ii) reports the spin temperatures Tspin according tothe magnetization values delineated in Fig. 4.21 i) and ii) correspondingly,i.e. the parameter B and A of eq. 4.23.
64 Ultrafast demagnetization in thin iron films
Koopmans et al. [43] and Carva et al. [49] for ferromagnets, electron-phononscattering can lead to spin-flip events whose amount and rate depend mainlyon the difference between Tspin and Tlattice. In a pump and probe experiment,after few hundreds of femtoseconds the lattice has already thermalized withthe electronic system while spins are in a strong out of equilibrium situation.In particular the total magnetization is decreased because of the ultrafastdynamics and should recover towards M(Tlattice). Since the reached latticetemperature depends on the initial value, the process should be stronglyinfluenced by T0, as observed.
On the other hand the interpretation of Fig. 4.21 panel ii) is not asstraightforward. The ultrafast demagnetization process doesn’t seem to beinfluenced by the ambient temperature. The only interesting parameters isthe laser fluence meaning that in the first picosecond the relevant role isplayed only by excited electrons. The resulting spin temperature as a func-tion the adsorbed energy is plotted in Fig. 4.22 panel ii). Although themagnetic order follows the electronic temperatures, the spin one displays asaturating like behaviour. The strong difference with respect to the slowprocess is a first hint that another interaction should be taken into account,an interaction not significantly influenced by the sample temperature andleading to a spin-flip rate proportional to Telectrons A dependence on the am-bient temperature is instead expected for Elliot-Yafet scattering events. Inparticular, as predicted by Koopmans at al. in Temperature Dependence ofLaser-Induced Demagnetization in Ni: A Key for Identifying the Underly-ing Mechanism published in 2012 [70], the ultrafast demagnetization shouldincrease with T0 [Fig. 4.23]. Such behaviour has not been observed in thestudied ranges of fluences and temperatures supporting the idea that anothermechanism occurs in iron thin films. According to the model proposed byCarpene et al. a demagnetization process driven by magnon creation shoulddepend only on the electronic temperature as well as its time constant. How-ever a deeper theoretical investigation is needed to exclude the presence ofother mechanism not related to scattering events (see chapter 1).
4.6 Conclusions
In this chapter we have studied the laser induced spin dynamics in ironthin films in the first few picoseconds. We demonstrated that the ultrafastdemagetization process and the slower remagnetization are driven by differentmechanisms. The latter can be explained by Elliot-Yafet scattering processes,strongly dependent on the sample temperature and the laser fluence. Inparticular the variation of the magnetization is not linear with respect to
4.6 Conclusions 65
Fig. 4.23: Solid lines: evaluated dependence of the ultrafast demagnetizationof nickel on the ambient temperature from 80− 480 K. Source [70].
these experimental parameters. The behaviour is due to the non linearity ofM(T ) in a temperature window in which the specific heat of Iron is more orless constant.
On the other hand no dependence on the ambient temperature has beenobserved in the first hundred femtosecond. The spin dynamics is influencedonly by the electronic temperature, i.e. the pump laser fluence, in contrastwith the Elliot-Yafet picture. In this regime another kind of process shouldbe considered. One possibility is offered by magnon generation, as proposedby Carpene et al. [2]. In this model, the demagnetization depends only onthe electronic temperature as well as its time constant.
Moreover, as discussed in section 4.3.2, recent works by other groupsshined a new light on the role of electron-magnon interaction in the firstfemtosecond. All these results strongly sustain this model for the ultrafastdemagnetization in ferromagnetic 3d metals.
Another interesting point comes out from our discussion. In the study oftemperature dependent spin dynamics it is necessary to consider the variationof the optical properties with the starting T0 that could modify the amountof absorbed pump energy. Not dealing with this issue, can lead to a wronginterpretation of the data.
66 Ultrafast demagnetization in thin iron films
Chapter 5Ultrafast demagnetization in TMR
systems
In this chapter I will present my experimental activity at the Radboud Uni-versity in Nijmegen (Netherlands) within my Ph.D. career. I spent six monthsfrom september 2011 to march 2012, in the ”Spectroscopy of Solids and Inter-faces” (SSI) group of Professor Dr. T. Rasing. Here the research activity ismainly focused on the study of phenomena occurring on extremely small spa-tial dimensions (nanophysics) and very short time-scales (femtoseconds). Inthis context I joined a wide collaboration involving Politecnico di Milano, theL-Ness laboratories in Como (Italy), the Uppsala university in Sweden andthe SSI group to study the mechanisms underlying the laser-induced demag-netization in metals. The main idea is to investigate the effect of the diffusionof photo-excited charges in particular tunnel magnetoresistance (TMR) mi-crostructures. These systems have been especially designed in order to studythe result of the optical excitation under the application of voltages andcurrents together with the possibility to measure photo-generated electricalsignals. With the help of Dr. M. Savoini, post doctoral researcher at SSI,I built the experimental set-up and carried out the first preliminary pump-probe measurements. The work has been carried on by Dr. Savoini after mydeparture in March by measuring the photo-induced electrical effects andsorting and rationalizing the whole set of data. However further measure-ment are still necessary and have been already scheduled in the near future.Therefore, in the following, I will try to describe only the most importantresults come to light up to now, without a detailed explanation. The dataanalysis is still in progress and more experiments are required.
The aim of this work is to investigate the superdiffusion process and even-tually propose an electro-optical device capable to exploit laser induce spindynamics. According to the superdiffusion theory [7] [14] discussed in sec-tion 5.2, photoexcited electrons experience a spin-dependent mobility withtwo main consequences: the generation of a spin polarized current and thedrain of majority spin from the irradiated area. These processes occur on thefemtosecond timescale concurring in the laser-induced ultrafast demagneti-zation. Moreover when the thickness of the sample is comparable with thelight absorption length, the excited electrons cross the buried interface, e.gwith a metallic substrate, and propagate for ten of nanometers. A currentperpendicular to the structure is therefore generated.
Electronic injection across interfaces is at the heart of the working mech-anism of many electronic devices. For example magnetoresistive systemsexploit a proper combination of magnetic and non magnetic thin metalliclayers to modulate the rei sistivity in the transverse direction. Thanks to anapplied magnetic field, the current through the junction can be tuned up to600% in case of tunneling magnetoresistance (TMR) devices [71].
The possibility of modifying the electric properties of a magnetic systemclearly offers an interesting test case for superdiffusive processes: photo-induced currents should be affected by a change in the resistivity with con-sequences on the ultrafast demagnetization.
In this work the response of TMR structures under femtosecond laserirradiation has been studied. The sample has been expecially designed for
5.2 Superdiffusion theory 69
this purpose with particular dimensions and large stability against high pho-ton intensities. The experimental setup combines the possibility to performoptical and electrical measurements in parallel. In particular we measuredthe pump induced current and the demagnetization process as a function ofapplied current (or voltage) and as a function the resistivity of the device.
5.2 Superdiffusion theory
In 2010 in an article published in Physical Review Letters [7], Battiato andco-workers proposed a new unconventional way to look at the ultrafast de-magnetization process. In their theoretical model called ”Superdiffusive Spintransport”, the motion of photon-excited electrons is sufficient to account forlaser induced magnetic dynamics on the femtosecond timescale. Surprisinglythey do not have to invoke any angular momentum dissipation channel. Theprocess relies on the draining from the irradiated area of majority electronsdue to spin-dependent transport properties. This motion is different fromthe well-known ballistic and diffusive description. As we will see in the fol-lowing, the variance of the displacement of the moving particles follows atime dependent law that lies in between the two models; this is the reasonwhy it is called superdiffusion. The model has been also further developedby the same authors in 2012 [14]. They solved the spin motion equations fortypical heterostructures non treated before, like ferromagnetic/nonmagnetic–insulator–substrate.
More in detail, they developed a semiclassical model of electron motionthat takes into account the whole process of multiple, spin-conserving inelas-tic scattering events. With this approach they treated the motion of excitedcharges after photon absorption in the femtosecond regime. In Ref. [7] aparticular example is shown in order to clarify the outstanding outcomes ofthe theory. The case study is a 15 nm Nickel film grown on an aluminumsubstrate. Here an excitation of 1.5 eV, with a time duration of 60 fs brings3d-electrons to sp-like empty states. Hot electrons will start to move in arandom direction in the system with a resulting flux that can be consideredisotropic over all solid angles because of the very small linear momentumcarried by light. In addition, considering that the electronic mean free path(up to a few tens of nm) is much smaller than the diameter of the laserspot typically used (tens of microns), only the z dependence is kept in thecalculations. A sketch of the process is shown in Fig. 5.1.
These electrons, called first-generation electrons, follow straight trajecto-ries up to the first scattering event. After that they lose part of the energyand create secondary cascade charges. The angular probability density of
70 Ultrafast demagnetization in TMR systems
Fig. 5.1: Sketch of the superdiffusive processes caused by laser excitation.Different mean free paths for majority and minority spin carriers are shownand also the generation of a cascade of electrons after an inelastic scattering(elastic scatterings are not shown for simplicity). The inset shows the geom-etry for the calculation of the electron flux term in the continuity equation.Source [7].
emission is again considered isotropic and uncorrelated to the initial direc-tion. Applying the same procedure it is possible to evaluate subsequentscaterring processes. At the end, the exact solution of the electronic fluxφ towards a surface normal to the z axis can be carried out with the mainapproximation of disregarding spin-flip events. The charge density n acrossthe surface is given by a set of k coupled transport equation, where k is thenumber of considered scattering events:
δnk
δt+
nk
τ=
(
−δφ
δz+ I
)(Snk + Sext
)(5.1)
τ is the electronic lifetime, I is the identity operator and S is the electronsource that accounts for laser excitation, labelled with ext, and the cascadegeneration.
The above described transport process is different from previous models.Standard diffusion is governed by Brownian motion and is characterized bythe variance of the displacement of a particle distribution σ2 which growslinearly with time: σ2 ∝ tγ , γ = 1. On the other hand, ballistic diffusion ischaracterized by γ = 2. The model of Battiato et al. is in the category ofsuperdiffusive processes 1 < γ < 2 with the further distinction that γ(t) istime dependent and goes from a ballistic regime (γ = 2) for small times tonormal diffusion (γ = 1) for long times.
In Fig. 5.2 the temporal evolution of the magnetization has been com-puted for the studied system. Here the interface to the vacuum is treated asa reflecting surface.
5.2 Superdiffusion theory 71
Fig. 5.2: Calculated spatial magnetization profile of Ni at three times causedby laser excitation (at t = 0fs). The resulting magnetization profile is givenby the full curve, the initial one by the dotted curve. The magnetizationprofile without electric field correction is given by the dashed curve. Thesurface of the film is at 0 nm depth, the Ni film extends up to 15 nm depth,the remaining is the Al film. Source [7].
The maximum of the laser excitation is at 0 fs, but due to its gaussiantemporal profile there is an effect already visible at t = 0fs; the magneti-zation begins to deviate from the initial values in the surface region. Thisprocess continues to t = 90fs, when it is considerably reduced. Now it isclear why demagnetization takes places: spin-dependent fast transport ofexcited electrons generates an unbalanced spin population in the irradiatedspot with a change in the total magnetization. The superdiffusive flow ofspin-up electrons into the Al film causes also a small magnetization of thesubstrate. At t = 300fs, well after the pump laser has vanished, the con-tinuing motion of excited electrons has created a further demagnetization,but the densities of carriers are already quite reduced because of inelasticscattering events, i.e. the thermalization process. Moreover the flow createscharged regions that generate an electric field. This field is not negligible forlaser fluences corresponding to demagnetizations rates of the order of tensof percent. It will, however, act equally on both spin channels without anyconsequences of the ultrafast demagnetization.
In brief, the effect is due to two main aspects: electrons in sp bands havehigh velocities (about 1nm = fs), and second, excited spin majority andminority electrons have different lifetimes. The former have a high mean free
72 Ultrafast demagnetization in TMR systems
path whereas the latter are much less mobile. This leads to a depletion ofmajority carriers in the magnetic film and a transfer of magnetization awayfrom the surface. Also cascade electrons, generated by inelastic interactions,may have enough energy to contribute to the demagnetization.
Up to now many experiments have been carried out in order to verifythe superdiffusion theory [72], [73] and [74]. Already in 2008, before thepublication of this work, Malinowsky et al. [75] observed a demagnetizationcontribution due to spin transport in multilayered structure. In 2011 a pho-toinduced magnetization in the Gold film of an Au/Fe structure has beendetected after the pump irradiation from the iron side [72]. However morerecently in [74] no electron diffusion has been observed on the nanoscale inCo/Pd multilayers.
The presence of conflicting results shows the importance of a deeper in-vestigation of the phenomena. Moreover, even if a superdiffusive mechanismmay be demonstrated, this can not be the only processes leading to the ultra-fast demagnetization. As already discussed in Chapter 1, many processes aretaking place in the first femtosecond after pump irradiation. The angular mo-mentum can be redistributed via electronic scattering with phonons [3] [76][77] [43], magnons [2] and other electrons [78] [79] [80] or dissipated by coher-ence effects induced by the laser electromagnetic field [52] [5]. Therefore, alsoa quantitative experimental estimation of the superdiffusive contribution tothe demagnetization process could be of high interest.
5.3 Sample: tunnel magnetoresistance device
In a standard pump and probe experiment, laser spot diameters range be-tween ten to few hundreds of microns. On the other hand, the endless devel-opment of nanotechnology is driving electronics towards increasingly minia-turizing with further advantages coming from quantum mechanics. TMRdevices, present in common hard disk drives, are based on quantum tun-nelling between two ferromagnetic metals separated by an insulating spacer.Typical dimensions are of the order of one hundred nanometers. Not only thethickness of the layers but also their lateral dimensions are crucial. The latterconstrains come from the difficulty to grow epitaxial heterojunctions withoutdefects that can create shortcuts between conductive sheets and prevent thetunnelling.
To match ”micrometer” optic with electronics we can shrink the spotdimensions to the diffraction limit i.e. with microscopy technique, or enlargethe dimensions of the devices using particular growing methods.
Thanks to the experience of the Spin Electronics (SE) group of professor
5.3 Sample: tunnel magnetoresistance device 73
Fig. 5.3: Multilayer structure of the device on the right, with a 3D represen-tation and a confocal microscopy image.
R. Bertacco at the L-Ness laboratory (Como, Italy), we explored the secondpath. While the optical set-up, as shown in section 5.4, is not suitable tomicroscopy, the SE group is able to build working TMR devices with sizableefficiency up to 500µm diameter.
In particular the studied sample contains circular devices with differentdimensions, from 4 µm to 750 µm, for a total number of 300 bits. Theyhave been grown by multiple step UV litography and characterized by AFMprofilometric measurements. Each is composed by a multilayer structure aspresented in Fig. 5.3, together with a 3D sketch and a confocal microscopyimage.
Starting from the bottom substrate, SiO2 on top of a Si (100) wafer,a series of layers have been deposited in order to obtain the lower latticemismatch in the metallic heterojunction Ta/IrMn (14nm)/Fe0.4Co0.4B0.2 (5nm). IrMn is the first magnetic compound, it is antiferromagnetic and pinsthe spin orientation of the above Fe0.4Co0.4B0.2 ferromagnetic film. After that3 nm of MgO and a 10 nm thick layer of Fe0.4Co0.4B0.2 are present. The MgOinsulating spacer has a double function: it decouples the magnetization ofthe surrounding ferromagnets and act as tunneling barrier. On top of thewhole structure, a transparent capping has been grown in order to protect thedevice and allow the building of electrical contacts. The gold circular stripeshas been designed to do not mask the upper layers upon laser irradiation.
Another feature needs to be mentioned besides the lateral dimensions.The thickness of the upper Fe0.4Co0.4B0.2 sheet has been especially increasedto 10 nm to guarantee higher laser absorption. It is more ore less twice the
74 Ultrafast demagnetization in TMR systems
Fig. 5.4: Magnetic and electrical characterization of a TMR device with adiameter of about 10 nm. The curves have been acquired as a function of theexternal field, in red the forward branch (from negative -400 Oe to positive+400 Oe) and in blue the backward. Panel (a) shows the hysteresis loops ofthe two magnetic layers, while panel (b) the resistance. In panel (c) there isa sketch of the positions of the magnetization in the ferromagnetic layers.
typical values of standard TMR devices.
The static magnetic and electric characterizations have been performedfor each considered structure. Fig. 5.4 , panel (a), reports the measuredmagneto optical Kerr effect as a function of the external field for a bit sizeof 10 nm. Two hysteresis loops are present: one large and centered at zerofield, the other weaker and shifted at about 150 Oe. The presence of a bias isa clear indication that the latter comes from the buried ferromagnetic layerof Fe0.4Co0.4B0.2. The pinning with IrMn forces its magnetization towards aparticular direction in space; two non-symmetric values of the external fieldare thus necessary to reorient it. As a proof of this statement we observe thatthe other hysteresis loop definitely belongs to the upper layer. The hysteresisis characterized by larger intensity, due to the higher laser absorptions, andis centered at zero external field, because the top layer is decoupled from therest of the structure by the MgO spacer.
5.4 Experimental setup 75
Arrows in panel (c) shows the reciprocal orientations of the magnetizationof the two Fe0.4Co0.4B0.2 layers. If the external field is negative the vectorsare parallel and parallel to H (left-hand direction in our convention). Fromzero to 100 Oe they are antiparallel, while above 150 Oe both point in thedirection of the external field (right-hand direction).
In panel (b) the resistance as a function of the external field is shown.A field dependent signal is clearly evident together with an hysteresis, redbranch for external field from negative to positive values and blue for thereversed path, as for the hysteresis loops. It is now clear how a TMR deviceworks: resistivity across the structure changes accordingly to the reciprocalorientations of the two magnetizations. When they are antiparallel orientedthe total reisistance increases. The efficiency of a TMR device is evaluatedas:
γ =RAP − RP
RP
(5.2)
where RP is the resistance for the parallel case and RAP for the antipar-allel one. In Fig. 5.4 the TMR efficiency is around 50%. Increasing the areaγ goes down: 40% for 50 nm diameter, 15% for 250 nm and around 2%for 500 nm (only few 750 nm valves showed a TMR close to one per cent).The behavior is explained by the presence of defects in the insulating MgOinterfaces that can create shortcuts between metallic electrodes.
To conclude circular TMR devices has been especially designed and grownfor pump and probe measurements. They are characterized by thick ferro-magnetic layers to ensure pump absorption and large active area withoutbeing masked by electrical contacts. The devices have a diameter rangingfrom 10 to 750 µm with efficiencies from 50% to few percents in the worstcase. However, due to problems with scattered light and signal to noise ratio,the results reported in the following sections have been acquired from junc-tions with diameter in the 100-150 µm range with measured TMR between5% and 12%
5.4 Experimental setup
The pump and probe experimental setup is reported in Fig. 5.5.The laser source is made by the Coherent Inc. MICRA oscillator plus the
RegA amplifier working at a repetition rate of 250 kHz. The photon energyis about 1.55 eV corresponding to 800 nm, while the pulse width is 60 fsmeasured by a cross correlator. The beam is split in two part. The pumppulse with most of the intensity is sent through a Beta-Barium-Borate BBO
76 Ultrafast demagnetization in TMR systems
Fig. 5.5: Sketch of the experimental setup for pump and probe measurements.The laser beam is split into two parts: the pump, in blue, has a wavelengthof 400 nm, after passing trough a non-linear BBO crystal that doubles itsfrequency, while the probe, in red, is at 800 nm.
crystal to double its frequency. The 400 nm beam is modulated by a choppertriggered at a frequency lower than the laser repetition rate. After that it isfocused and sent to the sample with an angle of about 70◦ from the normal tothe surface. Here the spot shape is strongly elliptical. Along the longitudinaldirection the dimension is about 75 µm while along the transverse it is 20µm. The probe beam is optically delayed by a mechanical stage with 0.1 µmstep size, equivalent to 0.67 fs, and a maximum delay of about 600 ps. Afterbeing focalized it impinges on the sample with an angle of about 45◦ andwith lateral spot dimensions of about 15 and 20 µm.
The reflected beam is collected by a balance detector that measures smallchanges of the light polarization. The signal feeds a lock-in amplifier triggeredat the chopper frequency. Another output of the detector brings informationabout the total intensity shining the diodes. With a second lock in amplifierit is possible to record at the same time the change in reflectivity.
An external field is applied parallel to the sample surface and the inci-dence plane. In addition a microamperometer current source together witha voltage supplier and an acquisition multimeter allow the static character-ization of the structure. To measure an electrical pump induced effect, thesample is plugged in parallel to another lock-in that amplifies a modulatedsignal at the laser frequency. Finally to locate the different TMR device weused a CCD camera with 20x magnification objective.
5.5 Data and discussion 77
Fig. 5.6: Conductance of a 150 µm TMR device as a function of the appliedvoltage. The data have been fitted by a second degree polynomial curve inred.
5.5 Data and discussion
The results reported in the following sections are acquired from junctionswith diameter of about 100 - 150 µm. The magnetic and electrical character-izations have been performed for every measured device. Their functional-ity has been checked confirming that the magnetoresistance is working well.Fig. 5.6 shows the conductance behavior as a function of the applied Volt-age. The polynomial fit conferms the V 2 dependence of the conductance, itis the mark of the occurrence of tunneling processes. Only few points havebeen acquired at high voltages and currents and a better characterization isnow in progress. Our experimental setup is capable of generating currentsup to 100 mA (corresponding to about 0.5 V) and voltages till 1 V(more orless 300 mA). For these values a sizeable TMR of the order of 10% has beenmeasured, the efficiency is slightly decreased, i.e. 5%, and no evident effectsdue to thermal heating or damages are present.
Two different types of pump and probe experiments have been carried out.In the first section the ultrafast demagnetization as a function of the appliedbias is studied. If a current crosses the interfaces an appreciable modulationof the signal is observable. After that we will show electrical photo-inducedeffects. In this case feeding a dc voltage to the structure results in a differentresponse depending on the bias intensity.
78 Ultrafast demagnetization in TMR systems
Fig. 5.7: (a) Hysteresis cycles without (black) and with (red) the pumppresence. For a fluence of about 3 mJ/cm2 the reduction in the magneticmoment of the top layer is approximately 10%. (b) TMR signals acquiredwithout (black) and with (red) the pump beam on the sample. The averageresistance is slightly increased without sizable effect on the TMR efficiency.
5.5.1 Pump and probe measurements
The main idea of this work relies on the possibility to study the superdiffusivecurrent injected from the first layer towards the TMR structure. Establish-ing which is the pump pulse interaction with the multilayer system is thusof fundamental interest. Ultrafast processes triggered by laser pump can in-volve also buried sheets, complicating the modelling of the process or evenhindering superdiffusive effects.
To address the problem we studied the effects on individual magneticlayers by looking at hysteresis loops at different pump and probe delays. InFig. 5.7 (a) measurements at a delay of about 0.5 ps, red curve, are reportedtogether with the no-pump case, in black. At this delay the maximum effectin the magnetization has been observed. The curves are shifted by about40 Oe because of a small asymmetry in magnetic field generated by theelectromagnet. The larger loop is affected by a demagnetization of about11% while the smaller is modified only in its shape. As already discussedthe former comes from the upper layer while the latter from the bottom.The change in shape, in particular the reduction of the coercivity, can beascribed to thermal effects. It shows for every pump and probe delays withouttemporal evolution. We can conclude that the laser repetition rate is highenough to induce an increase of the overall temperature in the device. Thisis observable also in the magnetic characterization. Fig. 5.7 (b) shows theaveraged effect on the resistance for different values of the external field. Thered curve, measured in the presence of the pump, has a higher resistance thanexpected at higher temperature, while the TMR efficiency is not affected.
5.5 Data and discussion 79
Fig. 5.8: Maximum ultrafast demagnetization plotted as a function of theimpinging intensity per unit area together with a linear fit.
This is the experimental evidence that no remarkable dynamics due to pumpabsorption is in progress in the buried layers. In addition, from ellipsometricmeasurements, we extrapolate the imaginary part of the refractive index ofabout 2.5 for FeCoB layer at a wavelength of 400 nm. The correspondingpenetration depth is about 12 nm that is comparable with the thickness ofthe top layer. The optical setup has been designed to shine the structure atgrazing incidence. A rough estimate confirms the experimental result thatmost of the intensity, up to 90%, is dissipated by the first layer. Moreoverthe presence of multiple interfaces further reduces the penetration.
The ultrafast demagnetization occurs within about 0.5 ps and depends onthe optical intensity per unit area. It scales linearly from 2.5% for 1 mJ/cm2
to 40% for 8.5 mJ/cm2 as shown in Fig. 5.8. The demagnetization timealso increases with the pump fluence according to previous measurementsreported in literature.
5.5.2 Ultrafast demagnetization: current modulation
In this section, we studied the ultrafast demagnetization as a function of acurrent applied to the structure. Three set of data have been acquired atdifferent pump fluences 0.5, 3 and 9 mJ/cm2; the bias has been settled in arange between -75 mA and +75 mA.
Fig. 5.9 shows the experimental results for the 3 mJ/cm2 case. For thisfluence the data are clearer and not affected by noise.
At zero current the ultrafast demagnetization is about 11.6% and occursin less than 500 fs. Under the bias application, a trend is evident: thedemagnetization reduces proportionally to the current up to 8.5% for -75mA. The results are summarized in the inset reporting the maximum 4M/M
80 Ultrafast demagnetization in TMR systems
Fig. 5.9: Demagnetization with about 3 mJ/cm2 pump fluence as function ofthe externally applied current. Inset: maximum demagnetization vs appliedcurrent.
as a function of the bias. Here we observe no dependence on the injectiondirection, i.e. the current sign, and the non linearity of the effect. It doesn’tseem to saturate and in particular, we can tune the ultrafast processes up to24% at the maximum applied current of 75 mA.
Changing the pump fluence affects both the ultrafast demagnetizationand its modulation by the bias. Fig. 5.10 reports the curves acquired with9 mJ/cm2. Here the demagnetization is around 41% and can be lowered to37% due to current injection. The behavior is observable especially in thebranch of positive bias as shown in the inset. Here the relative decrease in themagnetic moment is only 8% instead of 25% as in the previous measurements.
For low fluences instead (Fig. 5.11), only few cases have been consideredup to now. 4M/M is about 2.5% but, although noisy, it is evident that withonly 20 mA we can induce a relative change of the signal of about 10% whichis comparable with the measurements at 4.5 mJ/cm2.
To summarize we observed a non linear response of the ultrafast demag-netization to an applied current. The induced effect is independent on thedirection of the bias and shows a saturating like behaviour with respect tothe pump fluence.
This results can be interpreted in the framework of the superdiffusiontheory. The arrival of a pump pulse depletes the upper magnetic layer ofelectrons. The effect is proportional to the laser intensity and causes themeasured demagnetization. Injecting a current into the structure, the elec-trons flow with spins parallel to the majority band polarization because ofTMR magnetic properties. This traveling electrons sustain the top layerswith the counterbalancing effect of re-filling the drained zone by the pump
5.5 Data and discussion 81
Fig. 5.10: Demagnetization with about 9 mJ/cm2 pump fluence as function ofthe externally applied current. Inset: maximum demagnetization vs appliedcurrent.
Fig. 5.11: Demagnetization with about 0.5 mJ/cm2 pump fluence as functionof the externally applied current.
82 Ultrafast demagnetization in TMR systems
pulse. The quenching of the ultrafast demagnetization is thus explained andalso its symmetry in the current direction. If we consider a laser fluence ofabout 3 mJ/cm2 the relative maximum modulation is around 24% at 75 mA.With three times the optical power on the sample, i.e. 9 mJ/cm2, the effectof the current is almost three times lower. This behavior follows the ratiobetween absorbed photons and the injected current.
The non linearity can be explained considering the transport properties ofTMR devices: the resistance is not constant but is dependent on the appliedvoltage (or current), as shown in the previous section (Fig. 5.6). However afull static characterization at high currents is still missing. An extrapolationfrom our data at low applied voltages may not be reliable, perhaps the V 2
dependance doesn’t survive up to 0.5− 1VTo conclude, the effect of thermal heating has to be briefly discussed.
First of all it is important to mention that we didn’t observed a lowering inthe total magneto optical Kerr signal due to the presence of an applied currentin static measurements. Therefore joule heating is not sufficient to modifythe magnetization in the top part of the structure. Concerning the resistance,we have shown that the structure is durable and it not affected by currents upto 100 mA. We have already demonstrated that it can be modified by pumppulses because of an overall increase in the sample temperature independenton the pump–probe delay, and that this effect is very small, few percents.Therefore from these arguments, we can argue out temperature dependenteffects in the measured dynamics that should show genuine spin transportphenomena.
5.5.3 Photo-induced effects: voltage control
This section is dedicated to the presentation of electrical photo-induced ef-fects. The sample is electrically connected to a lock-in amplifier in-phasewith the laser beam. In this way we acquire the difference in the measuredvoltage/current with the pump shining the sample and when it is blocked.The experiment has been performed as a function of three experimental pa-rameters: laser fluence, applied tension and external magnetic field.
Fig. 5.12 shows the results for a pump fluence of about 3 mJ/cm2 whilesweeping an external field at fixed bias. Hext spans between -300 Oe and+350 Oe, values high enough to probe the three different alignments of themagnetic vectors. From section 5.3, we remind that we can couple the topand the bottom magnetic layers either antiparallel or parallel pointing to twodifferent directions. Furthermore the voltages has been set within a range of±150 mV, corresponding to a maxim current of about 130 mA.
The signal shows a non linear behavior strongly dependent on the bias
5.5 Data and discussion 83
Fig. 5.12: Photo-induced voltage as a function of the external magnetic field.Six curves are plotted accordingly to the applied bias. The inset summarizesthe results reporting the average values for parallel and antiparallel magneticcoupling together with their difference.
sign. Applying less than ±100 mV, we measure a flat line that apparentlychanges by few microvolts only depending on the direction of the voltage.Here it is remarkable that a pump induced voltage is generated also at 0mV. Incrementing the applied bias we exceed a threshold, i.e.±150 mV, andthe signal suddenly increases with a shape closely resembling the one mea-sured for TMR curves. In particular for +150 mV the modulation due to theexternal field can be as high as 100%: the effects are suppressed when theexternal field is around 100 Oe, i.e. the two magnetic vector are antiparallel.On the other hand, at the opposite voltage the quenching is lower and so themodulation. The results are summarized in the inset. Here the photoinducedeffects are reported distinguishing from the two orientation of the magneti-zation, together with their difference. It is apparent the strong non-linearityand the difference between parallel and antiparallel magnetic coupling.
In order to better understand the dependence on the external voltage, inFig. 5.13 the effect at fixed field as a function of the bias up to ±200 mV isplotted. The two curves in open symbols correspond to the parallel coupling(black) and the antiparallel (red). The green line represent their difference.The two parallel situations (positive and negative fields) are always equivalentand they are treated together.
Some features can be enlightened:
• starting from a negative field, below -110 Oe, the photoinduced voltageis constant for all curves and assumes slightly higher value for the
84 Ultrafast demagnetization in TMR systems
Fig. 5.13: Photoinduced voltage as a function of the external voltage forparallel coupling of the magnetic layers (black) and antiparallel (red). Ingreen is plotted the difference. The pump laser fluence is about 3 mJ/cm2.
antiparallel coupling;
• between -110 mV and +140 mV, the signal is noisy with a small in-creasing slope. The averages is around 4 µ V for both parallel andatiparallel cases;
• above +140 mV, the signals suddenly rises towards high positive values.The threshold voltage is different according to the magnetic orientation.After that the induced voltages become constant.
In general a different behavior for the two magnetic coupling results in aTMR like shape, while the presence of distinct thresholds at positive voltagesgenerates a spike in the blue curve and the previously observed non-linearity.
In Fig. 5.14 the same measurements have been made with three times thepump fluence, about 9 mJ/cm2. Here we pushed the voltage up to 1 mVcorresponding to a current of ∼ 300 mA. The photoinduced tension is threetimes higher than before and the behavior does not change. The signal showsa high jump also at negative values and after that, it tends to saturate.
In conclusion we observed that a voltage/current is injected inside thesample because of the pump irradiation. It increases proportionally to thelaser fluence and it can be tuned by an external field. When the magneticcoupling is antiparallel, i.e. the total resistivity of the sample increases, theeffect diminishes. For particular values of the external bias, photo-inducedeffects even drop to zero with a modulation of the voltage up to 100%.
5.6 Conclusions 85
Fig. 5.14: Photoinduced voltage as a function of the external voltage forparallel coupling of the magnetic layers (black) and antiparallel (red) with alaser fluence of about 9 mJ/cm2.
However, even if some features remains of difficult interpretations andfurther measurements are required, something can be argued about the pres-ence of spin superdiffusive phenomena. We measured a photo-induced volt-age/current (< 4µV ) even at zero applied voltage meaning that transportprocesses are taking place. They seem to be sensitive to the total resistanceof the device strengthening our interpretations: the voltage decreases whenthe two magnetic layer are antiparallel coupled. Choosing an external voltagein the same direction of the measured signal (negative values), we linearlyincrease the photoinduced voltage. In the opposite direction (positive val-ues), the bias turns the effect to zero and eventually changes its sign. In thisregime the photoexcited electrons moves under the applied potential in theopposite direction through the electrical connections. For values higher than±150 mV a threshold is present. We were not yet able to give a qualitativeexplanation of the phenomenon but a better characterization of the resistanceof the device will help. Moreover the effect on the ultrafast demagnetizationfor this particular threshold values has not been investigated yet.
5.6 Conclusions
In conclusion we have optically and electrically measured the response ofTMR structures under the irradiation of femtosecond laser pulses. The ultra-fast demagnetization process can be modulated by the presence of a currentthrough the structure and we observed a photo–induced voltage generated by
86 Ultrafast demagnetization in TMR systems
the absorption of a pump pulse. Some effects can be partially explained byelectronic superdiffusion processes, although our experimental observationsdo not strictly require the presence of spin–transport phenomena occurringon the femtosecond timescale. Up to now, a comprehensive picture of the ef-fect is still missing. For this purpose, more measurements have been alreadyscheduled especially to clarify the behaviour of the devices under the appli-cation of high currents and voltages. Also a wider static characterization willbe performed in this regime of strongly stressing operating condition. Webelieve that our study will shed new insight into the understanding of theultrafast demagnetization and possibly pave the way toward the control ofthe spin dynamics in the ultrafast time window.
Chapter 6All-optical sub-nanosecond coherent
spin switching
In this chapter we will demonstrate that, using short laser pulses, the magne-tization of a thin biaxial ferromagnetic layer can be optically and repeatedlycommuted between well-defined directions on a time scale of 100 ps. Ourmain goals are to operate under straightforward experimental conditions,i.e., in air and at room temperature, with a moderate optical excitation anda simple ferromagnetic 3d metals. In particular we will achieve the fullyoptical magnetic spin switching between easy axes of a thin iron film . Theunderneath mechanism is disclosed measuring the 3D trajectory with fem-tosecond resolution. It is driven by the fast heating of the sample and relies onthe magnitude of the external magnetic field relative to the time-dependentmagnetic anisotropy. Moreover the perfect repeatability of the switchingprocess is tested and demonstrated. Every single pump pulse modifies themagnetization direction in a fully predictable way.
The work has been published in 2011 in Physical Review B [32] in 2011:All-optical subnanosecond coherent spin switching in thin ferromagnetic lay-ers, E. Carpene, C. Piovera, C. Dallera, E. Mancini, E. Puppin 84, 134425(2011).
After few picoseconds since the arrival of the ultrashort laser pump pulse,the local thermalization of spin, phonon and electrons, is established. Themagnetic dynamics is mainly driven by processes resulting from the heat-ing of the irradiated area and characterized by temporal extents as large ashundreds of picosecond. Spin oscillations and phase transitions are only fewexamples of the possible phenomena.
In the next sections, we will focus on laser induced magnetic precessions,i.e. a coherent spin oscillation, that are the most effective route to con-trol the direction of the magnetization with interesting followups from thetechnological point of view.
6.1.1 Magnetic precession
In 2002 Kampen et al. [28], demonstrated that, after the ultrafast demagne-tization, the magnetic vector may undergo a time–dependent modification ofits direction. The observed motion started after few picoseconds and followeda precessional trajectory.
To explain the onset of such a movement let us first discuss the behaviourof a magnetic dipole m in an external field B = µ0H. If a non zero angle θexists between m and B, the magnetic moment will experience a torque:
T = m×B (6.1)
that is related to the variation of the angular momentum L by:
∂L
∂t= T = m×B (6.2)
Since γL = m (γ is the gyromagnetic ratio), we can re–write eq. 6.2 as:
γ∂L
∂t=
∂m
∂t= γm×B (6.3)
which describes a precessional motion of the angular momentum around themagnetic field. The frequency of the precession is given by:
ωL = |γ|B (6.4)
6.1 Introduction 89
ωL is called Larmor precession frequency and does not depend on the anglebetween m and B. For instance, if we consider the magnetic moment ofa single spin m = −geµB
~S where ge is the Lande g–factor, µb the Bohr
magneton and ~ the reduced Planck constant, we can roughly estimate aperiod of about ∼ 30− 40 ps in a magnetic field of 1 T.
During the precession, as described by eq. 6.3, the energy should conserve,thus θ will not change and the magnetic moment will never align with theexternal field. However friction forces, also at the atomic scale, damp themotion until m eventually stops parallel to B. For this reasons, an additionaltorque that guides the magnetic moment towards B, needs be introduced ineq. 6.3. The term must be perpendicular to m and T , i.e. proportional to:
−m×m×B. (6.5)
Moreover eq. 6.5 accounts for the further experimental observation that thedamping increases with by strengthening the applied magnetic field. The firstphenomenological description of the precessional motion of m was developedby Landau and Lifshitz in 1953 [81]. The so called Landau-Lifshitz equationis reported in the following:
∂m
∂t= γ
(
m×B− α
mm× (m×B)
)
(6.6)
where α is a phenomenological damping parameter and m is the modulusof the magnetic dipole. The link between the previous discussion and theequation of motion for the magnetization vector M of a ferromagnet passesthrough few steps. First of all, M is defined as the density of magnetic dipolesper unit volume, i.e M =
∑m/V . This is the macrospin approximation
in which the individual spins are mutually coupled and move coherently.Subsequently, it is necessary to consider the magnetic fields acting on M. Asdiscussed in details for an iron thin film (Chapter 4), the magnetization vectorin a ferromagnet lies on preferential directions called easy axis. This so–calledmagnetic anisotropy relies on many factors like the crystalline and the shapeanisotropy. This evidence can be modelled by the anisotropy fieldHan alignedto one of the easy axes and the demagnetizing fieldHdem, related to the shapeof the system. As a result, the total field acting on the magnetization vectorM is given by the vectorial sum of all this terms, known as effective field,Heff = Hext +Han +Hdem. Therefore, eq. 6.6 becomes:
∂M
∂t= γgM×Heff −
λ
MsM× (M×Heff) (6.7)
with γg = γµ0, Ms the saturation magnetization and λ > 0 the damping pa-rameter. Equivalently Gilbert proposed also the following formulation (LLG
equation) of the Landau–Lifshitz model 6.7 in which the direct dependenceon the effective field in the damping is not explicitly shown:
∂M
∂t= γg
[
M×Heff +η
MsM× ∂M
∂t
]
(6.8)
with η = (αγ)/(1 + α2).
To summarize the LL and LLG equation describes the precessional motionof the magnetization vector when M is not aligned with the effective feldHeff .
The duration of a damped magnetic precession is essentially around fewnanoseconds for common bulk metals. The Gilbert damping can be verysmall, e.g. η = 0.005 in epitaxially grown bulk cobalt, but considering thinfilms or multilayers, interfaces effects can increase the energy dissipation upto η ∼ 0.1− 0.2 [82] with a consequent decrease of the relaxation time τ .
Therefore, to observe an oscillation of the magnetization vector in thetime–domain it is necessary to modify the direction of Heff at a rate higherthan τ and, as well, measure the magnetization position with a compara-ble temporal resolution. Reminding that Heff = Hext + Han + Hdem, wecan operate on the applied external field and on some sample properties. In2001 Gerrits and coworkers [83] measured for the first time spin oscillationin a micrometric permalloy structure triggered by a pulsed field Hext withpicosecond duration. They adopted a pump–probe technique in which theapplication of Hext was followed by delayed laser pulses to optically mea-sure the magnetic response as a function of time. Later in 2002 [84], theydemonstrated the possibility to actually control the precessional dynamicswith subsequent magnetic pulses conveniently delayed. However the methodrequired lithographically defined structures on the sample, limiting the ap-plicability of the technique.
In the same year, Kampen et al. [28] demonstrated that is possible to ex-cite and measure the precessional motion exploiting an all-optical technique.They performed TR-MOKE on a 7 nm thick polycrystalline nickel film onsilicon with a particular experimental geometry, as depicted in Fig. 6.1. Hext
was applied in near-hard-axis directions, i.e. perpendicular to the film plane,resulting in a non–collinear arrangement of Hext and Han. After the photonabsorption and the local thermalization, the temperature raises with a con-sequent degrease of the magneto crystalline anisotropy. This quantity showsindeed a strong temperature dependence, i.e. it drops to zero close to thecurie point of the material [85], therefore, also Han is subject to a reduction.This effects results in a sudden canting of Heff within a couple of picosec-onds. Since the change is faster than the corresponding precession period,
6.1 Introduction 91
the magnetization vector will not be able to follow the field and will start toprecess around its new equilibrium axes.
Fig. 6.1: a) panel: TR-MOKE measurements of the out–of–plane componentof the magnetization vector in 7 nm Ni film as a function of delay time. Theprecession displays a frequency of about 9.98 GHz and a damping parameterη = 0.05. b) panel: the excitation process. (I) t < 0 the magnetization Mpoints in equilibrium direction (dotted line); (IIa) t < 1 ps the magnitudeof M and the anisotropy decrease due to heating, thereby altering the equi-librium orientation; (IIb) 0 < t < 10 ps M starts to precess around its newequilibrium; (III) t > 10 ps with the heat diffusion the magnitude of M andanisotropy are restored thus the equilibrium axis start moving towards itsinitial direction. Source [28].
Another interesting way to excite magnetic oscillation needs to be brieflymentioned. The inverse Faraday effects has been demonstrated and success-fully used to induce spin oscillation by Kimel et al. in 2005 [86]. The angularmomentum associated to the circular polarization of photons, together withthe high pick intensity of ultrashort laser pulses affects the magnetizationthe same way as a femtosecond magnetic field up to 5 T does. In Fig. 6.2the two transient magnetization dynamics have been acquired with oppositepump ellipticity in DyFeO3. Due to the different sign of the delivered angu-lar momentum, the precessional motions evolves with opposite phases and adifferent amplitudes.
A similar effect has been observed in magnetic garnet by Hansteen etal. in 2005 [87] pumping with linear polarized light. Here the magneticoscillation changes sign depending on the direction of the pump electric field,see Fig. 6.3. This phenomenon has been explained by a dichroic non–thermal
Fig. 6.2: Circularly polarized pump pulses of opposite helicities excite os-cillations of opposite phases. Inset shows the geometry of the experiment.Vectors H+ and H− represent the effective magnetic fields induced by right-handed σ+ and left-handed σ− circularly polarized photons, respectively.Source [86].
modification of the magnetocrystalline anisotropy. Excited electrons transferbetween ions on nonequivalent sites in the crystal, according to the lightpolarization, and this process leads to a fast, i.e. within few picoseconds,redistribution of ions and thus to a change in the lattice structure.
Summarizing, all these results underline the importance of studying spinoscillation by all-optical techniques. Well-established methods are exploitedby many groups both to retrieve quantitative information on the magneticanisotropies and damping mechanisms [88] [89] and also for the study offundamental light matter interaction physics. In addition, the possibility toexplore the motion with sub–nanosecond resolution allows one to study manyinteresting phenomena like, for instance, superparamagnetism in nanoparti-cles [90] and spatial anisotropies of the Gilbert damping parameter [91]. Nev-ertheless the technique is also successfully used for ultrafast photo-magnonics[92] and, as we will shown in the next sections, to permanently switch themagnetization direction in ferromagnets [93] [32]. All these results, togetherwith the potential opportunities offered by the magnetic dynamics in thefirst femtoseconds, pave the way to design all-optical magnetic devices withworking rate in the sub–nanosecond regime.
6.1 Introduction 93
Fig. 6.3: Coherent precession of the polar component of the magnetizationtriggered by linearly polarized laser pulses in garnet samples. The orientationof the pump polarization affects the phase of the oscillations. Source [87].
6.1.2 Magnetic switching: towards all-optical switch-
ing
In this section we will discuss the switching process of the magnetic vec-tor M. Generally speaking with this term one indicates the motion of themagnetization from one position to another in space. If the system is char-acterized by one easy axis, the magnetization can modify its orientation bya 180◦ inversion, while in biaxial systems four different arrangements of Mare possible. The magnetic switching is the mechanism underlying the in-formation storage of magnetic recording devices where a write–head alignsthe magnetization along one of the two possible directions according to abinary logic. The speed of this process is the performance bottleneck ofmodern calculators being the clock rate of computing processors faster thanone nanosecond. One of the most challenging issues from the technologicalpoint of view, is to achieve the fastest possible speed of data writing.
The easiest way to move the magnetization vector is applying an externalfield Hext along one easy axis. If a certain threshold is exceeded M abruptlyswitches. The reorientation is mainly determined by domain wall motion andoccurs in few nanoseconds. However this is a quite slow process if comparedwith spin precessions. Characteristic rates can be three orders of magnitude
faster, i.e few picoseconds, and, according to eq. 6.4, the only limit to in-creasing the switching speed should be the maximum available external fieldstrength and its duration.
To launch a magnetic precession it is necessary to applyHext not collinearlyto the magnetic vector M. In particular to overcome the hard–axis–direction,i.e. the energetic barrier that prevents the inversion, the external field shouldbe located in its proximity, as shown in Fig. 6.4 (for a system with onlyone easy axis, the free–energy maximum corresponds to the sample surface).Once M has precessed by an angle large enough to cross the barrier, it willrelax into the opposite direction. If Hext is switched off before M crosses thehard axis, the magnetization relaxes back to its original direction, hence noswitch is observed. Interesting, in the same geometry, we can switch back themagnetic vector without inverting the polarity of Hext but simply applyingagain the switching field.
Fig. 6.4: A fast way of reversing the magnetization vector M is to launcha precessional motion. For an uniaxial magnetic system a short field pulseHext is applied perpendicular to M. Source [94].
For these reasons, precessional switching is a very attractive alternativefor magnetic recording devices however, the generation of strong pulsed mag-netic fields remains a challenging task, thus the research for more feasibletechniques is still in progress. An interesting possibility emerging in the lastyears is the so–called all-optical switching in which ultrashort optical exci-tations promote magnetic inversion. Other methods not less important arebeing developed, like spin torque [95], racetrack memories [96] or multiferroicmaterials [97].
The first experimental demonstration of magnetic recording with 6 psmagnetic field pulses has been successfully achieved by Siegmann and cowork-ers in 1995 [98]. They shot the finely focused 46.6 GeV electron beam of theStanford Linear Accelerator Center (SLAC) perpendicular to two magneticCoPt alloys with different stoichiometry and anisotropies, one with in–planeand the other with out–of–plane magnetization. In both samples 15 consecu-tive ultrashort electronic bunches were enough to reorient the magnetizationdirection. In this experiment Hext resembles the one generated by a straight
6.1 Introduction 95
current-carrying wire, with circular field lines concentric about the beamdirection. The electronic bunches are sent perpendicular to the samples,triggering a precession when M is not collinear with Hext [Fig. 6.5].
Fig. 6.5: Principle of the experiment realized at the Stanford Linear Acceler-ator Center with ultrashort magnetic pulses. The highly relativistic electronbunch generates magnetic field lines equivalent to the ones from a straightcurrent carrying wire. The temporal duration is determined by the spatialspread of the electron bunch and its speed. Source [20].
Similar experiments were repeated later on by Back et al. [99] [100] withmagnetic pulses of 2–3 ps. In 2004 Tudosa et al. [20] demonstrated thatprecessional switching in magnetic media no longer occurs with magneticfield shorter than 2 ps. According to the authors this behaviour can beexplained by a momentary collapse of the ferromagnetic order under theload of the short and high-field pulse. In this fast regime the spins coherenceis broken and chaotic motion sets in. This fact established an ultimate limitto the speed of precessional switching and magnetic recording.
Another demonstration of magnetic switching by pulsed external fieldhas been performed by Gerrit et al in 2002 [101]. They showed that in mi-crometer elliptical permalloy structures it is possible to reorient the magne-tization direction in about 200 ps without exploiting ultraintense relativisticelectron bounces. They developed a electro-optical device in which GaAs-photoconductive switches generates ultrashort current discharge into a guidedriving the magnetic field in the proximity of the sample.
Concearning the optical route for magnetic switching, it has been firstexplored by the so–called thermally assisted recording [9]. Here a laser isused to momentarily heat the sample and reduce its coercivity below thatof an applied magnetic field. The switching is ultimately driven by Hext
applied along one easy axis with the proper polarity. Therefore the processdoes not relies on precessional motion and should be characterized by a rela-
tively slow dyanamics. The magnetization inversion has been investigated inthe time domain using TR-MOKE by et Hohlfeld et al. [102] who obtainedtimes around ∼ 1 ns in GdFeCo compounds. In 2010 Bunce and et al. [103]achieved sub–nanosecond switching with specially designed CoPt multilay-ers. However, in 2007 Stanciu and coworkers [11] seemed to put an end tothe challenge for the fastest switching speed with a very surprising result.They measured the thermally assisted inversion in a different stoichiometryof GdFeCo and observed the inversion of the faraday magnetic signal in lessthan one picosecond after pump absorption. This result has been attributedto a magnetic switching taking place in ∼ 700 fs and has been confirmed byTR-XMCD measurements in 2011 [104] [Fig. 6.6]. GdFeCo belongs to a par-ticular class of compounds, called ferrimagnets, characterized by the presenceof two subarrays coupled by antiferromagnetic exchange interaction. Sincethe two sub–lattices have different magnetic behaviours as a function of tem-perature, there exist a particular value at which the total magnetization van-ishes, named magnetic compensation point Tm, in general different from theangular momentum compensation point Ta. This two temperatures changesaccording to the stoichiometry. In comparison with the previous results byHohlfeld et al. [102], the experiment was performed on a sample showing aTa slightly above room temperature. The laser–induced heating drives theirradiated area close to the angular momentum compensation point wherethe precession frequency and the Gilbert damping increase drastically [105]with a consequent acceleration of the switching process. Despite that, it isnecessary to stress that the underlying mechanism is still debated. Thesefindings are in fact in contrast with the previously demonstrated switchinglimit of 2 ps [20] in common ferromagnets.
Another striking results has been obtained by the same scientific group in2007: the so–called all–optical magnetic switching [12]. They demonstratedthe possibility to revert the direction of M without any applied external fieldin ferrimagnetic GdFeCo with particular stoichiometries. After each irradi-ation by a femtosecond laser pulse, the magnetization changes its directionwithin about 30 ps, as shown in Fig. 6.7. The phenomenon depends on theamount of absorbed energy but not on the light polarization. In 2012 Ostleret al. [106] demonstrated that the ultrafast heating is a sufficient stimulusfor magnetization reversal disregarding any previous hypotheses on inversemagneto–optical effects. This phenomenon should be driven by the differentpicosecond demagnetization dynamics of the two magnetic sub–system anda consequent transient modification of the exchange interaction. After heat-ing, the sample is in a strongly non-equilibrium state where the exchangerelaxation can stimulate the reversal of the total magnetization.
Even if related to an antiferromagnetic systems, also the laser induced
6.1 Introduction 97
Fig. 6.6: Transient magnetization of Fe and Gd sub–lattices in GdFeCo fer-rimagnetic compounds measured by time–resolved x–ray magnetic circulardichroism. The spin switching occurs in the sub–picosecond time windowwith different dynamics for the two materials. The ultrafast magnetizationreversal is assisted by an applied external field. Source [104].
spin reorientation in TmFeO3 [108] and the inertia driven process in HoFeO3
[109], demonstrated by Kimel and coworkers, needs to be accounted. In thefirst case the spin switching is achieved via the strong temperature-dependentanisotropy of the sample that after the heating ,undergoes a magnetic phasetransition. In the latter system instead, the authors demonstrated that themajor role is played by the inverse Faraday effect. It transfer sufficient mo-mentum to the spin system to overcome energy barriers even long after theaction of the stimulus. Even if the spin switching demonstrate to be onlytransitorial, the combined effect of heating and the photon magnetic field hasbeen used in other orthoferrite antiferromagnets, i.e. (SmPr)FeO3, to createa transient ferromagnetic state in which the direction of the magnetizationis established by the light ellipticity [110].
All the results discussed up to now regards magnetic system with onlyone easy axis, thus the magnetic switching can be achieved only by the inver-sion of the north and south poles. However an intriguing possibility, so farscouted only in (Ga,Mn)As magnetic semiconductors,[13] [111] , is offered bymaterials with biaxial magnetic anisotropy, resulting in the presence of twoequivalent preferential axes (i.e., four likely orientations of the magnetiza-tion). Recent experiments on (Ga,Mn)As have shown a large photoinduced
Fig. 6.7: All-optical switching in GdFeCo. The last column shows the finalstate of the domains after a few seconds. The circles delimit the areas actuallyaffected by pump pulses, black and white represents two different orientationsof the magnetization vector while σ+ and σ−− are the left and right circularpolarization. After the excitation the magnetization changes its sign, thepolarization dependence ought to dichroic absorption effects [107].
reduction of the coercive field that leads to magnetization reversal [112], seeFig. 6.8. The recovery time of the coercivity was found to be in the fewnanoseconds range, which sets the maximum writing speed for this material.A practical drawback of (Ga,Mn)As is its Curie temperature of 25 K, whichrequires cooling facilities during the experiment.
In this chapter, we will show that optical magnetic switching can beachieved also in a simple ferromagnet like iron. In our experiment M isrepeatedly commuted between well-defined directions on a time scale of 100ps. The method exploits the precessional motion launched by the excitationand the thermal dependence of the magnetic anisotropy. In particular thesystem is characterized by an in–plane biaxial anisotropy, like (Ga,Mn)As,with the interesting technological followup of allowing one to record two bitsof information on the same spot.
6.2 Experimental geometry
The studied samples are 8 nm thick iron films. The magnetic properties ofthis system have been extensively discussed in Chapter 4.2. Therefore thissection will be mainly dedicated to the experimental geometry to achieve themagnetic spin switching.
For the sake of clarity, we first describe in short the magnetic anisotropyof iron thin films. The magnetization M lies on the film plane because of thestrong shape anisotropy. The epitaxial nature of the layer leads to preferential
6.2 Experimental geometry 99
Fig. 6.8: Optically induce magnetic reorientation in (GaMn)As samples. Thehysteresis loops before and after the pump arrival are plotted together withthe corresponding magnetization orientations. The switching occurs betweentwo different easy axes. Source [13].
in-plane orientations along the [100] or [010] crystallographic directions (theeasy axes), as a direct consequence of the magnetocrystalline anisotropy. Byapplying a magnetic field H along the film surface but not aligned to an easyaxis, the magnetization vector will coherently rotate assuming the in-planeorientation that minimizes the free energy (eq. 4.10).
In our experiments the external field H points between easy axes, i.e.θ ∼ 44◦ in Fig. 6.9 (a). In such a case, as shown in Fig. 6.9 (b), a peculiarsituation is achieved with two almost-symmetric minima of the free energyclose to the [100] and to the [010] directions, even for relatively weak externalfields (a few hundreds of Oe).
The TR-MOKE experiments are performed at room temperature with ap-polarized probe in order to detect all the three components of the magneticvector (see Chapter 2.2). The setup is described in Chapter 3.2.
Sweeping H between -300 Oe and + 300 Oe, we obtain the transverseMtras and longitudinal Mlong hysteresis loops plotted in Fig. 6.10 panel (a)and (b). The solid curve represents the branch for an external field movingfrom positive to negative values while the dashed is the branch acquired inthe opposite sweeping direction. According to Fig. 6.9, H is perpendicular tothe light incidence plane, for positive values it points up while for negative,it points down. Mtras is the component of M aligned with the external fieldwhile Mlong is in-plane and normal to H. Sharp transitions occur in corre-spondence to the coercive fields of about 10 Oe in the transverse directionand 200 Oe in the longitudinal direction. They describe the magnetizationjumping from one easy axis to the other as depicted in the 2D plot of the
Fig. 6.9: (a) The epitaxial Fe(001) film has two in-plane easy axes along the[100] and [010] crystallographic directions. The external magnetic field isapplied in the transverse direction, along the film and normal to the lightincidence plane. The longitudinal direction is parallel to the film and theincidence planes, and the polar direction is normal to the film. θ and φ arethe angles formed by the field and the magnetization, respectively, with the[100] axis. (b) Free-energy contour plot (in false colors) as a function of φ(horizontal) and H (vertical) depicting the energy minima (red solid lines)that correspond to the equilibrium orientation of the magnetization. Thegraph refers to an angle θ = 44◦ between the applied field and the [100] axis.
magnetic trajectory in Fig. 6.10 panel (c). The small colored circles markMtran and Mlong for specific intensities of the external field H = +130 Oe(red circle) and H = −130 Oe (yellow circle) and the corresponding coloredarrows in panel (c) show the real positions of the magnetic vector.
In this work two different kind of acquisition methods have been em-ployed. In the following section we will show the effects of multiple pumppulses on the magnetization exploiting the experimental configuration of sec-tion 3.3.3 while after that we will present the picosecond switching dynamicsmeasured through the method described in section 3.3.4.
6.3 The effect of multiple pump pulses
In order to investigate the effect of multiple pump pulses on the magnetiza-tion, the repetition rate of the probe beam is reduced to 250 Hz (the laserrepetition rate is 1 kHz), and a proper temporal sequence of pump, probe,and an additional pulsed magnetic field, used to restore the non-irradiatedcondition after each probe, is employed (see chapter 3.3.3). In this experi-ment, the time delay between pump and probe is at least 1 ms, long enough
6.3 The effect of multiple pump pulses 101
Fig. 6.10: Transverse (top panel) and longitudinal (bottom left panel) hys-teresis loops. Mtras is the component of M aligned with the external fieldwhile Mlong is in-plane and normal to H, see . In the bottom right panel thetwo components are projected in a 2D plot showing the trajectory describedby the magnetization vector on the sample surface. The solid curve repre-sents the branch for an external field moving from positive to negative valueswhile the dashed is the branch acquired in the opposite sweeping direction.The small colored circles together with the corresponding arrows mark M forspecific intensities of the external field H = +130 Oe (red) and H = −130Oe (yellow).
to ensure the absence of transient effects. The ultrafast evolution of themagnetization will be analyzed in the next section.
Fig. 6.11 reports the Mtran and Mlong hysteresis cycles. Each point ofthe loop is measured after irradiating the sample with a given number oflaser pump pulses, ranging from zero [Fig. 6.11 (b)] to three [Fig. 6.11 (e)].The transverse hysteresis loop is reported only once since it does not varywith the number of pump pulses. The red arrows in Fig. 6.11 (f) - (i) showthe real-space orientation of the magnetic vector on the sample plane foran external field of about +130 Oe. In our geometry and for the adoptedfluence of 12 mJ/cm2, in fact the magnetic switching takes place in a narrowregion of values of H around 130 Oe. In the following discussion, we willfocus on the branch of the hysteresis loops obtained spanning the externalfield from positive to negative values (solid lines). The other branch (dashedlines) leads to identical results.
Starting from Fig. 6.11 (a) and Fig. 6.11 (f) we have:
• Zero-pulse case. It denotes the absence of optical excitations. For anexternal field of +130 Oe [Fig. 6.11 (f)], the magnetization vector pointsclose to the [100] easy axis.
• One-pulse case, Fig. 6.11 (c) and (g). After one optical excitation M
[Fig. 6.11 (g)] has switched from the [100] easy axis to the [010] one. Inparticular the transverse loop (not reported here) is unaffected, but thelongitudinal projection clearly reveals that, within a well-defined rangeof external field values around ±130 Oe, Mlong has reversed its sign[Fig. 6.11(c)]. For higher and lower intensities, no change is observedas compared to the zero-pump case.
• Two-pulses case, Fig. 6.11 (d) and (b). The longitudinal hysteresis loop[Fig. 6.11 (d)] has recovered the original shape of the non-irradiatedcase [Fig. 6.11 (b)]. In particular, for an applied field of +130 Oe, themagnetization vector has switched back to the initial orientation closeto the [100] axis [Fig. 6.11 (h)].
• Three-pulses case, Fig. 6.11 (e) and (i). The third laser shot reproducesthe features observed after the first pulse. In Fig. 6.11 (i)M (red arrow)is now close to the [010] direction.
Although not shown here, we have tested the perfect repeatibility of theseevents up to nine laser pump shots. These measurements demonstrate thatthe magnetization vector can be repeatedly and reproducibly switched be-tween two given orientations with short optical pulses. However, the com-mutation between easy axes takes place only for specific intensities of the
6.3 The effect of multiple pump pulses 103
Fig. 6.11: (a) Transverse and (b) - (e) longitudinal hysteresis loops showingthe modification induced on the magnetization by increasing the number oflaser pump pulses: zero pulses (a, b), one pulse (c), two pulses (d), andthree pulses (e). The external magnetic field is applied along the transversedirection (refer to Fig. 6.9 (a)) at an angle θ = 44◦ from the [100] crystallo-graphic axis. The red circles in (a) - (e) mark the magnetization componentsat the external field H = +130 Oe on the same branch of the loops: theyare used to visualize the real-space orientation of M on the sample plane atH = +130 Oe, as sketched in (f) - (i). These cartoons clearly demonstratehow the magnetic vector systematically and repeatedly commutes betweentwo easy axes after each optical excitation.
Fig. 6.12: Evolution of the magnetization as a function of the pump-probedelay for two intensities of the external field: (a) (c) +130 Oe and (d) (f)+230 Oe. The red dots are the experimental data, and the solid lines arethe simulation according to the Landau-Lifshitz equation. The polar (a),(d) and the longitudinal (b), (e) components are used to reconstruct themagnetization trajectory (c, f) projected on the plane normal to the externalfield [as schematically sketched on top of (a) and (d)].
external field, in particular, for H = ±130 Oe. Higher or lower magneticfields do not lead to any switching.
6.4 The switching dynamics
In order to clarify the physical mechanism and disclose the time scale ofthe process, we have analyzed the temporal evolution of the magnetizationtriggered by a single pump pulse for two fixed values of H = +130 and +230Oe, where only the lower field results in a switched magnetic vector. Fig. 6.12reports the polar (normal to the sample) and longitudinal components of themagnetization vector as a function of the pump-probe delay for the two aforementioned intensities of the external magnetic field.
We begin analyzing the results for H = +130 Oe [Fig. 6.12 (a) - (c)]. Atzero pump-probe delay, the polar component [Fig. 6.12 (a)] is absent (withinthe experimental errors), while the longitudinal projection [Fig. 6.12 (b)] haspositive value. Recalling Fig. 6.11 (b) and (f), this situation correspondsto the M vector being on the film plane and pointing close to the [100]crystallographic axis. As the time delay increases, the polar projection showsa damped oscillatory behavior, while the longitudinal projection changes signwithin 100 ps and oscillates around a new equilibrium position centered atnegative values. Although the dynamics is restricted to a time interval of
6.5 Discussion 105
500 ps, the oscillations will eventually stop, and the magnetization will settleclose to the [010] crystallographic direction, as observed in Fig. 6.11 (c), whichdepict the situation after a pump-probe delay of 1 ms. Fig. 6.12 (c) reportsthe projection of the magnetization trajectory on the plane perpendicular tothe external field. Here the route of M and the precessional nature of theprocess are particularly evident.
If we now consider the magnetization dynamics forH =+230 Oe [Fig. 6.12(d) (f)], the situation at zero delay is similar to the one previously described,with the magnetization lying on the film plane and pointing close to the [100]axis. After 100 ps, the longitudinal component [Fig. 6.12 (e)] has fully re-versed its sign, but at 250 ps delay it has recovered its original orientation.From this point on, no further switching is observed, and only the dampedoscillatory behavior is noticeable. The hysteresis loops in Fig. 6.11 confirmthat M at (H = 230 Oe) has the same position as the non irradiated case.As in the previous case, the magnetization trajectory has been projectedon the plane perpendicular to the external field [Fig. 6.12 (f)] revealing theprecessional behaviour of the dynamics.
6.5 Discussion
The effect of the pump irradiation is to locally heat the sample. The energyabsorbed by the electrons moves to the lattice and the spins establishing thelocal thermal equilibrium within a few picoseconds. As discussed in Chapter4, the temperature of the irradiated volume can easily reach 800-900 K inIron thin films with a consequent decrease of the saturation magnetization.In our case with a pump fluence of about 12 mJ/cm2, we can roughly estimatea maximum T of about 1000 K, thus very close to the iron Curie point (1043K), by simple thermal considerations [see section 4.4].
Moreover, the anisotropy constant K1 shows a very strong dependence onthe temperature [85]. For our discussion, the quantity 2K1/M0µ0, identifyingthe so–called anisotropy field Han, is of major interest (see Chapter 4.2). Infact the vectorial sum ofHan, the external field H and the demagnetizing oneHdem, gives the effective field Heff which locate the spatial position of themagnetization at the equilibrium [see Fig. 6.13 panel a]. In our specific caseof M lying on the film plane, Hdem acts only on the out-of-plane componentof the magnetization. According to ref. [85], Han is about 500 Oe at 300K and drops to zero close to the Curie point. Therefore the anisotropy fieldsuddenly vanishes after few picoseconds the pump arrival. Since the externalfield is unaffected by the laser pulse and no polar component exists in thefirst picoseconds, Heff decreases and rotates toward H [Fig. 6.13 panel b].
Fig. 6.13: Two–dimensional cartoon of the temporal evolutions of the mag-netic vector M (red arrow), the anisotropy field Han (in violet) and the ef-fective field Heff (in orange). In particular panel a) depicts the equilibriumcondition before the pump arrival (negative delays): Heff is given by the vec-torial sum of Han and Hext (blue arrow) which represents the external field.Panel b) depict the situation after the sample heating: at about 1000 K theanisotropy field vanishes and the magnetization vector is no longer alignedto the effective field (equal to Hext) and it experiences a torque that launchesthe precessional motion, as displayed in panel c). When the anisotropy fieldsrecovers and overcomes the external one, it traps M close to the nearesteasy axis. If Hext = +130 Oe, M will eventually settle in a new equilibriumcondition resulting in a magnetic switching, panel d). The oscillations arehampered by the dissipative damping that eventually stops the motion afterhundreds of picoseconds.
6.5 Discussion 107
The magnetization vector is no longer aligned to the effective field and itexperiences a torque that launches the precessional motion around the time-dependent Heff , as shown in Fig. 6.13 panel c [see section 6.1.1]. This motionis described by the well-known Landau-Lifshitz (LL) equation:
∂M
∂t= −γgM×Heff − γ
α
MsM× (M×Heff ) (6.9)
where γ is the gyromagnetic ratio and α is a damping coefficient. Eq. 6.9has been numerically solved taking into account the time evolution of Heff ,Hdem and M. The simulations of the magnetization trajectories for the twovalues of the external field (+130 and +230 Oe) are reported in Fig. 6.12 assolid lines, showing a satisfactory agreement with the experimental data. Itshould be mentioned a slight field-dependent damping coefficient has beenassumed: in particular, we used α = 0.02 for H = 130 Oe and α = 0.013 forH = 230 Oe.
Fig. 6.14 displays the estimated time evolutions of the magnetization M
[panel a], the local temperature T [panel b] and the anisotropy field Han
[panel c]. Since the temperature dependence M(T ) of iron is known [Ref.[68]and Fig. 4.17] a temporal profile of T (t) can be numerically extracted fromour magnetization data [113]. Fig. 6.14 panel (a), red dots, reports the time-dependent modulus of the normalized Mnorm(T ) experimentally measured atremanence where no precession is present. Thus, using the estimated T (t)[Fig. 6.14 b], the dynamics of the anisotropy fieldHan(t) is obtained [Fig. 6.14c]. The black line represents the optimized values used in the LL simulation.
According to our analysis, T (t) reaches a maximum temperature in theirradiated spot of about 1000 K and then recovers towards its initial condi-tion with a characteristic rate of about 100 ps, essentially determined by theheat transport properties of the material (and the substrate). Consequently,Han(t) drops to zero and remains much weaker than the external fields con-sidered in the previous analysis (130 and 230 Oe) within the first 100 ps. Forthese reasons, in this time window, Heff is mainly determined by H (plusthe demagnetizing field acting on the out-of-plane component of M). Sinceit points in the transverse direction [Fig. 6.13 b], i.e., at the highest angulardistance from M, the amplitude of the gyroscopic motion is large enough todetermine the longitudinal switching observed in Fig. 6.12 (b) and (e), asdepicted in Fig. 6.13 (c).
At longer delays (> 150 ps), the anisotropy field, which has its maxi-mum intensity along the easy axes, recovers and overcomes the values of theexternal field. Therefore, the effective field is mainly determined by Han,and the precessional motion occurs around an easy axis. Keeping in mindthat the frequency of the precession increases with the field intensity, eq 6.4,
Fig. 6.14: Temporal evolution of (a) the normalized modulus of the magneti-zation, (b) the local temperature in the irradiated spot, and (c) the intensityof the magnetocrystalline anisotropy field. Solid lines are the simulation usedto numerically solve the Landau-Lifshitz equation. The normalized magne-tization in (a) is compared with the experimental data (red dots) measuredat remanence (i.e., with no external field), where no precessional motion ispresent.
6.6 Conclusions 109
within the first 100 ps past the optical excitation and for H = 230 Oe, themagnetization vector performs an almost complete orbit aroundH before theintensity of the anisotropy field is large enough to trapM around an easy axis[see Fig. 6.12 (f)]. For H = 130 Oe, on the other hand, the precession fre-quency is slower, and when the longitudinal projection of the magnetic vectorhas switched to negative values, the anisotropy field has already overcomeH. In this case, the magnetization is trapped by Han in the proximity of the[010] easy axis [see Fig. 6.12 (c)] and will eventually settle there, resulting ina switched magnetic orientation [Fig. 6.13 d].
6.6 Conclusions
To summarize, we have demonstrated that the magnetization in a thin epi-taxial ferromagnetic layer with biaxial anisotropy can be controlled usingshort optical pulses. In particular, it is possible to reproducibly and repeat-edly commute the magnetic vector between preferential directions with aproper orientation and intensity of the external field. The switching mecha-nism is thermally driven and relies on the magnitude of the external magneticfield relative to the time-dependent magnetic anisotropy field. The switchingtime is essentially determined by the applied field and resides in the 100-pstime window for our specific design. We believe these results can triggerthe research of new materials with optimized parameters in view of a fasterswitching process, but they can also open interesting prospects on the con-tinuously developing field of ultrafast magnetic recording devices.
Time-resolved magneto-optical Kerr effect is a powerful tool for studying thelaser induced spin dynamics in ferromagnetic materials. However its inter-pretation on the femtosecond time scales has been contraversially debated.Optical contribution can altered the measured transient magnetic evolutionleading to wrong interpretation of the observed phenomena. Nowadays, itis well-established that TR-MOKE is a reliable technique to investigate thegenuine spin dynamics under particular condition, i.e. weak laser intensityand pump-probe delays longer than electronic thermalization time (few fem-toseconds), however a deep study in a non-perturbative regime has not beenyet carried out. In this chapter we will demonstrate that laser induced chargedynamics can affect TR-MOKE measurements up to 50 ps after the pumpirradiation masking the pure magnetic evolution. We measured and com-pared Kerr rotation and ellipticity in half–metallic CrO2 and Fe epitaxialsamples. The two quantities have the same dynamics in the metallic systemwhile differ in the oxide film for tens of picoseconds. We demonstrate thatneither Kerr rotation nor ellipticity display the real magnetic dynamics. Inparticular we propose a method to extract the pure spin signal that requiresthe acquisition of both the two aforementioned quantities.
The work presented in this chapter arises from a collaboration with ofexperimental groups of Prof. Dr. M. Munzenberg at the I. PhysikalischesInstitut of Georg–August–Universitat Gottingen (Germany) and Prof Dr.A. Gupta from the department of chemistry of the University of Alabama(USA).
It is a well known fact that time-resolve magneto-optical Kerr measurementscontain a charge contribution not directly related to the magnetization ofthe studied system. However it is still under debate to which extent thiscontribution enters in the total signal and what could be its behaviour uponfemtosecond laser irradiation. Such dynamics might, in principle, falsify thepure magnetic evolution leading to a wrong interpretation of the experimentaldata.
Ever since the first pioneering work of Beaurepaire et al. [1], the atten-tion has been especially focused on the first femtoseconds of the magneticdynamics. In this regime non linear effects dominates. Because of photon ab-sorption, the electronic population changes its occupation close to the fermilevel and consequently its optical properties. The transient saturation ofelectron transitions, bleaching and state-blocking effects, may result in time-dependent changing of the magneto optical response not related to the spinorder [114]. In 2000 Koopmans and coworkers [15] measured simultaneouslyKerr ellipticity and Kerr rotation on epitaxial Ni thin films. They reporteda different time dependent behavior of the two quantities, although bothare proportional to the magnetization vector. In particular, experimentalfacts, Fig. 7.1, show differences only before a pump and probe delay of about0.5− 1 ps. This has been considered the evidence that the quenching of themagneto-optical contrast cannot be related to an ultrafast demagnetizationat least in first few hundreds of femtoseconds. However, the problem was alsoquestioned in many other experimental works showing no differences between
7.1 Introduction 113
Fig. 7.1: Comparison of the induced Kerr ellipticity (open circles) and Kerrrotation (filled diamonds) as a function of pump-probe delay measured byKoopmans and coworkers in 2000. The sample is a (111) oriented 3 nmthick nickel film and the pulse energy 0.6 nJ. The thick line represents thepump-probe cross correlation trace. Source [15].
Kerr rotation and ellipticity for particular samples, like ferromagnetic CoPt3and Co grown on Si substrates, and for certain laser fluences and thicknessesof the magnetic film [16] [115],[116] and [117]. Experimental methods havebeen proposed to distinguish the true spin dynamics however none gave anultimate answer to the debate. It is important to stress that optical artifactsinfluences all the time-resolved optical-magnetic probe techniques like x-raymagnetic circular dichroism [118], terahertz emission [45] [60] and surfacesecond harmonic generation [119].
Recently in 2012, a paper appearing in Physical Review X from ChanLa-O-Vorakiat and coworkers [120], addressed the problem exploiting a novel ex-perimental method. They excite ferromagnetic nickel films by near-infraredoptical pulses and probe the spins dynamics via resonant transitions (M2,3
edges) using extreme ultraviolet light. In particular at an energy of 66 eV,nickel 3p core electrons are excited into empty 3d valence levels responsible ofthe atomic magnetic moment. The main idea is that the optical contributionshould be hindered thanks to the resonance. They measured a dynamicsanalogous to the one found with conventional infrared and visible MOKEsuggesting that TR-MOKE is a reliable probe of the ultrafast magnetic be-haviour. However, it should be mentioned that still here it is not possible tocompletely neglect optical contributions although in principle very small.
Also many theoretical works addressed the problem [114], [121] and [4].
114 Charge and spin dynamics in TR-MOKE
Paradigm of the time-resolved magneto-optical Kerr effect for femtosecondmagnetism of Zhang coworkers [4] seemed to set a milestone in the de-bate. According to their model, the correspondence between magnetic andmagneto-optical response sensitively depends on the wavelength and thepulse length. In particular, if the laser pulse is longer than the charge dephas-ing time (10 fs) the observed Kerr signal will strictly follow the magnetizationevolution. However, also in this work very strong constrains have been im-posed in the theoretical evaluation that cannot definitely account for all theaforementioned experimental results. In conclusion, up to very recently, thequestion whether the TR-MOKE in the sub–picosecond regime is representa-tive of a pure magnetic effect or embodies any pump induced optical variationof the optical contrast is still debated.
On the other hand, concerning the slow magnetic dynamics (after thelocal thermalization within few picoseconds) no experimental evidences ofoptical contributions have been observed up to now. This fact has beenconsidered a proof of the reliability of the TR-MOKE technique in the pi-cosecond regime. Usually for metals, the local heating of the sample inducesa weak variation of the refractive index that is so small that can be safelyneglected.
However, the investigations were restricted to thin layers in the perturba-tive regime, i.e. weak pump intensity.Nevertheless interesting spin dynamicsoften raises with intense light pulses capable of large variation of the MOKEsignal well beyond a mere perturbation. In this chapter we show that ro-tation and ellipticity might considerably differ also for a pump-probe delaylonger than 50 ps. A detailed analysis of the TR-MOKE signals on two rep-resentative cases of ferromagnetic samples reveals that optical contributionare responsible for this discrepancy. In this case neither Kerr rotation norellipticity display the real magnetic dynamics. In particular, we propose amethod to extract the pure spin signal from both the two aforementionedquantities.
Starting from section 7.2, we give a brief description of the CrO2 and Festudied samples. Section 7.3 is dedicated to the experimental technique. Wedevelop an experimental procedure capable to retrieve the Kerr rotation andellipticity for two different light polarization (namely s and p, according toour framework) and to extract the transient dynamics of the complex indexof refraction and the off-diagonal component of the dielectric tensor. Insection 7.4 we reported the experimental results enlightening the differencesbetween CrO2 and Fe. The data are hence discussed in the following section,7.5. Here, a method is proposed to explain the discrepancy between Kerrrotation and ellipticity and to disentangle the optical contribution from thereal spin dynamics.
7.2 Samples: Fe and CrO2 thin films 115
7.2 Samples: Fe and CrO2 thin films
In this work we studied the laser induced magnetic dynamics in Fe (001) andCrO2 (100) epitaxial films.
The iron sample has been fabricated at the VESI laboratory of Politec-nico di Milano. The film, with a thickness of about 100 nm, has been grownon a single crystalline MgO (001) substrate by molecular beam epitaxy. Themagnetic properties are the same described for the thinner film (8 nm) inChapter 4.2. The magnetization M lies on the sample plane because of theshape anisotropy while the magnetocrystalline anisotropy, that is a directconseguence of the epitaxial nature of the metallic layer, leads to a pref-erential in-plane orientations of M along the [100] or [010] crystallographicdirections.
The CrO2 (100) film has been grown by chemical vapor deposition at theDepartment of Chemistry of the University of Alabama by the group of Prof.Dr. Gupta [122]. The sample thickness is about 300 nm while the substrateis a TiO2 (100) single crystal. CrO2 (100) has a tetragonal crystallographicstructure with the c-axis lying on the sample plane. It is ferromagnetic andcharacterized by a uniaxial magnetic anisotropy that forces the magnetiza-tion vector on the c–axis oriented along [001] [123] [124]. CrO2 is attractingincreasing attention in these years because of its electronic and magneticproperties unusual among common 3d transition metal oxides. In additionto the magnetic order, CrO2 shows a spin polarization around 95 − 98% atthe Fermi level [125] [126] [127] [128] [129]. This kind of materials are knownas half–metals [130] [131] [132], where only majority spin electrons form theFermi surface, while minority exhibit a gap. This results in unique transportproperties that make all half–metallic systems interesting for spintronics ap-plications [133]. In particular CrO2 has been extensively studied since itdisplays almost fully polarized conduction electrons and is widely used inmagnetic recording media. For all these reasons, the ultrafast spin dynamicshas been also investigated from the femtosecond and sub–nanosecond timescale mainly through TR-MOKE [134] [135] [91] [6] [51]. Special effort to thecomprehension of the slow demagnetization dynamics showed by half–metalsin general, comes from the work of Muller and coworkers [6]. As alreadydiscussed in section 4.1.2, the authors demonstrate that spin-flip events inthe femtosecond regime are strongly hindered due to the weak band mixingfor spin-up and spin-down states. Further insights into the aforementionedmodel have been recently developed by Mann et al. [51].
To conclude, the film thicknesses have been chosen larger than the opti-cal penetration depth λ in order to avoid optical artifacts due to the lightreflection at the film-substrate interface. At the probe wavelength (800 nm)
116 Charge and spin dynamics in TR-MOKE
λ is about 17 nm for Iron and 60 nm for chromium dioxide.
7.3 Experimental methods
7.3.1 Experimental setup
The optical analysis has been performed in our laboratory at the Physicsdepartment of Politecnico di Milano with the experimental setup describedin chapter 2. The pump beam has been focused to a spot size of about 200 µmwith an average fluence of a few mJ/cm2. The MOKE measurements havebeen performed with the external field Hext parallel to the light scatteringplane and to the easy axis (longitudinal MOKE), Fig. 7.2. The probe beamreflected by the sample enters a photodiode after passing through a Glan-Thompson polarizer, called analyzer in Fig. 7.2. Its optical orientations isgiven by the angle θa with respect to the scattering plane. The polarizationof the probing light has been chosen in a non-conventional manner in order toretrieve the Kerr rotation θ and ellipticity ε in two different ways, as discussedin the following section. We exploited the acquisition method described insection 3.3.2. The method allows to collect the dynamics of the only magneticpart of the MOKE signal while the transient reflectivity has been measuredseparately. We have restricted our investigation to a time-window of 50 ps,neglecting the temporal structure around the zero pump-probe delay whichgoes beyond the scope of our investigation.
Fig. 7.2: Experimental geometry. The probing beam impinges on the samplewith an angle θi with respect to the normal to the sample and passes througha Glan-Thompson polarizer rotated of θa from the incidence plane. Theexternal magnetic field Hext is applied along the scattering plane. The M
vector represents the sample magnetization.
7.3 Experimental methods 117
7.3.2 Kerr rotation and ellipticity
The spin dynamics measured for Fe and CrO2 films have been characterizeddetecting both the Kerr rotation and ellipticity. In particular we acquiredthe transient θ and ε for p and s polarizations of the incident beam, namelyθp,s and εp,s. These quantities can be evaluated for the considered experi-mental geometry using the formalism developed in chapter 2. Since only thelongitudinal component of the magnetization is present, i.e. ml = M/Ms,mt = 0 and mp = 0, by eq. 2.4 he Fresnel scattering matrix becomes:
S =
(rpp rlps/ml
−rlps/ml rss
)
(7.1)
We recall that rpp and rps are complex numbers. Both depend on the refrac-tive index of the material n = n+ ik while only the out-of-diagonal term rpsembodies the magneto–optical constant Q. The Kerr angle is defined as:
θp = <(
rlpsrpp
)
(7.2)
for a p-polarized incidence light. While for an s-polarized:
θs = <(
rlpsrss
)
(7.3)
The tangent of the ellipticity angle is instead given by the imaginary part ofthe same quantities:
tan(εp) = =(
rlpsrpp
)
(7.4)
tan(εs) = =(
rlpsrss
)
(7.5)
Since the ellipticity is of the order of few milliradiants, tan(εp,s) ∼= εp,s.According to Fig. 7.2, we extract θp,s and εp,s exploiting a particular com-
binations of incident beam polarizations and orientations of the analyzer θa.In particular we choose a linearly polarized light at 45◦ with respect to thescattering plane and a circular polarization. Six different measurements havebeen performed. We acquired the transient magnetization in the followingexperimental conditions (all the angles are given with respect to the scatter-ing plane):
We will first formally treat the case of 45◦ linearly polarization. In theJones matrix formalism (chapter 2), the probing electromagnetic field is de-scribed by:
1√2
(11
)
(7.6)
Multiplying the vector 7.6 for the Fresnel matrix given by eq. 7.1, we obtainthe following expression for the reflected beam:
(mlr
lps+m2
lrpp√
2−mlr
lps+m2
lrss√
2
)
(7.7)
At this point the light crosses a polarizer with an orientation θa with respectto the scattering plane. The corrisponding matrix is:
(cos2(θa) cos(θa) sin(θa)
sin(θa) cos(θa) sin2(θa)
)
(7.8)
Choosing θa equal to 0◦ and 90◦ we can respectively separate the term pro-portional to Ep from the one proportional to Es in eq. 7.7. The totalintensity measured by the photodiode is the squared modulus of the elec-tric field. Neglecting the terms proportional to Q2 and considering thatm2
l = |M/Ms|2 = 1, the intensity for θa = 0 can be computed as:
I = 1/2|rpp|2︸ ︷︷ ︸
transient reflectivity
+ ml<(r∗ppr
lps
)
︸ ︷︷ ︸
transient magnetization
(7.9)
The magnetic and the reflectivity parts have been acquired separately. Divid-ing the transient magnetization by the total measured reflectivity |rpp|2 = Rp
we can finally extract the Kerr rotation θp:
<(r∗ppr
lps
)
|rpp|2= <
(
rpprlps
|rpp|2
)
= <(
r∗pprlps
rppr∗pp
)
= <(
rlpsrpp
)
= θp (7.10)
7.3 Experimental methods 119
In order to retrieve θs, it is necessary to repeat the same procedure rotatingthe angle θa by 90◦. In this way the we obtain a total intensity equal to:
I =1
2|rss|2 +ml<
(r∗ssr
lps
)(7.11)
from which we can extract<(r∗ssrlps)
|rss|2 = θs (|rss|2 = Rs).To measure the ellipticity it is necessary to shine the studied sample with
a circular polarized light. In this case the vectorial expression of the incidencelight contains the imaginary unit i:
1√2
(1i
)
(7.12)
Eq. 7.12 after the reflection by the sample, becomes:
(imlr
lps+m2
lrpp√
2−imlr
lpsim
2
lrss√
2
)
(7.13)
This expression closely reminds eq. 7.7 for the only exception that the termsproportional to the magnetization embody the imaginary unit. Thereforefixing the angle θ = 0◦ and evaluating the squared modulus of the firstelement of eq. 7.13, we obtain a total intensity proportional to the imaginarypart of
(r∗ppr
lps
):
I = 1/2|rpp|2︸ ︷︷ ︸
transient reflectivity
− ml=(r∗ppr
lps
)
︸ ︷︷ ︸
transient magnetization
(7.14)
If we now divide the magnetic part of eq. 7.14 by the total reflectivity Rp,we get εp :
=(r∗ppr
lps
)
|rpp|2= =
(
rpprlps
|rpp|2
)
= =(
r∗pprlps
rppr∗pp
)
= =(
rlpsrpp
)
= εp (7.15)
Following the same procedure for θa = 90◦ allows one to extract the leastquantity εs.
7.3.3 Refractive index and off-diagonal term of the di-
electric tensor
The four measured rotations and ellipticities allows to retrieve the dynamicsof the refractive index n and the off diagonal element of the dielectric tensor
120 Charge and spin dynamics in TR-MOKE
˜εxy. In fact both θ and ε are function of rpp,ss(n) and rlps(n, Q) that can beexplicit written as analytical functions of the complex quantities n = n+ ikand Q = Q0e
iq, see eq. 2.9 and 2.11. In particular the magneto–opticalconstant Q is related to the element ˜εxy = ε′xy+iε′′xy by the following relation:
Q =˜εxy˜εxx
(7.16)
where ˜εxx is the diagonal component of the dielectric tensor. It is a complexnumber that can be expressed as a function of the real and imaginary partof the index of refraction:
˜εxx = ε′xx + iε′′xx = (n2 − k2) + i(2nk) (7.17)
Therefore knowing Q and n, it is possible to invert eq. 7.16 and evaluate˜εxy.The four measured quantities θs θp εs and εp are thus function of the fourindependent variables n k ε′xy and ε′′xy. Employing a numerical procedurewe can unambigusly evaluate their laser induced dynamics. For the sake ofcompleteness the explicit dependence of the kerr rotation is reported by thefollowing expressions:
θp,s = <(
rlps(n, Q)
rpp,ss(n)
)
= <(rll(n) ˜εxyrpp,ss(n)
)
(7.18)
where:
rl =rps˜εxy
=rpsQ ˜εxx
=βiγ
β ′ (nβ + β ′) (β + nβ ′) ˜εxx(7.19)
β = cos θi, γ = sin θi and√
1− (γ2/n2) depend only on experimental pa-rameters, i.e. the probe incidence angle θi see Fig. 7.2. The ellipticity can
be evaluated in the same way given that ε = =(
rlpsrpp,ss
)
= =(
rll(n) ˜εxy
rpp,ss(n)
)
.
7.4 Experimental results
In this section we will present the TR-MOKE experimental dat acquired forthe two studied samples.
Fig. 7.3 reports the optical measurements for CrO2 (in the left column)and Fe (right column). The first row, called (a), shows the temporal evo-lution of Kerr rotations, θs and θp, and ellipticities, εs and εp as a functionof the pump-probe delay. Row (b) report the same data of row (a), butnormalized to the values at negative delay. The normalization clearly high-lights how the dynamics of rotations and ellipticties in CrO2 differ from each
7.4 Experimental results 121
0,4
0,6
0,8
1,0
1,2
0,85
0,90
0,95
1,00
0 10 20 30 40 50
1,00
1,01
1,02
0,85
0,90
0,95
1,00
0,00,20,40,60,81,0
0 10 20 30 40 50
1,00
1,04
1,08
1,12
0,0
0,3
0,6
0,9
1,2
0,2
0,4
0,6
0,8
1,0
d
c
b
s p
s pa
delay (ps)
s-pol p-pol
Fe
s-pol p-pol
s p
s p
CrO2
s p
s p
, (m
rad)
R/R
0
s-pol p-pol
,
s p
s p
||/|
|
spin{
s-pol p-pol}charge
Fig. 7.3: Left–hand–side shows the experimental results for CrO2, right-hand-side for Fe. Panels (a): time–resolved Kerr rotations (θs and θp) andellipticities (εs and εp). Panels (b): same data shown in panels (a), butnormalized to the values at negative delays. Panels (c): time-resolved nor-
(d): normalized transient reflectivities for Rp and Rs.
122 Charge and spin dynamics in TR-MOKE
other (Fig. 7.3 (b), left panel). On the other hand, in Fe all four curves areessentially identical (Fig. 7.3 (b), right panel). This is the very first strikingresult emerging from our investigation. For the CrO2 sample the magneticdynamics cannot unambiguously extracted by only measuring either θ or εwithin 50 ps. Panels (c) show the normalized modulus of the Kerr angles
|Θs| = (θ2s + ε2s)1/2 and |Θp| =
(θ2p + ε2p
)1/2. It is interesting to notice how
|Θs| and |Θp| closely match in CrO2, despite the different dynamics of rota-tion and ellipticity shown in Fig. Fig. 7.3 b (left).
In the bottom part of Fig. 7.3 the normalized transient reectivities, Rs
and Rp, are reported in row (d). Even if we used similar absorbed pumpenergies (830 J/cm3 in CrO2 and 1050 J/cm3 in Fe), the relative variation ofthe reflectivity in CrO2 is an order of magnitude larger than in Fe.
7.5 Discussion
We will start discussing the results about the normalized moduli of the Kerrangles reportd in c. In particular we will clarify why |Θs| and |Θp| displaysthe same dynamics. According to the definition of rotation and ellipticitygiven in section 7.3.2, the modulus of the Kerr angle, as measured in ourexperimental geometries, can be expressed as:
|Θs| =(θ2s + ε2s
)1/2=
<(
rlpsrss
)2
+ =(
rlpsrss
)2
1/2
= |rpsrss
| (7.20)
and
|Θp| =(θ2p + ε2p
)1/2=
<(
rlpsrpp
)2
+ =(
rlpsrpp
)2
1/2
= |rpsrpp
| (7.21)
Since |rss|2 = Rs and |rpp|2 = Rp, it is straightforward to show that |Θp|2/|Θs|2 =√Rs/Rp. The same relation holds for the normalized quantities as well.
From the reflectivity data reported in Fig. 7.3 panels (d), it can be easilydeduced that the ratio
√Rs/Rp never exceeds 1.005 in Fe or 1.03 in CrO2.
Therefore, the normalized moduli of the Kerr angles |Θ|/|Θ0| differ not morethan 0.5% in Fe or 3% in CrO2.
We can now move to the discussion of the magneto-optical data shownin panels (b) and (c) of Fig. 7.3. The transient ellipticity ε and rotation θ(in the following, we drop the p and s subscripts for clarity) show differentevolutions in CrO2 while closely match in Fe. Understanding which is the
7.5 Discussion 123
real spin dynamics ∆|M |/|M0| for the Chromium dioxide system is thus offundamental importance. Here, we show a method to retrieve ∆|M |/|M0|without any additional optical contribution. First of all we have to remindthat θ and ε are the real and the imaginary parts, respectively, of the samecomplex quantity, i.e. the Kerr angle (eqs. 7.20 and 7.21). According toeq. 7.20 and 7.21, Θ can be written as the product f(n)εxy, where all theexplicit dependence on the refractive index n is attributed to the complexfunction f = rps/εxy
rss,pp= rl
rss,ppand εxy is the off-diagonal term of the dielectric
tensor. As discussed in section 7.3.3, rl and rpp,ss depend only on n while εxyis responsible for the magnetic Kerr response. In particular, |Θ| = |f(n)εxy.Moreover, following the argumentation in Ref. [16], one can use the ex-pression εxy = αM by assuming linear magneto-optical response. M is themagnetization (a real number), while α is a complex quantity deriving fromthe off-diagonal element of the conductivity tensor, thus containing all infor-mation about the matrix elements of the spin-orbit coupling. To resume |Θ|can be expressed as |α||f(n)|M and by differentiation, we obtain:
∆|Θ|/|Θ| = ∆|α|/|α|∆|f(n)|/|f(n)|∆M/M. (7.22)
The temporal variation of ∆|Θ|/|Θ| upon laser irradiation, Fig. 7.3, thus de-pend on |α|, |f(n)| and M . |α| is essentially determined by charge dynamicsas well as |f(n)|. In fact the charge distribution determines also the refractiveindex n. Therefore if any dynamics is to be expected for these two terms afterthe pump pulse, it should be closely related to the dynamics of the transientreflectivity R since it is only determined by n. In other words, the relativevariation ∆α/α and |f(n)| should qualitatively mimic the relative change ofreflectivity ∆R = R. In conclusion we note that eq. 7.22 clearly exhibit thepresence of a charge, (|α| and |f(n)|), and the spin (M) contributions to themagneto-optical signal.
With this in mind, we can now start looking at the magnetic experimentalresults of Fig. 7.3 row (c) by taking into account the reflectivity dynamicsof Fig. 7.3 (d). In the case of Fe, the relative variation of the transient re-flectivity R/R0 (Fig. 7.3 d, right) is roughly an order of magnitude smallerthan the optically-induced variation of the Kerr signal ∆|Θ|/|Θ| (Fig. 7.3 b,right). This implies that charge dynamics alters only marginally the coeffi-cients |α| and |f(n)|. Thus, in Fe the Kerr angle signal is dominated by thespin dynamics (M).
The situation is more complex for CrO2. The variation of the transientreflectivity can be as large as 12% (see Fig. 7.3 d, left). Thus, charge dy-namics should give a non negligible contribution to ∆|Θ|/|Θ|. However, thetemporal behavior of the reflectivities Rs/R0 and Rp/R0 displays a prompt
124 Charge and spin dynamics in TR-MOKE
-0.060.000.06
1
2
3
0 10 20 30 40 50
0.2
0.4
0.6
0.8
1.0
1.2
| xy|
'xy ''xy
nxy
k
n
b
| p| (data)
|
p|, |f(
n)|,
| xy|
(nor
m.)
delay (ps)
| xy||f(n)| |f(n)|x| xy|
a
Fig. 7.4: Time evolution of the complex refractive index n = n + ik andthe off–diagonal element of the dielectric tensor ˜εxy = ε′xy + iε′′xy of CrO2 asextrapolated from the experimental data shown in Fig. 7.3 a. (b) Dynamicsof the normalized | ˜εxy| and |f(n)| and comparison between the extrapolatedand the measured |Θp|.
change at zero pump-probe delay and a rather flat and featureless dynamicsafterwards. On the other hand, all MOKE signals (Fig. 7.3 b and c, left)display an exponential-like decay for positive pump-probe delay. This be-comes especially evident in Fig. 7.3 c (left) for the normalized modulus ofthe Kerr angle. The prompt variation at zero pump-probe delay resemblethe behavior of the transient reflectivity and is therefore attributed to chargedynamics. The subsequent evolution of the signal clearly deviates from theone observed in the reflectivity and is ascribed to the spin dynamics.
In order to provide a more quantitative proof, we have used the fourmeasured rotations and ellipticities curves of CrO2 shown in Fig. 7.3 (a)(left) to retrieve the dynamics of the refractive index n = n+ ik and the off-diagonal element of the dielectric tensor ˜εxy = ε′xy + iε′′xy. In particular theraw data at positive delays have been fitted with simple exponential decays
7.6 Conclusions 125
in order to reduce the uncertainties introduced by the experimental noiseand, after that, these curves have been treated with the procedure explainedin section 7.3.3 to extract the four quantities n, k, ε′xy and ε′′xy.
The results are reported in panel (a) of Fig. 7.4. Starting from n and k,we notice a steep change close to the zero pump-probe delay and a subsequentrather constant temporal evolution. This is a behavior compatible with thedynamics of the reflectivity signal (Fig. 7.3 d). Moreover, the prompt de-crease of k, the absorptive part of the refractive index, suggests that CrO2
tends to become more transparent upon laser irradiation at 800 nm wave-length.
The dynamics of ε′xy and ε′′xy also display a strong and prompt variationwith the pump arrival According to eq. 7.18, we observe that the kerr rotationθ and the ellipticity ε are proportional to <( ˜εxy) = ε′xy and =( ˜εxy) = ε′′xy,respectively. The very different dynamics of the real and imaginary partscan thus explain the observed discrepancy between θ and ε.
On the other hand the modulus |εxy| only shows marginal change closeto zero delay. | ˜εxy| has been plotted, after normalization, in Fig. 7.4 panel(b) together with |f(n)|/|f(n)0| and the computed |Θ|/|Θ0|. The temporalvariation of |f(n)| can be evaluated by the transient evolution of the refractiveindex while |Θ| = |f(n)||εxy|.
Making a comparison between |f(n)| and |εxy| we notice that the formerdisplays a sudden change at zero pump-probe delay and then settles arounda constant value (mimicking the reflectivity) while the latter follows a slowexponential decay after only a small variation close to zero. This indicatesthat the charge dynamics mainly affects the |f(n)| term, while |εxy| is dom-inated by spin dynamics. Therefore, reminding that | ˜εxy| = |α|M , we canargue that |α| is weakly affected by the optical excitation. To conclude wenotice that extrapolated function |Θ|/|Θ0| nicely matches the experimentaldata, providing the proof that the prompt variation of the Kerr angle at zeropump-probe delay is determined by charge dynamics (i.e. |f(n)|), while thesubsequent evolution genuinely represents the magnetization M .
7.6 Conclusions
In conclusion, we have performed a scrupulous magneto-optical investigationon two ferromagnetic benchmark systems (Fe and CrO2) in order to clarify towhat extent the TR-MOKE technique can reliably reveal the laser-inducedspin dynamics. We demonstrated that the measured Kerr rotations and el-lipticity can differ up to a pump-probe delay of 50 ps. This result may beof general validity every time the pump induced variation of reflectivity sig-
126 Charge and spin dynamics in TR-MOKE
nal is of the same order of magnitude as the induced demagnetization. Asa conseguence Kerr rotation and ellipticity do not unambiguously show thetrue spin dynamics. Restricting the investigation only to these quantities canlead to controversial interpretation of the experimental data, as in the case ofCrO2. However, the reliability of the technique is not harmed. We show thatthis uncertainty is due to optical contributions to the MOKE signal that canbe disentangled from the real magnetic dynamics with our proposed method.In particular, our analysis first shows that a quick comparison between thetemporal behavior of the Kerr angle and transient reflectivity is a simple testto judge whether charge dynamics might alter the magneto-optical responseof the system or the latter is dominated by the spin evolution, as in the caseof Fe. However, this is not a sufficient condition to assert reliability and adeeper investigation is necessary. In CrO2 we have demonstrated that thereal and imaginary parts of the physical quantity carrying the magnetic in-formation, i.e. the off-diagonal term ε′′xy of the dielectric tensor, can severelyand promptly differ after an optical excitation, though its modulus does notdisplay such features. This is the main cause of the observed discrepancybetween Kerr rotation and ellipticity. A possible way to overcome this diffi-culty is to consider the modulus of the Kerr signal (which still requires themeasurements of both rotation and ellipticity) since it is unaffected by phasevariation of the complex quantities, allowing a clearer evidence of possibleoptical artifact.
Conclusions and outlooks
The laser induced dynamics in ferromagnetic systems has been the mainsubject of this work. The light absorption in the near–infrared spectrumgenerates a cascade of phenomena taking place on very different timescalesfrom few femtoseconds to hundreds of picoseconds. This temporal windowhas been widely investigate using time–resolved magneto–optical Kerr effectin order to clarify not only some important aspects of foundamental physics,but also to develop a new experimental technique capable of controlling themagnetic order by means of laser pulses.
Concerning spin response in the femtosecond regime, we focussed ourattention on both spin scattering events and transport phenomena. Themain experimental findings are the following:
• The ultrafast demagnetization in thin iron films can be explained by thefemtosecond generation of magnons occurring shortly after the thermal-ization of the optically excited electronic population. Demagnetizationrates are about 50–75 fs. The experiment has been performed at dif-ferent pump intensities and ambient temperatures and the results havebeen analyzed with respect to the absorbed energies. From this point ofview, interesting results have been argued. The quenching of the spinorder increases linearly and no dependency on the temperature hasbeen observed in a range between 80 K and 500 K. In particular thisfact has been recognize as the demonstration that scattering mechanismlike Elliot–Yafet electron–phonon interaction are not strictly involvedin ultrafast demagnetization.
• The study of ultrafast dynamics in tunnelling magnetoresistance (TMR)revealed the presence of spin transport phenomena. The ultrafast de-magnetization process was affected by the application of electrical cur-rents and voltages through the structure. At the same time the pump
128 Charge and spin dynamics in TR-MOKE
excitation was also capable of generating a current/voltage stronglydependent on the intensity and direction of the applied external field.All these facts could be the evidence of ultrafast transport mechanismas predicted by the electronic superdiffusion theory. However, othermeasurements and a better characterization of the observed effects willhelp the interpretation. We believe that such studies will reveal thepresence of laser induced spin transport phenomena and will be ableto quantitatively estimate their contribution to the ultrafast demagne-tization process.
On the picosecond timescale, we studied the coherent spin oscillation, i.e.magnetic precession, in iron thin films. It is a well–known effect triggeredby the fast heating due to photon absorption. We demonstrated that, inparticular condition of laser intensity and applied external field, it is possibleto launch a precessional motion that switches the magnetization positionbetween two easy axis. In particular:
• we have been able to reproducibly and repeatedly commute the mag-netic vector between easy axes in about 100 ps and using only laserpulses. This is a very remarkable results from the point of view oftechnological applications. Our process resembles the working methodof magnetic recording devices in which the orientation of the magneti-zation indicates the status of the logical bit but is capable of a writingrate at least ten times faster than modern devices. In comparison toother all-optical switching methods our main goals were to operate un-der straightforward experimental conditions, i.e., in air and at roomtemperature, with a moderate optical excitation and with a simple fer-romagnetic 3d metals. An additional valuable feature is that we workedwith a material showing a biaxial magnetic anisotropy that allows towrite two bits of information on the same spot. In brief, we devel-oped a method to optically switch the magnetization that is of verygeneral applicability. Since the speed of the process relies on the time-dependence of the anisotropy, we believe that our results can triggerthe research of new materials with optimized parameters in view of afaster switching process and can also open interesting prospects on thecontinuously developing field of ultrafast magnetic recording devices.
As last issue of this work, we addressed, once again, the enduring debateabout the reliability of the TR-MOKE technique in retrieving laser inducedmagnetic dynamics:
Conclusions 129
• we observed different transient Kerr rotation and ellipticity up to pump–probe delays of 50 ps in CrO2 samples. This fact has been ascribed toa strong optical contribution not related to the genuine spin behaviourthat can lead to a wrong interpretation of the experimental results andharm the reliability of the technique. However, we demonstrated thatthanks to a very accurate characterization of the complex Kerr angle,i.e. both rotation and ellipticity, it is possible to extract the magneti-zation dynamics from the measured magneto–optical Kerr effect. Thisprocedure is of general validity and should be carried out regularly.
130 Conclusions
Acknowledgments
First of all I would like to thank all the people I work with during thesethree long years. I spent the largest part of my days here, at the PhysicsDepartment of Politecnico di Milano. I get inspired, motivated and stim-ulated. Every person I met taught me something sharing its own baggageof experiences. The will to help each others and enjoying the pleasure ofdiscussing and suggesting are only some of the greatest things I found. Ithink it has been very important, not only for my job, more important thanfinding the damned overlap or trying to figure out while the measurementswere too noisy.
Many thanks to Claudia and Ettore, I shared many moments with themand not only strictly related to our working activities. They taught me thejob, how to move in the lab, to solve puzzling problems and at the sametime how to enjoy a good result. They have been my primary source ofinspiration. I always try to get the more than I can from who I meet, thus Ihave to admit that they had a large role in shaping me. Thank you.
There is a person with whom I spent a lot of my time since the last yearof our master degrees to the too many coffee and very loooooooong lunchbreaks of our PhDs. He has been always present like a physics wing man, evenabroad, ready to talk about working problems as well as laughing about ourdumbness :) After many talks about girls, travels (by the way...good luck!!),our hopes and worries for the future, the question is always the same: hell,I graduated, again, now what? What about that idea of opening a club inCopacabana..?? Thank you, Matteo.
Thanks to Matteo N., a guy that I have been very happy to discover inthe last couple of years. He is a good friend with whom I spent really goodtimes, both in the lab and especially during conferences (you are an evil!).
Thanks to Fabio and Hamoon, they showed so enthusiasm and desireto learn that they gave me extra energies. I tried to share with them all I
132 Acknowledgments
could, some tricks in the lab and my tiny knowledge of physics. This yearpassed very fast and you did a lot of progresses. Fabio, you have shown acommitment out of the norm, it’s amazing .. continue on this way!
Finally I will have few words for everyone I know in the department, butsince they are too many I am obliged to only mention them. Thus manythanks to Eduardo, Alberto, Federico, Andrea, Michele, Lorenzo, Dario,Margherita, Gianmaria, Cristain, Greta and Stefano.
I spent seven months in Nijmegen, Nederlands.. a city ”in the middle ofnowhere”. There, I found the support of Matteo and Laura, the affectionthey have shown towards me, was incredible. Their attitude almost paternalshocked me. From the human point of view, it was a great teaching! wow!Without considering the help in the lab.. Thanks Matteo, it was crucial andyou have taught me many, many things.
Then, it useless to say that, what I have done outside my working hoursis also what mostly influenced my life and thus my work itself.
Let’s start from the capoeira-monza group. Guys really, thanks for thefriendship, the undisputed support and the feelings that all of you is able totransmit. It will be one of the things I gonna miss most if I will move. Itis something unique that I have never found anywhere else. It is difficult todescribe the energy and force that tie all of you. For each of you, camaradas,all forty, I would have something to write... but I’ll just say Ax!
Thank You..yes I’m talking about you who are standing and sustainingme since the last almost three years. As you know, I’ve never been good withwords so I will not even try because anything I would say would be wrongand never enough... I always try every day, every moment, from morningto night and with all my strength to show what you mean to me. It is thefirst thing that I told you, and I do not forget: you are like dynamite. Yourenergy has shaken my life leading me to do things that I have never imaginedand with a simplicity that I am still trying to learn... without consideringthe patience in the past two months during the writing of the thesis! ThanksAlice, you are a stone upon I stand.
And finally, thanks to my family, fixed point in the universe, shelter andnest. It could upset the world if necessary to help any of its components. Nomatter what you do, where you are.. they are always present. My brotherGabriele with his authenticity, ingenuity and carefreeness is the best personto talk to when you want to ”leave” the stressing world, take a break and feelgood. My sister Roberta quite moody, sometimes a stormy sea and othersa blue lagoon; we are very close, although sometimes it seems I forget it(sorry), but, I ensure you, it cannot happen. You grew up, you’ve foundyour way and I’m proud of you. I am convinced that you have a really hugeenergy and a infinite potential. Use it! I must say that this wonderful thing,
Acknowledgments 133
this family, is just because of my parents. You are an example to follow. Youhave done a wonderful thing, rare and to be proud of. Thanks!
134 Bibliography
Bibliography
[1] E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot, “Ultra-fast spin dynamics in ferromagnetic nickel,” Phys. Rev. Lett., vol. 76,pp. 4250–4253, May 1996.
[2] E. Carpene, E. Mancini, C. Dallera, M. Brenna, E. Puppin, andS. De Silvestri, “Dynamics of electron-magnon interaction and ultrafastdemagnetization in thin iron films,” Phys. Rev. B, vol. 78, p. 174422,Nov 2008.
[3] B. Koopmans, J. J. M. Ruigrok, F. D. Longa, and W. J. M. de Jonge,“Unifying ultrafast magnetization dynamics,” Phys. Rev. Lett., vol. 95,p. 267207, Dec 2005.
[4] G. P. Zhang, W. Hubner, G. Lefkidis, Y. Bai, and T. F. George,“Paradigm of the time-resolved magneto-optical kerr effect for fem-tosecond magnetism,” Nature Physics, vol. 5, pp. 499–502, 2009.
[5] M. V. Jean-Yves Bigot and E. Beaurepaire, “Coherent ultrafast mag-netism induced by femtosecond laser pulses,” Nature Physics, vol. 5,pp. 515–520, May 2009.
[6] G. M. Muller, J. Walowski, M. Djordjevic, G.-X. Miao, A. Gupta,A. V. Ramos, K. Gehrke, V. Moshnyaga, K. Samwer, J. Schmalhorst,A. Thomas, A. Hutten, G. Reiss, J. S. Moodera, and M. Munzenberg,“Spin polarization in half-metals probed by femtosecond spin excita-tion,” Nature Materials, vol. 428, pp. 1476–1122, 2009.
[7] M. Battiato, K. Carva, and P. M. Oppeneer, “Superdiffusive spin trans-port as a mechanism of ultrafast demagnetization,” Phys. Rev. Lett.,vol. 105, p. 027203, Jul 2010.
136 Bibliography
[8] M. Krauß, T. Roth, S. Alebrand, D. Steil, M. Cinchetti, M. Aeschli-mann, and H. C. Schneider, “Ultrafast demagnetization of ferromag-netic transition metals: The role of the coulomb interaction,” Phys.Rev. B, vol. 80, p. 180407, Nov 2009.
[9] M. Kryder, E. Gage, T. McDaniel, W. Challener, R. Rottmayer, G. Ju,Y.-T. Hsia, and M. Erden, “Heat assisted magnetic recording,” Pro-ceedings of the IEEE, vol. 96, pp. 1810 –1835, nov. 2008.
[10] J. Hohlfeld, E. Matthias, R. Knorren, and K. H. Bennemann,“Nonequilibrium magnetization dynamics of nickel,” Phys. Rev. Lett.,vol. 78, pp. 4861–4864, Jun 1997.
[11] C. D. Stanciu, A. Tsukamoto, A. V. Kimel, F. Hansteen, A. Kiri-lyuk, A. Itoh, and T. Rasing, “Subpicosecond magnetization reversalacross ferrimagnetic compensation points,” Phys. Rev. Lett., vol. 99,p. 217204, Nov 2007.
[12] C. D. Stanciu, F. Hansteen, A. V. Kimel, A. Kirilyuk, A. Tsukamoto,A. Itoh, and T. Rasing, “All-optical magnetic recording with circularlypolarized light,” Phys. Rev. Lett., vol. 99, p. 047601, Jul 2007.
[13] G. V. Astakhov, A. V. Kimel, G. M. Schott, A. A. Tsvetkov,A. Kirilyuk, D. R. Yakovlev, G. Karczewski, W. Ossau, G. Schmidt,L. W. Molenkamp, and T. Rasing, “Magnetization manipulation in(Ga,Mn)As by subpicosecond optical excitation,” Applied Physics Let-ters, vol. 86, no. 15, p. 152506, 2005.
[14] M. Battiato, K. Carva, and P. M. Oppeneer, “Theory of laser-inducedultrafast superdiffusive spin transport in layered heterostructures,”Phys. Rev. B, vol. 86, p. 024404, Jul 2012.
[15] B. Koopmans, M. van Kampen, J. T. Kohlhepp, and W. J. M. de Jonge,“Ultrafast magneto-optics in nickel: Magnetism or optics?,” Phys. Rev.Lett., vol. 85, pp. 844–847, Jul 2000.
[16] L. Guidoni, E. Beaurepaire, and J.-Y. Bigot, “Magneto-optics in theultrafast regime: Thermalization of spin populations in ferromagneticfilms,” Phys. Rev. Lett., vol. 89, p. 017401, Jun 2002.
[17] G. Bertotti, Hysteresis in Magnetism. San Diego: Academic Press,1998.
Bibliography 137
[18] R. Skomski, Simple Models of Magnetism. Oxford, UK: Oxford Uni-versity Press, 2008.
[19] M. Getzlaff, Magnetism: From Fundamentals to Nanoscale Dynamics.Berlin: Springer, 2006.
[20] I. Tudosa, C. Stamm, A. B. Kashuba, F. King, H. C. S. J. Stohr, G. Ju,B. Lu, and D. Weller, “The ultimate speed of magnetic switching ingranular recording media,” Nature, vol. 428, pp. 831–833, 2004.
[21] J. Stohr and H. Siegmann, Magnetism. From Fundamentals toNanoscale Dynamics. Berlin: Springerr, 2006.
[22] J. A. Hertz and D. M. Edwards, “Electron-magnon interactions in itin-erant ferromagnetism. i. formal theory,” Journal of Physics F: MetalPhysics, vol. 3, no. 12, p. 2174, 1973.
[23] D. M. Edwards and J. A. Hertz, “Electron-magnon interactions in itin-erant ferromagnetism. ii. strong ferromagnetism,” Journal of PhysicsF: Metal Physics, vol. 3, no. 12, p. 2191, 1973.
[24] R. J. Elliott, “Theory of the effect of spin-orbit coupling on magneticresonance in some semiconductors,” Phys. Rev., vol. 96, pp. 266–279,Oct 1954.
[25] Y. Yafet, Solid State Physics, vol. 14. Philadelphia: Academic NewYork, 1963.
[26] C. Stamm, T. Kachel, N. Pontius, R. Mitzner, T. Quast, K. Holldack,S. Khan, C. Lupulescu, E. F. Aziz, M. Wietstruk, H. A. Durr, andW. Eberhardt, “Femtosecond modification of electron localization andtransfer of angular momentum in nickel,” Nature Materials, vol. 6,pp. 740–743, 2007.
[27] C. Boeglin, E. Beaurepaire, V. Halte, V. Lopez-Flores, C. Stamm,N. Pontius, H. A. Durr, and J. Y. Bigot, “Distinguishing the ultra-fast dynamics of spin and orbital moments in solids,” Nature, vol. 465,pp. 458–461, 2010.
[28] M. van Kampen, C. Jozsa, J. T. Kohlhepp, P. LeClair, L. Lagae,W. J. M. de Jonge, and B. Koopmans, “All-optical probe of coher-ent spin waves,” Phys. Rev. Lett., vol. 88, p. 227201, May 2002.
138 Bibliography
[29] A. Delin, O. Eriksson, B. Johansson, S. Auluck, and J. M. Wills, “Cal-culated magneto-optical properties of cubic and tetragonal fe, co, andni,” Phys. Rev. B, vol. 60, pp. 14105–14114, Nov 1999.
[30] Z. Qiu and S. Bader, “Surface magneto-optic kerr effect (SMOKE),”J. Magn. Magn. Mater, vol. 200, p. 664, 1999.
[31] W. Voigt, Magneto- und Electrooptik. B.G. Teubner, 1908.
[32] E. Carpene, C. Piovera, C. Dallera, E. Mancini, and E. Puppin, “All-optical subnanosecond coherent spin switching in thin ferromagneticlayers,” Phys. Rev. B, vol. 84, p. 134425, Oct 2011.
[33] W. Ashcroft and N. D. Mermin, Solid State Physics. Philadelphia:Saunders College, 1976.
[34] N. Del Fatti, R. Bouffanais, F. Vallee, and C. Flytzanis, “Nonequilib-rium electron interactions in metal films,” Phys. Rev. Lett., vol. 81,pp. 922–925, Jul 1998.
[35] R. Knorren, G. Bouzerar, and K. H. Bennemann, “Dynamics of excitedelectrons in copper: The role of auger electrons,” Phys. Rev. B, vol. 63,p. 094306, Feb 2001.
[36] H. Petek, H. Nagano, M. Weida, and S. Ogawa, “The role of augerdecay in hot electron excitation in copper,” Chemical Physics, vol. 251,no. 13, pp. 71 – 86, 2000.
[37] P. B. Allen, “Theory of thermal relaxation of electrons in metals,”Phys. Rev. Lett., vol. 59, pp. 1460–1463, Sep 1987.
[38] J.-Y. Bigot, “Femtosecond magneto-optical processes in metals.,” C.R. Acad. Sci.Paris, vol. t. Serie IV 2, pp. 1483–1504, 2001.
[39] S. I. Anisimov, B. L. Kapeliovich, , and T. L. Perelman, “Electronemission from metal surfaces exposed to ultrashort laser pulses,” Sov.Phys. JETP, vol. 39, p. 375, 1975.
[40] C.-K. Sun, F. Vallee, L. H. Acioli, E. P. Ippen, and J. G. Fuji-moto, “Femtosecond-tunable measurement of electron thermalizationin gold,” Phys. Rev. B, vol. 50, pp. 15337–15348, Nov 1994.
[41] A. Vaterlaus, D. Guarisco, M. Lutz, M. Aeschlimann, M. Stampanoni,and F. Meier, “Different spin and lattice temperatures observed byspin-polarized photoemission with picosecond laser pulses,” Journal ofApplied Physics, vol. 67, no. 9, pp. 5661–5663, 1990.
Bibliography 139
[42] A. Vaterlaus, T. Beutler, and F. Meier, “Spin-lattice relaxation time offerromagnetic gadolinium determined with time-resolved spin-polarizedphotoemission,” Phys. Rev. Lett., vol. 67, pp. 3314–3317, Dec 1991.
[43] B. Koopmans, G. Malinowski, F. D. Longa, D. Steiauf, M. Fhnle,T. Roth, M. Cinchetti, and M. Aeschlimann, “Explaining the para-doxical diversity of ultrafast laser-induced demagnetization,” NatureMaterials, vol. 9, p. 259265, 2010.
[44] A. Scholl, L. Baumgarten, R. Jacquemin, and W. Eberhardt, “Ultrafastspin dynamics of ferromagnetic thin films observed by fs spin-resolvedtwo-photon photoemission,” Phys. Rev. Lett., vol. 79, pp. 5146–5149,Dec 1997.
[45] E. Beaurepaire, G. M. Turner, S. M. Harrel, M. C. Beard, J.-Y. Bigot,and C. A. Schmuttenmaer, “Coherent terahertz emission from ferro-magnetic films excited by femtosecond laser pulses,” Applied PhysicsLetters, vol. 84, no. 18, pp. 3465–3467, 2004.
[46] W. Hubner and G. P. Zhang, “Ultrafast spin dynamics in nickel,” Phys.Rev. B, vol. 58, pp. R5920–R5923, Sep 1998.
[47] C. Stamm, N. Pontius, T. Kachel, M. Wietstruk, and H. A. Durr,“Femtosecond x-ray absorption spectroscopy of spin and orbital angu-lar momentum in photoexcited Ni films during ultrafast demagnetiza-tion,” Phys. Rev. B, vol. 81, p. 104425, Mar 2010.
[48] S. Khan, K. Holldack, T. Kachel, R. Mitzner, and T. Quast, “Fem-tosecond undulator radiation from sliced electron bunches,” Phys. Rev.Lett., vol. 97, p. 074801, Aug 2006.
[49] K. Carva, M. Battiato, and P. M. Oppeneer, “Ab Initio investigation ofthe elliott-yafet electron-phonon mechanism in laser-induced ultrafastdemagnetization,” Phys. Rev. Lett., vol. 107, p. 207201, Nov 2011.
[50] M. Wietstruk, A. Melnikov, C. Stamm, T. Kachel, N. Pontius, M. Sul-tan, C. Gahl, M. Weinelt, H. A. Durr, and U. Bovensiepen, “Hot-electron-driven enhancement of spin-lattice coupling in Gd and Tb 4fferromagnets observed by femtosecond x-ray magnetic circular dichro-ism,” Phys. Rev. Lett., vol. 106, p. 127401, Mar 2011.
[51] A. Mann, J. Walowski, M. Munzenberg, S. Maat, M. J. Carey, J. R.Childress, C. Mewes, D. Ebke, V. Drewello, G. Reiss, and A. Thomas,
140 Bibliography
“Insights into ultrafast demagnetization in pseudogap half-metals,”Phys. Rev. X, vol. 2, p. 041008, Nov 2012.
[52] G. P. Zhang and W. Hubner, “Laser-induced ultrafast demagnetizationin ferromagnetic metals,” Phys. Rev. Lett., vol. 85, pp. 3025–3028, Oct2000.
[53] B. Heinrich, Z. Celinski, J. F. Cochran, A. S. Arrott, and K. Myrtle,“Magnetic anisotropies in single and multilayered structures (invited),”Journal of Applied Physics, vol. 70, no. 10, pp. 5769–5774, 1991.
[54] E. Carpene, E. Mancini, C. Dallera, E. Puppin, and S. D. Silvestri,“Femtosecond laser spectroscopy of spins: Magnetization dynamics inthin magnetic films with spatio-temporal resolution,”
[55] E. C. Stoner and E. P. Wohlfarth, “A mechanism of magnetic hysteresisin heterogeneous alloys,” Philosophical Transactions of the Royal Soci-ety of London. Series A, Mathematical and Physical Sciences, vol. 240,no. 826, pp. 599–642, 1948.
[56] R. P. Cowburn, S. J. Gray, J. Ferre, J. A. C. Bland, and J. Mil-tat, “Magnetic switching and in-plane uniaxial anisotropy in ultrathinAg/Fe/Ag(100) epitaxial films,” Journal of Applied Physics, vol. 78,no. 12, pp. 7210–7219, 1995.
[57] E. Carpene, E. Mancini, C. Dallera, E. Puppin, and S. D. Sil-vestri, “Three-dimensional magnetization evolution and the role ofanisotropies in thin Fe/MgO films: Static and dynamic measurements,”Journal of Applied Physics, vol. 108, no. 6, p. 063919, 2010.
[58] T. Kampfrath, R. G. Ulbrich, F. Leuenberger, M. Munzenberg, B. Sass,and W. Felsch, “Ultrafast magneto-optical response of iron thin films,”Phys. Rev. B, vol. 65, p. 104429, Feb 2002.
[59] H. B. Zhao, D. Talbayev, Q. G. Yang, G. Lupkea, A. T. Hanbicki,C. H. Li, O. M. J. van t Erve, G. Kioseoglou, and B. T. Jonker, “Ul-trafast magnetization dynamics of epitaxial Fe films on AlGaAs (001),”Applied Physics Letters, vol. 86, p. 152512, 2005.
[60] D. J. Hilton, R. D. Averitt, C. A. Meserole, G. L. Fisher, D. J. Funk,J. D. Thompson, and A. J. Taylor, “Terahertz emission via ultrashort-pulse excitation of magnetic metalfilms,” Opt. Lett., vol. 29, pp. 1805–1807, Aug 2004.
Bibliography 141
[61] A. B. Schmidt, M. Pickel, M. Donath, P. Buczek, A. Ernst, V. P.Zhukov, P. M. Echenique, L. W. Sandratskii, E. V. Chulkov, andM. Weinelt, “Ultrafast magnon generation in an fe film on cu(100),”Phys. Rev. Lett., vol. 105, p. 197401, Nov 2010.
[62] A. Weber, F. Pressacco, S. Gunther, E. Mancini, P. M. Oppeneer, andC. H. Back, “Ultrafast demagnetization dynamics of thin Fe/W(110)films: Comparison of time- and spin-resolved photoemission with time-resolved magneto-optic experiments,” Phys. Rev. B, vol. 84, p. 132412,Oct 2011.
[63] J. Schafer, D. Schrupp, E. Rotenberg, K. Rossnagel, H. Koh, P. Blaha,and R. Claessen, “Electronic quasiparticle renormalization on the spinwave energy scale,” Phys. Rev. Lett., vol. 92, p. 097205, Mar 2004.
[64] R. Maglic, “Van hove singularity in the iron density of states,” Phys.Rev. Lett., vol. 31, pp. 546–548, Aug 1973.
[65] Kittel, Introduction to solid state physics. Wiley, 7th edition”, year =1996 ed.
[66] H. Jisang and D. L. Mills, “Spin dependence of the inelastic electronmean free path in Fe and Ni: Explicit calculations and implications,”Phys. Rev. B, vol. 62, pp. 5589–5600, Sep 2000.
[67] V. P. Zhukov, E. V. Chulkov, and P. M. Echenique, “Lifetimes of ex-cited electrons in Fe and Ni: First-principles GW and the T-matrixtheory,” Phys. Rev. Lett., vol. 93, p. 096401, Aug 2004.
[68] S. D. Hanham, A. S. Arrott, and B. Heinrich, “Dependence ofanisotropy field on magnetization in iron,” Journal of Applied Physics,vol. 52, no. 3, pp. 1941–1943, 1981.
[69] Y. S. Touloukian and C. Y. Ho, Thermophisical Properties of Matter,vol. 1-4. New York: Plenum, 1970.
[70] T. Roth, A. J. Schellekens, S. Alebrand, O. Schmitt, D. Steil, B. Koop-mans, M. Cinchetti, and M. Aeschlimann, “Temperature dependenceof laser-induced demagnetization in ni: A key for identifying the un-derlying mechanism,” Phys. Rev. X, vol. 2, p. 021006, May 2012.
[71] S. Ikeda, J. Hayakawa, Y. Ashizawa, Y. M. Lee, K. Miura, H. Hasegawa,M. Tsunoda, F. Matsukura, and H. Ohno, “Tunnel magnetoresistanceof 604% at 300 K by suppression of Ta diffusion in CoFeB/MgO/CoFeB
142 Bibliography
pseudo-spin-valves annealed at high temperature,” Applied PhysicsLetters, vol. 93, no. 8, p. 082508, 2008.
[72] A. Melnikov, I. Razdolski, T. O. Wehling, E. T. Papaioannou, V. Rod-datis, P. Fumagalli, O. Aktsipetrov, A. I. Lichtenstein, and U. Boven-siepen, “Ultrafast transport of laser-excited spin-polarized carriers inAu/Fe/MgO(001),” Phys. Rev. Lett., vol. 107, p. 076601, Aug 2011.
[73] D. Rudolf, C. La-O-Vorakiat, M. Battiato, R. Adam, J. M. Shaw,E. Turgut, P. Maldonado, S. Mathias, P. Grychtol, H. T. Nembach,T. J. Silva, M. Aeschlimann, H. C. Kapteyn, M. M. Murnane, C. M.Schneider, and P. M. Oppeneer, “Ultrafast magnetization enhancementin metallic multilayers driven by superdiffusive spin current,” NatureCommunications, vol. 3, SEP 2012.
[74] B. Vodungbo, J. Gautier, G. Lambert, A. B. Sardinha, M. Lozano,S. Sebban, M. Ducousso, W. Boutu, K. Li, B. Tudu, M. Tortarolo,R. Hawaldar, R. Delaunay, V. Lopez-Flores, J. Arabski, C. Boeglin,H. Merdji, P. Zeitoun, and J. Luening, “Laser-induced ultrafast demag-netization in the presence of a nanoscale magnetic domain network,”Nature Communications, vol. 3, AUG 2012.
[75] G. Malinowski, F. D. Longa, J. H. H. Rietjens, P. V. Paluskar, R. Hui-jink, H. J. M. Swagten, and B. Koopmans, “Control of speed and ef-ficiency of ultrafast demagnetization by direct transfer of spin angularmomentum,” Nature Physics, vol. 4, pp. 855–858, 2008.
[76] M. Cinchetti, M. Sanchez Albaneda, D. Hoffmann, T. Roth, J.-P.Wustenberg, M. Krauß, O. Andreyev, H. C. Schneider, M. Bauer, andM. Aeschlimann, “Spin-flip processes and ultrafast magnetization dy-namics in co: Unifying the microscopic and macroscopic view of fem-tosecond magnetism,” Phys. Rev. Lett., vol. 97, p. 177201, Oct 2006.
[77] D. Steiauf and M. Fahnle, “Elliott-yafet mechanism and the discus-sion of femtosecond magnetization dynamics,” Phys. Rev. B, vol. 79,p. 140401, Apr 2009.
[78] M. Krauß, T. Roth, S. Alebrand, D. Steil, M. Cinchetti, M. Aeschli-mann, and H. C. Schneider, “Ultrafast demagnetization of ferromag-netic transition metals: The role of the coulomb interaction,” Phys.Rev. B, vol. 80, p. 180407, Nov 2009.
[79] D. Steil, S. Alebrand, T. Roth, M. Krauß, T. Kubota, M. Oogane,Y. Ando, H. C. Schneider, M. Aeschlimann, and M. Cinchetti,
Bibliography 143
“Band-structure-dependent demagnetization in the Heusler AlloyCo2Mn1−xFexSi,” Phys. Rev. Lett., vol. 105, p. 217202, Nov 2010.
[80] B. Y. Mueller, T. Roth, M. Cinchetti, M. Aeschlimann, and B. Reth-feld, “Driving force of ultrafast magnetization dynamics,” New Journalof Physics, vol. 13, no. 12, p. 123010, 2011.
[81] S. I. Anisimov, B. L. Kapeliovich, and T. L. Perelman, “Theory of thedispersion of magnetic permeability in ferromagnetic bodies,” Phys. Z.Sowjetunion, vol. 8, pp. 153–169, 1953.
[82] Y. Tserkovnyak, A. Brataas, and G. E. W. Bauer, “Enhanced gilbertdamping in thin ferromagnetic films,” Phys. Rev. Lett., vol. 88,p. 117601, Feb 2002.
[83] T. G. et al., “Precession dynamics in nife thin films, induced by shortmagnetic in-plane field pulses generated by a photoconductive switch,”J. Magn. Soc. Jpn, vol. 25, pp. 192–197, 2001.
[84] T. Gerrits, H. van den Berg, J. Hohlfeld, O. Gielkens, L. Br, andT. Rasing, “Picosecond control of coherent magnetisation dynamics inpermalloy thin films by picosecond magnetic field pulse shaping,” Jour-nal of Magnetism and Magnetic Materials, vol. 240, no. 13, pp. 283 –286, 2002. 4th International Symposium on Metallic Multilayers.
[85] H. P. Klein and E. Kneller, “Variation of magnetocrystalline anisotropyof iron with field and temperature,” Phys. Rev., vol. 144, pp. 372–374,Apr 1966.
[86] A. V. Kimel, A. Kirilyuk, P. A. Usachev, R. V. Pisarev, A. M. Bal-bashov, and T. Rasing, “Ultrafast non-thermal control of magnetiza-tion by instantaneous photomagnetic pulses,” Nature, vol. 435, pp. 655–657, 2005.
[87] F. Hansteen, A. Kimel, A. Kirilyuk, and T. Rasing, “Femtosecondphotomagnetic switching of spins in ferrimagnetic garnet films,” Phys.Rev. Lett., vol. 95, p. 047402, Jul 2005.
[88] M. Djordjevic, G. Eilers, A. Parge, M. Munzenberg, and J. S. Mood-era, “Intrinsic and nonlocal gilbert damping parameter in all opticalpump-probe experiments,” Journal of Applied Physics, vol. 99, no. 8,p. 08F308, 2006.
144 Bibliography
[89] J. Walowski, M. D. Kaufmann, B. Lenk, C. Hamann, J. McCord, andM. Munzenberg, “Intrinsic and non-local gilbert damping in polycrys-talline nickel studied by ti:sapphire laser fs spectroscopy,” Journal ofPhysics D: Applied Physics, vol. 41, no. 16, p. 164016, 2008.
[90] L. H. F. Andrade, A. Laraoui, M. Vomir, D. Muller, J.-P. Stoquert,C. Estournes, E. Beaurepaire, and J.-Y. Bigot, “Damped precession ofthe magnetization vector of superparamagnetic nanoparticles excitedby femtosecond optical pulses,” Phys. Rev. Lett., vol. 97, p. 127401,Sep 2006.
[91] G. M. Muller, M. Munzenberg, G.-X. Miao, and A. Gupta, “Activa-tion of additional energy dissipation processes in the magnetizationdynamics of epitaxial chromium dioxide films,” Phys. Rev. B, vol. 77,p. 020412, Jan 2008.
[92] B. Lenk, H. Ulrichs, F. Garbs, and M. Munzenberg, “The buildingblocks of magnonics,” Physics Reports, vol. 507, no. 45, pp. 107 – 136,2011.
[93] G. V. Astakhov, A. V. Kimel, G. M. Schott, A. A. Tsvetkov,A. Kirilyuk, D. R. Yakovlev, G. Karczewski, W. Ossau, G. Schmidt,L. W. Molenkamp, and T. Rasing, “Magnetization manipulation in(Ga,Mn)As by subpicosecond optical excitation,” Applied Physics Let-ters, vol. 86, no. 15, p. 152506, 2005.
[94] R. Hertel, “For faster magnetic switchingdestroy and rebuild,” Physics,vol. 2, p. 73, 2005.
[95] L. Liu, C.-F. Pai, Y. Li, H. W. Tseng, D. C. Ralph, and R. A. Buhrman,“Spin-torque switching with the giant spin hall effect of tantalum,”Science, vol. 336, no. 6081, pp. 555–558, 2012.
[96] S. S. P. Parkin, M. Hayashi, and L. Thomas, “Magnetic domain-wallracetrack memory,” Science, vol. 320, no. 5873, pp. 190–194, 2008.
[97] R. Ramesh and N. A. Spaldin, “Multiferroics: progress and prospectsin thin films,” Nature Materials, vol. 6, pp. 21–29, 2007.
[98] H. Siegmann, E. Garwin, C. Prescott, J. Heidmann, D. Mauri,D. Weller, R. Allenspach, and W. Weber, “Magnetism with picosecondfield pulses,” Journal of Magnetism and Magnetic Materials, vol. 151,no. 12, pp. L8 – L12, 1995.
Bibliography 145
[99] C. H. Back, R. Allenspach, W. Weber, S. S. P. Parkin, D. Weller, E. L.Garwin, and H. C. Siegmann, “Minimum field strength in precessionalmagnetization reversal,” Science, vol. 285, no. 5429, pp. 864–867, 1999.
[100] C. H. Back, D. Weller, J. Heidmann, D. Mauri, D. Guarisco, E. L.Garwin, and H. C. Siegmann, “Magnetization reversal in ultrashortmagnetic field pulses,” Phys. Rev. Lett., vol. 81, pp. 3251–3254, Oct1998.
[101] T. Gerrits, H. A. M. van den Berg, J. Hohlfeld, L. Bar, and T. Rasing1,“Ultrafast precessional magnetization reversal by picosecond magneticfield pulse shaping,” Nature, vol. 418, pp. 509–512, 2002.
[102] J. Hohlfeld, T. Gerrits, M. Bilderbeek, T. Rasing, H. Awano, andN. Ohta, “Fast magnetization reversal of GdFeCo induced by femtosec-ond laser pulses,” Phys. Rev. B, vol. 65, p. 012413, Dec 2001.
[103] C. Bunce, J. Wu, G. Ju, B. Lu, D. Hinzke, N. Kazantseva, U. Nowak,and R. W. Chantrell, “Laser-induced magnetization switching in filmswith perpendicular anisotropy: A comparison between measurementsand a multi-macrospin model,” Phys. Rev. B, vol. 81, p. 174428, May2010.
[104] I. Radu, K. Vahaplar, C. Stamm, T. K. amd N. Pontius, H. A.Drr, T. A. Ostler, J. Barker, R. F. L. Evans, R. W. Chantrell,A. Tsukamoto, A. Itoh, A. Kirilyuk, T. Rasing, and A. V. Kimel,“Transient ferromagnetic-like state mediating ultrafast reversal of an-tiferromagnetically coupled spins,” Nature, vol. 472, p. 205, 2011.
[105] C. D. Stanciu, A. V. Kimel, F. Hansteen, A. Tsukamoto, A. Itoh,A. Kirilyuk, and T. Rasing, “Ultrafast spin dynamics across compen-sation points in ferrimagnetic GdFeCo: The role of angular momentumcompensation,” Phys. Rev. B, vol. 73, p. 220402, Jun 2006.
[106] T. Ostler, J. Barker, R. Evans, R. Chantrell, U. Atxitia, O. Chubykalo-Fesenko, S. Moussaoui, L. L. Guyader, E. Mengotti, L. Heyderman,F. Nolting, A. Tsukamoto, A. Itoh, D. Afanasiev, B. Ivanov, A. Kalash-nikova, K. Vahaplar, J. Mentink, A. Kirilyuk, T. Rasing, and A. Kimel,“Ultrafast heating as a sufficient stimulus for magnetization reversal ina ferrimagnet,” Nature Communications, vol. 3, p. 1, 2012.
[107] A. R. Khorsand, M. Savoini, A. Kirilyuk, A. V. Kimel, A. Tsukamoto,A. Itoh, and T. Rasing, “Role of magnetic circular dichroism in all-
146 Bibliography
optical magnetic recording,” Phys. Rev. Lett., vol. 108, p. 127205, Mar2012.
[108] A. V. Kimel, A. Kirilyuk, A. Tsvetkov, R. V. Pisarev, and T. Ras-ing1, “Laser-induced ultrafast spin reorientation in the antiferromagnetTmFeO3,” Nature, vol. 429, p. 850, 2004.
[109] A. V. Kimel, B. A. Ivanov, R. V. Pisarev, P. A. Usachev, A. Kirilyuk,and T. Rasing, “Inertia-driven spin switching in antiferromagnets,”Nature Physics, vol. 5, pp. 727–731, 2009.
[110] J. A. de Jong, I. Razdolski, A. M. Kalashnikova, R. V. Pisarev, A. M.Balbashov, A. Kirilyuk, T. Rasing, and A. V. Kimel, “Coherent controlof the route of an ultrafast magnetic phase transition via low-amplitudespin precession,” Phys. Rev. Lett., vol. 108, p. 157601, Apr 2012.
[111] Y. Zhu, X. Zhang, T. Li, X. Huang, L. Han, and J. Zhao, “Ultrafastdynamics of four-state magnetization reversal in (Ga,Mn)As,” AppliedPhysics Letters, vol. 95, no. 5, p. 052108, 2009.
[112] A. H. M. Reid, G. V. Astakhov, A. V. Kimel, G. M. Schott, W. Ossau,K. Brunner, A. Kirilyuk, L. W. Molenkamp, and T. Rasing, “Single pi-cojoule pulse switching of magnetization in ferromagnetic (Ga,Mn)As,”Applied Physics Letters, vol. 97, no. 23, p. 232503, 2010.
[113] E. Carpene, E. Mancini, D. Dazzi, C. Dallera, E. Puppin, and S. D. Sil-vestri, “Ultrafast three-dimensional magnetization precession and mag-netic anisotropy of a photoexcited thin film of iron,” Phys. Rev. B,vol. 81, p. 060415, Feb 2010.
[114] P. M. Oppeneer and A. Liebsch, “Ultrafast demagnetization in ni:theory of magneto-optics for non-equilibrium electron distributions,”Journal of Physics: Condensed Matter, vol. 16, no. 30, p. 5519, 2004.
[115] J.-Y. Bigot, L. Guidoni, E. Beaurepaire, and P. N. Saeta, “Femtosecondspectrotemporal magneto-optics,” Phys. Rev. Lett., vol. 93, p. 077401,Aug 2004.
[116] R. Wilks, R. J. Hicken, M. Ali, B. Hickey, J. D. R. Buchanan, A. T. G.Pym, and B. K. Tanner, “Investigation of ultrafast demagnetizationand cubic optical nonlinearity of ni in the polar geometry,” Journal ofApplied Physics, vol. 95, p. 7441, 2004.
Bibliography 147
[117] A. Comin, M. Rossi, C. Mozzati, F. Parmigiani, and G. Banfi., “In-vestigation of ultrafast demagnetization and cubic optical nonlinearityof ni in the polar geometry,” Solid State Communications, vol. 129,p. 227, 2004.
[118] K. Carva, D. Legut, and P. M. Oppeneer, “Influence of laser-excitedelectron distributions on the x-ray magnetic circular dichroism spec-tra: Implications for femtosecond demagnetization in ni,” EPL (Euro-physics Letters), vol. 86, no. 5, p. 57002, 2009.
[119] H. Regensburger, R. Vollmer, and J. Kirschner, “Time-resolvedmagnetization-induced second-harmonic generation from the ni(110)surface,” Phys. Rev. B, vol. 61, pp. 14716–14722, Jun 2000.
[120] C. La-O-Vorakiat, E. Turgut, C. A. Teale, H. C. Kapteyn, M. M. Mur-nane, S. Mathias, M. Aeschlimann, C. M. Schneider, J. M. Shaw, H. T.Nembach, and T. J. Silva, “Ultrafast demagnetization measurementsusing extreme ultraviolet light: Comparison of electronic and magneticcontributions,” Phys. Rev. X, vol. 2, p. 011005.
[121] A. Vernes and P. Weinberger, “Formally linear response theory ofpump-probe experiments,” Phys. Rev. B, vol. 71, p. 165108, Apr 2005.
[122] X. W. Li, A. Gupta, T. R. McGuire, P. R. Duncombe, and G. Xiao,“Magnetoresistance and hall effect of chromium dioxide epitaxial thinfilms,” Journal of Applied Physics, vol. 85, no. 8, pp. 5585–5587, 1999.
[123] M. Pathak, H. Sato, X. Zhang, K. B. Chetry, D. Mazumdar, P. LeClair,and A. Gupta, “Substrate-induced strain and its effect in CrO2 thinfilms,” Journal of Applied Physics, vol. 108, no. 5, p. 053713, 2010.
[124] M. Guoxing, G. Xiao, and A. Gupta, “Variations in the magneticanisotropy properties of epitaxial CrO2 films as a function of thick-ness,” Phys. Rev. B, vol. 71, p. 094418, Mar 2005.
[125] K. Schwarz, “CrO2 predicted as a half-metallic ferromagnet,” Journalof Physics F: Metal Physics, vol. 16, no. 9, p. L211, 1986.
[126] I. I. Mazin, D. J. Singh, and C. Ambrosch-Draxl, “Transport, optical,and electronic properties of the half-metal CrO2,” Phys. Rev. B, vol. 59,pp. 411–418, Jan 1999.
[127] N. E. Brener, J. M. Tyler, J. Callaway, D. Bagayoko, and G. L. Zhao,“Electronic structure and fermi surface of CrO2,” Phys. Rev. B, vol. 61,pp. 16582–16588, Jun 2000.
148 Bibliography
[128] J. M. D. Coey and M. Venkatesan, “Half-metallic ferromagnetism: Ex-ample of CrO2 (invited),” Journal of Applied Physics, vol. 91, no. 10,pp. 8345–8350, 2002.
[129] J. Kunes, P. Novak, P. M. Oppeneer, C. Konig, M. Fraune, U. Rudi-ger, G. Guntherodt, and C. Ambrosch-Draxl, “Electronic structure ofCrO2 as deduced from its magneto-optical kerr spectra,” Phys. Rev. B,vol. 65, p. 165105, Apr 2002.
[130] R. A. de Groot, F. M. Mueller, P. G. v. Engen, and K. H. J. Buschow,“New class of materials: Half-metallic ferromagnets,” Phys. Rev. Lett.,vol. 50, pp. 2024–2027, Jun 1983.
[131] J.-H. Park, E. Vescovo, H.-J. Kim, C. Kwon, R. Ramesh, andT. Venkatesan, “Direct evidence for a half-metallic ferromagnet,” Na-ture, vol. 392, pp. 794–796, Apr 1998.
[132] M. I. Katsnelson, V. Y. Irkhin, L. Chioncel, A. I. Lichtenstein, andR. A. de Groot, “Half-metallic ferromagnets: From band structure tomany-body effects,” Rev. Mod. Phys., vol. 80, pp. 315–378, Apr 2008.
[133] G.-X. Miao, M. Munzenberg, and J. S. Moodera, “Tunneling pathtoward spintronics,” Reports on Progress in Physics, vol. 74, no. 3,p. 036501, 2011.
[134] Q. Zhang, A. V. Nurmikko, A. Anguelouch, G. Xiao, and A. Gupta,“Coherent magnetization rotation and phase control by ultrashort op-tical pulses in CrO2 thin films,” Phys. Rev. Lett., vol. 89, p. 177402,Oct 2002.
[135] Q. Zhang, A. V. Nurmikko, G. X. Miao, G. Xiao, and A. Gupta, “Ul-trafast spin-dynamics in half-metallic CrO2 thin films,” Phys. Rev. B,vol. 74, p. 064414, Aug 2006.
List of publications
1. “Magnetization dynamics in thin magnetic films with spatio-temporalresolution”, C. Piovera, Nuovo Cimento C 34, 05 (2011).
2. “All-optical subnanosecond coherent spin switching in thin ferromag-netic layers”, E. Carpene, C. Piovera, C. Dallera, E. Mancini, E. PuppinPhysical Review B 84, 134425 (2011).
