applied sciences

Article Ultrafast Modulation of Magnetization Dynamics in Ferromagnetic (Ga, Mn)As Thin Films

Hang Li 1,2, Xinhui Zhang 2,3,*, Xinyu Liu 4,*, Margaret Dobrowolska 4 and Jacek K. Furdyna 4

1 College of Medical Laboratory, Dalian Medical University, Dalian 116044, China; [email protected] 2 State Key Laboratory of Superlattices and Microstructures, Institute of Semiconductors, Chinese Academy of Sciences, Beijing 10083, China 3 College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, Beijing 100049, China 4 Department of Physics, University of Notre Dame, Notre Dame, IN 46556, USA; [email protected] (M.D.); [email protected] (J.K.F.) * Correspondence: [email protected] (X.Z.); [email protected] (X.L.); Tel.: +86-010-82304486 (X.Z.); +1-574-6319787 (X.L.)


Received: 31 August 2018; Accepted: 7 October 2018; Published: 11 October 2018


Abstract: Magnetization precession induced by linearly polarized optical excitation in ferromagnetic (Ga,Mn)As was studied by time-resolved magneto-optical Kerr effect measurements. The superposition of thermal and non-thermal effects arising from the laser pulses complicates the analysis of magnetization precession in terms of magnetic anisotropy fields. To obtain insight into these processes, we investigated compressively-strained thin (Ga,Mn)As films using ultrafast optical excitation above the band gap as a function of pulse intensity. Data analyses with the gyromagnetic calculation based on Landau-Lifshitz-Gilbert equation combined with two different magneto-optical effects shows the non-equivalent effects of in-plane and out-of-plane magnetic anisotropy fields on both the amplitude and the frequency of magnetization precession, thus providing a handle for separating the effects of non-thermal and thermal processes in this context. Our results show that the effect of photo-generated carriers on magnetic anisotropy constitutes a particularly effective mechanism for controlling both the frequency and amplitude of magnetization precession, thus suggesting the possibility of non-thermal manipulation of spin dynamics through pulsed laser excitations.

Keywords: spintronics; magneto-optical Kerr effect; (Ga,Mn)As; magnetization precession

1. Introduction Investigation of multiple functionalities of ferromagnetic semiconductors in the picosecond range lays the ground for future opportunities for high-speed spintronic devices. Time-resolved magneto-optical Kerr effect (MOKE) spectroscopy has been widely used for studying ultrafast photon-induced collective spin dynamics in ferromagnetic semiconductors. Based on this technique, Mn-based III–V ferromagnetic semiconductors have been extensively investigated from the point of view of both fundamental physics and spintronic applications [1–6]. Ultrafast magneto-optical investigation of collective spin excitations in ferromagnetic (Ga,Mn)As thin films has demonstrated the possible multi-functionality of ferromagnetic semiconductors when incorporated in spintronic devices [4,7–9]. Transient modulation involving either thermal or non-thermal mechanisms investigated by laser excitation has been shown to contribute to ultrafast coherent precession of magnetization [10–23]. Modulation of magnetic anisotropy stimulated by transient increases of either local temperature or photocarrier density in (Ga,Mn)As has demonstrated multiple possibilities of modulating the precession of magnetization by linearly polarized pump pulses.

Appl. Sci. 2018, 8, 1880; doi:10.3390/app8101880 www.mdpi.com/journal/applsci Appl. Sci. 2018, 8, 1880 2 of 10

Recently, several types of ultrafast mechanisms for manipulating coherent spin excitations have been discovered in (Ga,Mn)As, such as optical spin transfer torque (OSTT), in which the angular momentum of photo-generated carriers is transferred to the collective magnetization of the system [10]; and optical spin-orbit torque (OSOT), in which torque is exerted on the local magnetic moments of Mn by non-equilibrium spin polarization of photo-excited holes through spin-orbit coupling [19]. Photoionization-like excitation of Mn2+ has been recently proposed to account for the photoinduced modulation of perpendicular effective field [23]. Intrinsically, one or more of such mechanisms could simultaneously trigger a collective precession of magnetization [4,7,14,21], and they would compete with each other as to how they contribute to the precession process. On the other hand, they may also compensate each other in their contributions to data storage in the magnetic recording. Previous studies reported that hole cooling after pulse excitation is one of the limiting factors for ultrafast control of carrier-mediated magnetization precession, while thermal dissipation after laser heating is considered as the barrier for the high speed of data storage [11–14,24–27]. In this sense, the interplay between such thermal and non-thermal modulations upon laser pulse excitation is one of key issues in the context of ultrafast manipulation of magnetization. In this paper, we report a study by means of time-resolved magneto-optical spectroscopy of photo-induced collective spin dynamics triggered by both thermal and non-thermal mechanisms. Using different intensities of linearly polarized optical excitation, we could relate the influence of both laser heating and photo-carrier generation on the precession of magnetization precession, and show how this is connected to modulations of the in-plane and out-of-plane anisotropy fields that result from such excitation. Specifically, for moderately-doped (Ga,Mn)As films with in-plane compressive strain, it is shown that the variation of precession frequency and precession amplitude depend on the superposition of both thermal and non-thermal effects through anisotropy fields of this material. Theoretical calculations show that the out-of-plane anisotropy field via non-thermal mediation mainly contributes to nonlinear variation of magnetization precession, thus pointing to the important role of ultrafast optical spin manipulation in ferromagnetic materials via non-thermal paths.

2. Materials and Methods

Ferromagnetic Ga0.964Mn0.036As films with thickness of 97 nm were grown by means of low-temperature molecular-beam epitaxy (LT-MBE). The layers were grown on [001]-oriented GaAs substrates. The hole concentration p of the as-grown film was estimated to be ~2 × 1020 cm−3. ◦ 20 −3 After annealing at 250 C in N2 for 1 h, p was estimated to increase to ~3 × 10 cm . Superconducting quantum interference device (SQUID) measurements showed that the Curie temperatures TC of the annealed and as-grown samples were ~80 K and ~60 K, respectively. The magnetic anisotropy properties of the investigated (Ga,Mn)As layers were characterized by ferromagnetic resonance (FMR) measurements at different temperatures. Time-resolved pump-probe magneto-optical Kerr effect was measured using a Ti:sapphire laser with repetition rate of 80 MHz and spectral width of 10 nm. Pump-induced magnetization dynamics of Mn spins were studied via time-delayed probe pulses. Both the pump pulse and the probe pulse were linearly polarized with the same photon energy ranging from 1.53 eV (810 nm) to 1.58 eV (785 nm). The pump intensity was varied from 1.8 µJ/cm2 to 28 µJ/cm2, and the probe intensity was fixed at 0.6 µJ/cm2. The samples were mounted in a Janis subcompact cryostat. The experiments were performed at 10 K unless noted otherwise. There is no external magnetic field applied in the experiments.

3. Results Ultrafast photon excitation of (Ga,Mn)As ferromagnetic film can strongly disturb the equilibrium between holes, localized Mn spins, and the lattice [14]. On the subpicosecond time scale, laser pulse excitation leads to a coherent phase of nonequilibrium photoexcited carriers. However, the well-defined coherent phase of carriers quickly decays due to electron–electron, hole–hole, and electron–hole scattering. In this extremely short time regime, the time evolution of the coherent phase of Appl. Sci. 2018, 8, x FOR PEER REVIEW 3 of 10 Appl. Sci. 2018, 8, 1880 3 of 10 carrier energy distribution function cannot be characterized by a temperature. After the carriers transfer their excess energy to the lattice (within a few picoseconds), the system acquires a nonequilibrium photoexcited carriers is controlled by nonlinear optical excitation, and the carrier quasi-equilibrium temperature. The enhancement of both the local lattice temperature and the hole energy distribution function cannot be characterized by a temperature. After the carriers transfer concentration by photoexcitation can then modulate the magnitude of magnetic anisotropy fields, their excess energy to the lattice (within a few picoseconds), the system acquires a quasi-equilibrium which reorients the direction of the easy axes, thus triggering the magnetization dynamics on a time temperature. The enhancement of both the local lattice temperature and the hole concentration by scale of ~100 ps. photoexcitation can then modulate the magnitude of magnetic anisotropy fields, which reorients the Magnetization precession of the coupled Mn spin system triggered by such magnetic direction of the easy axes, thus triggering the magnetization dynamics on a time scale of ~100 ps. anisotropy modulation is distinct from photomagnetic phenomena such as Magnetization precession of the coupled Mn spin system triggered by such magnetic optical-spin-transfer-torque (OSTT). Specifically, it requires no injection of angular momentum, and anisotropy modulation is distinct from photomagnetic phenomena such as optical-spin-transfer-torque can thus be triggered by a linearly-polarized laser pulse. Figure 1 shows a typical magnetization (OSTT). Specifically, it requires no injection of angular momentum, and can thus be triggered by precession response to such a pulse at 10 K for the annealed (Ga,Mn)As sample excited by a a linearly-polarized laser pulse. Figure1 shows a typical magnetization precession response to linearly-polarized pump beam at 1.58 eV. As shown in Figure 1a, the temporal evolution of the such a pulse at 10 K for the annealed (Ga,Mn)As sample excited by a linearly-polarized pump photoexcited magnetization observed by time-resolved magneto-optical measurement in beam at 1.58 eV. As shown in Figure1a, the temporal evolution of the photoexcited magnetization ferromagnetic (Ga,Mn)As can be fitted by an exponentially damped sine function superimposed on observed by time-resolved magneto-optical measurement in ferromagnetic (Ga,Mn)As can be fitted by a pulse-like function [7,21], an exponentially damped sine function superimposed on a pulse-like function [7,21], ⁄ ⁄ θ =+ + + , (1) −t/t0 −t/τD θk = a + be + Ae sin(ωt + φ), (1) where A, τD, ω, and ϕ represent, respectively, the oscillation amplitude, the relaxation time of magnetization,where A, τD, ωthe, and frequencyφ represent, of oscillation, respectively, and the the phase oscillation of the amplitude,magnetization the oscillation; relaxation a time is the of offsetmagnetization, of background; the frequency and b and of oscillation,t0 are the amplitude and the phase and decay of the time magnetization parameters oscillation; of the pulse-likea is the signal,offset ofcharactering background; the and slowb and recoveryt0 are theprocess. amplitude Earlier and studies decay reported time parameters that the pulse-like of the pulse-like signal whichsignal, persists charactering above the the slow Curie recovery temperature process. is Earlier related studies to the reported recovery that process the pulse-like of nonequilibrium signal which electron–holepersists above pairs the Curie in the temperature GaAs substrate is related [10,28], to the an recoveryd only the process oscillatory of nonequilibrium part is directly electron–hole related to thepairs inferromagnetic the GaAs substrate order [ 10,of28 ], and(Ga,Mn)As only the oscillatory[12]. The part numerical is directly relatedfitting to theresult ferromagnetic by the Landau-Lifshitz-Gilbertorder of (Ga,Mn)As [12]. (LLG) The numerical equation shown fitting resultin Figu byre the 1b Landau-Lifshitz-Gilbertis focused on the precession (LLG) part equation of the observedshown in Kerr Figure rotation,1b is focused which on reflects the precession the unifor partm precession of the observed of magnetization Kerr rotation, in which the annealed reflects (Ga,Mn)Asthe uniform film precession [21]. The of collective magnetization spin excitation in the annealed and modulation (Ga,Mn)As of film the [dynamics21]. The collectiveof precession spin discussedexcitation below and modulation will mainly of focus the dynamics on the characteristics of precession of discussed the oscillatory below signal will mainlymodulated focus by on laser the excitation.characteristics of the oscillatory signal modulated by laser excitation.

FigureFigure 1. (Color(Color online) TemporalTemporal profileprofile of of Kerr Kerr rotation rotation excited excited by by linearly-polarized linearly-polarized pump pump beam beam at at1.58 1.58 eV eV with with an excitationan excitation intensity intensity of 10.9 ofµ J/cm10.9 2μforJ/cm the2 for annealed the annealed (Ga,Mn)As (Ga,Mn)As sample. sample. (a) The solid (a) The line solid(red color)line (red shows color) the shows best fit the by best an exponentially-damped fit by an exponentially-damped sine function. sine (b function.) The solid (b line) The (blue solid color) line (blueshows color) numerical shows fitting numerical result fitting to LLG result equation. to LLG Theequation. initial The pulse-like-signal initial pulse-like-signal persists to persists abovethe to aboveCurie temperature,the Curie temperature, and is associated and is associated with non-equilibrium with non-equilibrium electron–hole electron–hole pairs in the pairs GaAs in the substrate. GaAs substrate.The fitting The is focused fitting on is thefocused oscillatory on the part oscillato of the Kerrry part rotation, of the which Kerr represents rotation, awhich uniform represents precession a uniformof magnetization precession in of the magnetization (Ga,Mn)As film in the [21 ].(Ga,Mn)As film [21]. Appl. Sci. 20182018,, 88,, x 1880 FOR PEER REVIEW 44 of of 10 10

The observed dependences of the precession frequency and precession amplitude on pump intensityThe are observed shown dependencesin Figure 2. One of thecanprecession clearly see frequencythe nonlinear and behavior precession of precession amplitude frequency on pump andintensity precession are shown amplitude in Figure as2 the. One pump can clearlyintensity see increasing the nonlinear from behavior 1.8 μJ/cm of2 precession to 28 μJ/cm frequency2. According and 2 2 toprecession the LLG amplitude equation, as it the is pumpthe total intensity effective increasing magnetic from field 1.8 µ J/cmthat determinesto 28 µJ/cm the. According precession to theof magnetization.LLG equation, itIn is theprinciple, total effective the total magnetic effective field magnetic that determines field includes the precession the exchange of magnetization. field, the demagnetizationIn principle, the totalfield, effective the external magnetic magnetic field includes field, and the magnetic exchange anisotropy field, the demagnetization fields [4]. Since field, the precessionthe external and magnetic relaxation field, of and hole magnetic spins ar anisotropye much faster fields than [4]. those Since of the Mn precession spin, the and p-d relaxationexchange fieldof hole itself spins cannot are muchaffect fasterthe precession than those frequency of Mn spin, [19,29]. the Additionally,p-d exchange fieldthe signal itself of cannot magnetization affect the precession frequencyhas no relationship [19,29]. Additionally, to the nonequilibrium the signal of magnetization electron-hole precession pairs that has could no relationship also be generatedto the nonequilibrium in GaAs substrate electron-hole [12,30]. pairsMoreover, that couldthe ultrafast also be demagn generatedetization in GaAs is characterized substrate [12, 30by]. theMoreover, subpicosecond the ultrafast time demagnetizationscale, so it will not is influe characterizednce the magnetization by the subpicosecond precession time on scale, the time so it scale will ofnot hundreds influence of the picoseconds magnetization either precession [27,31]. Therefore, on the time when scale the of hundreds external magnetic of picoseconds field is either absent, [27 it,31 is]. theTherefore, optical whenexcitation the external induced magnetic by magnetic field anisotro is absent,py it field is the modulation optical excitation that mainly induced determines by magnetic the valueanisotropy of precession field modulation frequency. that That mainly is, the determines optical absorption the value results of precession in a transient frequency. variation That of is, magneticthe optical anisotropy absorption fields results (and in thus a transient of the variationmagnetization) of magnetic in the anisotropy(Ga,Mn)As fieldslayer due (and to thus transient of the variationmagnetization) of both in the the lattice (Ga,Mn)As temperature layer due and to photo- transientexcited variation carrier of density. both the Thus, lattice the temperature thermal effect and arisingphoto-excited from laser carrier heating density. and Thus, the non-thermal the thermal effecteffect arising due to from photo-excitation laser heating of and carriers the non-thermal can affect theeffect frequency due to photo-excitation of magnetization of pr carriersecession can by affect respective the frequency changes of in magnetization magnetic anisotropy precession fields by causedrespective by these changes two in pr magneticocesses [13,14,21,23]. anisotropy fields caused by these two processes [13,14,21,23].

Figure 2.2. (Color(Color online) online) Precession Precession frequency frequency and and precession precession amplitude amplitude as a function as a function of pump of intensity pump intensityfor the annealed for the annealed sample, obtainedsample, obtained with linearly-polarized with linearly-polarized 1.58 eV pump1.58 eV beam pump at beam 10 K. Noat 10 external K. No externalmagnetic magnetic field was field applied. was Pumpapplied. intensity Pump wasintensity varied was from varied 1.8 µ J/cmfrom 21.8to 28μJ/cmµJ/cm2 to2 28. The μJ/cm extended2. The extendedgrey dashed grey line dashed and grey line dash-dotted and grey are dash-do drawntted to clearly are drawn show theto nonlinearclearly show dependence the nonlinear of both dependencethe precession of frequencyboth the precession and the amplitude frequency on and pump the amplitude intensity. on pump intensity.

According to to ferromagnetic ferromagnetic resonance resonance (FMR) (FMR) meas measurements,urements, magnetic magnetic anis anisotropyotropy fields fields are are a functiona function of oftemperature temperature and and carrier carrier density density [14,32]. [14,32 For]. Forthe investigated the investigated (Ga,Mn)As (Ga,Mn)As thin thinfilms, films, our previousour previous ferromagnetic ferromagnetic resonance resonance (FMR) (FMR) measurem measurementent has has revealed revealed that: that: the the increase increase of of both H p H p temperaturetemperature andand holehole densitydensity leads leads to to a a decrease decrease of of in-plane in-plane anisotropy anisotropy fields fields4|| H(T,4||(T,) andp) and2|| H(T,2||(T,); πM pThe); The out-of-plane out-of-plane anisotropy anisotropy field 4fieldeff 4isπ alsoMeff reducedis also reduced by increasing by increasing temperature, temperature, but is increased but byis increasedthe increase by ofthe hole increase concentration of hole concentration that results from that annealingresults from [21 annealing]. [21]. For our annealed (Ga, Mn)As thin film, film, we esti estimatemate that a temperature increase could induce πM H H average decreases ofof 44πMeffeff,, H4||4|| and H2|| byby about about 21.51 Oe/K, 11.89 Oe/K and and 0.45 Oe/K,Oe/K, respectively.respectively. In In addition addition to the to thetemperature temperature influe influence,nce, about about20% increase 20% increase in carrier in density carrier (~20% density × 20 −3 20 ×−3 πM p 10(~20% cm )10 causedcm by) causedannealing by annealingresults in resultsan average in an increase average increaseof 4πMeff of (p 4) of effabout( ) of 635.61 about Oe, 635.61 but Oe, in decreasesbut in decreases of H4||( ofp) Hand4|| (Hp2||) and(p) ofH 2||about(p) of392.3 about Oe 392.3and 148.85 Oe and Oe, 148.85 respectively. Oe, respectively. Appl. Sci. 2018, 8, 1880 5 of 10 Appl. Sci. 2018, 8, x FOR PEER REVIEW 5 of 10

NoteNote that that the increasethe increase of pump of pump intensity intensity from from 1.8 µ 1.8J/cm μJ/cm2 to 282 toµ 28J/cm μJ/cm2 at21.58 at 1.58 eV iseV observed is observed to to − − causecause an increasean increase of phototexcited of phototexcited carrier carrier concentration concentration of about of about 30 × 103017 ×cm 10173 –120cm−3–120× 10 17× 10cm17 3cm, −3, basedbased on pulseon pulse absorption absorption of photonof photon energy. energy. It It can can then then be be estimated estimated that that this this 3–12% 3–12% increaseincrease of of photoexcitedphotoexcited carrier carrier density density due due to tooptical optical absorption absorption results results in an inincrease an increase of 4πMeff of of 4 aboutπMeff 95.34–of about381.4 95.34–381.4 Oe, and Oe,in decreases and in decreasesof H4|| and of HH2||4|| ofand aboutH2|| 58.84–235.38of about 58.84–235.38Oe and 22.33–89.31 Oe and Oe, 22.33–89.31respectively. Oe, respectively. It isIt known is known that thethat lattice the lattice constant constant of the of zinc the blende zinc blende (Ga,Mn)As (Ga,Mn)As is larger is thanlarger that than of GaAs,that of so GaAs, that so the (Ga,Mn)Asthat the (Ga,Mn)As film is compressively film is compressively strained when strained epitaxily when grown epitaxily on GaAs grown substrate, on GaAs as sketched substrate, in as Figuresketched3[ 33]. in For Figure the compressively-strained 3 [33]. For the compressively-st (Ga,Mn)Asrained film (Ga,Mn)As studied in thisfilm work, studied the in influence this work, of the magneticinfluence anisotropy of magnetic field modulation anisotropyon field magnetization modulation precession on magnetization frequency precession can be directly frequency described can be by thedirectly expression described for theby FMRthe expression frequency. for With the the FMR magnetization frequency. With lying the in themagnetization plane of the lying sample, in the the precessionplane of the frequency sample, the can precession be expressed frequency as [32,34 can]: be expressed as [32,34]:  2  ∥ ω = 4 + H+2k , (2) = H 4∥πM +H +∥ , (2) γ 4k e f f 4k 2 where γ is the gyromagnetic ratio (γ = 1.7588 Hz/Oe for g factor = 2.0023); H4|| and H2|| are the wherein-planeγ is the cubic gyromagnetic and uniaxial ratio anisotropy (γ = 1.7588 fields, Hz/Oe respectively; for g factor and = 4 2.0023);πMeff is theH4|| effectiveand H 2||perpendicularare the in-planeuniaxial cubic anisotropy and uniaxial field, anisotropy 4πMeff = 4 fields,πM − H respectively;2⊥, where H2 and⊥ is 4theπM out-of-planeeff is the effective perpendicular perpendicular uniaxial uniaxialanisotropy anisotropy field. field, When 4π Mtheeff =pump 4πM −intensityH2⊥, where increaHses,2⊥ is the the in-plane out-of-plane magnetocrystalline perpendicular uniaxialanisotropy anisotropyfields H field.4|| and When H2|| the are pump observed intensity to increases, decrease the monotonically, in-plane magnetocrystalline presumably anisotropydue to increasing fields H4||temperatureand H2|| are and observed increasing to decrease carrier density monotonically, caused presumablyby increase of due pump to increasing intensity. temperature On the other and hand, increasingthe dependence carrier density of 4 causedπMeff on by increasetemperature of pump and intensity.carrier density On the othershows hand, variations the dependence in opposite of 4directionsπMeff on temperature(as argued andabove, carrier 4πM densityeff decreases shows with variations increasing in opposite temperature, directions but increases (as argued with above,increasing 4πMeff decreasescarrier density). with increasing This indicates temperature, that the but magnetization increases with precession increasing frequency carrier density). decreases Thislinearly indicates when that thethe magnetizationdecreasing ofprecession in-plane magnetic frequency anisotropy decreases linearly field dominates when the decreasingthe behavior of of in-planemagnetization magnetic anisotropyprecession field either dominates through the thermal behavior or of nonthermal magnetization effects. precession This eitherinfluence through of the thermalin-plane or nonthermal magnetic effects.anisotropy This field, influence however, of the in-planecannot explain magnetic the anisotropy nonlinear field, dependence however, of cannotprecession explain thefrequency nonlinear on dependencepump intensity of precession shown in frequency Figure 2. onThus, pump the intensity strong increase shown in of Figure 4πMeff2 .due Thus,to theincreasing strong increase photoexcited of 4πM carriereff due density to increasing offers photoexcited the possibility carrier of slowing density down offers the the rate possibility of decline of slowingof magnetization down the rateprecession of decline frequency. of magnetization precession frequency.

FigureFigure 3. Coordinate 3. Coordinate system system used used in this in this paper. paper. The The initial initial magnetization magnetization lies lies in the in planethe plane of the of the samplesample along along [100] [100] direction. direction. The [100]The [100] direction, direction, [010] direction[010] direction and [001] and direction [001] direction are defined are defined as the as

directionsthe directions of x axis, ofy axis,x axis, and y zaxis,axis, and respectively. z axis, respectively. The magnetic The anisotropy magnetic fieldanisotropyHx-y is infield the H planex-y is ofin the the film,plane and of the magneticfilm, and anisotropythe magnetic field anisotropyHz is out field of the H planez is out of of the the film. plane The of arrows the film. in (Ga,Mn)AsThe arrows in layer(Ga,Mn)As represent thelayer direction represent of compressivethe direction strainof compressive in the plane. strain in the plane.

To obtainTo obtain a quantitative a quantitative insight insight into into the the nonlinear nonlinear influence influence of in-planeof in-plane and and out-of-plane out-of-plane magneticmagnetic anisotropy anisotropy fields onfields magnetization on magnetization precession, precession, the magnetization the magnetization precession was precession numerically was simulatednumerically by employing simulated LLG by equationemploying combined LLG equation with two combined different with MO two effects, different polar MO Kerr effects, rotation polar Appl. Sci. 2018, 8, 1880 6 of 10 Appl. Sci. 2018, 8, x FOR PEER REVIEW 6 of 10 andKerr magnetic rotation birefringenceand magnetic (LLG-2MO)birefringence [ 13(LLG-2MO),23]. The micromagnetic[13,23]. The micromagnetic modeling could modeling be expressed could asbe [14 expressed,28,35] as [14,28,35] * * ∂M * * α * ∂M ==−−γM××H + M ×× , ,(3) (3) ∂t e f f M ∂t wherewhereM Mis theis the local local magnetization magnetization contributed contributed from from Mn ions,Mn ions,Heff is H theeff is effective the effective field (which field (which includes theincludes in-plane the in-plane and out-of-plane and out-of-plane anisotropy anisotropy fields), fields), and andα isα is the the GilbertGilbert damping damping coefficient. coefficient. ForFor compressively-strained compressively-strained (Ga,Mn)As(Ga,Mn)As films, films, the in initialitial magnetization magnetization before before excitation excitation lies lies along along thethe easy easy axesaxes directiondirection in the the plane plane of of the the sample. sample. In Inthe the simulation simulation program, program, the initial the initial state stateof the of themagnetization magnetization is set is to set be to along be along the x the axis x in axis the in x-y the planex-y plane(i.e., in (i.e., the plane in the of plane the film), of the and film), z axis and is z axisnormal is normal to the tofilm the plane, film plane,as seen as in seenFigure in 3. Figure Thus,3 .H Thus,x-y and HHx-yz correspondand Hz correspond to the effect to of the H effect4|| and of H44||πMandeff, respectively. 4πMeff, respectively. δHx-y andδH x-yδHandz correspondδHz correspond to the to modulated the modulated value value of ofH4||H 4||andand 4π 4πMMeff,eff , respectively.respectively. The The totaltotal magneto-opticalmagneto-optical signal is th thee combined response response caused caused by by the the out-of-plane out-of-plane componentcomponent ofof thethe magnetization,magnetization, which is sensed by by the the polar polar Kerr Kerr effect effect (PKE), (PKE), together together with with the the in-planein-plane component component ofof thethe magnetization,magnetization, which is is sensed sensed mainly mainly by by the the magnetic magnetic birefringence birefringence for for whichwhich the the magnetization-induced magnetization-induced refractive refractive index index change change is is sufficiently sufficiently significant significant to to contribute contribute to to the observedthe observed MO signal MO insignal (Ga,Mn)As in (Ga,Mn)As film [36 –film39]. To[36–39]. avoid complicationsTo avoid complications arising from arising the superposition from the superposition of PKE and MB in the gyromagnetic calculation, we analyze the behavior of Mz and of PKE and MB in the gyromagnetic calculation, we analyze the behavior of Mz and Mx-y components separately.Mx-y components For details separately. regarding For thedetails gyromagnetic regarding the theory gyromagnetic and the simulation, theory and we the refer simulation, the reader we to refer the reader to Reference [13]. Reference [13]. In Figure 4, the LLG-2MO calculation results show that the precession frequency is a linear In Figure4, the LLG-2MO calculation results show that the precession frequency is a linear function of the in-plane magnetic anisotropy field Hx-y. These results suggest that, as the pump function of the in-plane magnetic anisotropy field Hx-y. These results suggest that, as the pump intensity increases, the reduction of the in-plane magnetic anisotropy field caused either by laser intensity increases, the reduction of the in-plane magnetic anisotropy field caused either by laser heating or by increasing carrier density only contributes to a linear decrease of precession frequency. heating or by increasing carrier density only contributes to a linear decrease of precession frequency. However, Figure 5 shows an increase of the out-of-plane magnetic anisotropy field Hz can lead to However, Figure5 shows an increase of the out-of-plane magnetic anisotropy field H can lead to an exponential increase of the precession frequency. From the FMR results, we note thatz only the an exponential increase of the precession frequency. From the FMR results, we note that only the out-of-plane anisotropy field increases due to the non-thermal effect of increasing carrier out-of-plane anisotropy field increases due to the non-thermal effect of increasing carrier concentration concentration due to the increase of pump intensity. Thus, the decrease of magnetization precession duefrequency to the increase can be ofregarded pump intensity.as a slow-down Thus, the caused decrease by ofan magnetizationincrease of the precession out-of-plane frequency magnetic can beanisotropy regarded asfield a slow-downthat follows caused from the by anincrease increase of ofcarrier the out-of-plane density due magneticto optical anisotropy excitation. fieldIn this that followscase, we from conclude the increase that the of nonlinear carrier density variation due of to the optical precession excitation. frequency In this shown case, we in concludeFigure 2 results that the nonlinearmainly from variation the ofnon-thermal the precession contribution frequency shownof photoexcited in Figure2 resultscarriers mainly and fromtheir theeffect non-thermal on the contributionout-of-plane ofmagnetic photoexcited anisotropy carriers field. and It theirshould effect be noted on the that out-of-plane the increase magnetic of photoexcited anisotropy carrier field. Itdensity should causes be noted an thatincrease the increasein the value of photoexcited of 4πMeff of about carrier 380 density Oe, but causes laser heating an increase causes in thea decrease value of 4πinM 4effπMofeff about of about 380 21 Oe, Oe/K. but laser If we heating ignore causesthe saturation a decrease for inthermal 4πMeff effects,of about optical 21 Oe/K. excitation If we at ignore an 2 theintensity saturation of 15 for μJ/cm thermal2 leads effects, to a opticallocal lattice excitation temperature at an intensity increase of of 15 10µ J/cmK basedleads on earlier to a local studies lattice temperature[12]. increase of 10 K based on earlier studies [12].

FigureFigure 4. 4.(Color (Color online) online) PrecessionPrecession frequencyfrequency simulated by by LLG LLG equation equation as as a afunction function the the in-plane in-plane

magneticmagnetic anisotropy anisotropy fieldfieldH Hx-yx-y for annealed compressively-strained compressively-strained (Ga,Mn)As (Ga,Mn)As film. film. Appl. Sci. 2018, 8, 1880 7 of 10 Appl. Sci. 2018, 8, x FOR PEER REVIEW 7 of 10

FigureFigure 5. 5. (Color(Color online) online) LLG LLG simulation simulation of magnetizatio of magnetizationn precession precession frequency frequency as a function as a function of the

modulatedof the modulated value valueof out-of-plane of out-of-plane magnetic magnetic anisotropy anisotropy field field (δH (δz)H z)for for the the annealed annealed compressively-strainedcompressively-strained (Ga,Mn)As (Ga,Mn)As film. film. The The inset inset shows shows details details of of precession precession frequency frequency changes changes nearnear zero zero field. field. 4. Discussion 4. Discussion As shown in Figure2, with the pump intensity varying from 1.8 µJ/cm2 to 28 µJ/cm2, the joint As shown in Figure 2, with the pump intensity varying from 1.8 μJ/cm2 to 28 μJ/cm2, the joint thermal and non-thermal effects associated with the incident pulses cause the precession frequency thermal and non-thermal effects associated with the incident pulses cause the precession frequency to decrease by about 17.5 GHz. Although it is difficult to distinguish the accurate proportion of the to decrease by about 17.5 GHz. Although it is difficult to distinguish the accurate proportion of the thermal and nonthermal effects, the 3 GHz slowdown by 4πMeff could be considered as the nonthermal thermal and nonthermal effects, the 3 GHz slowdown by 4πMeff could be considered as the contribution due to photoexcited carriers. We can therefore estimate that at least 17% of the observed nonthermal contribution due to photoexcited carriers. We can therefore estimate that at least 17% of effect on the precession frequency can be ascribed to nonthermal causes. the observed effect on the precession frequency can be ascribed to nonthermal causes. As already shown in Figure2, the increase of precession amplitude is accelerated near the As already shown in Figure 2, the increase of precession amplitude is accelerated near the same pump intensity as the accelerated reduction of precession frequency. We simulated the change same pump intensity as the accelerated reduction of precession frequency. We simulated the of magnetization precession under different in-plane and out-of-plane magnetic anisotropy fields. change of magnetization precession under different in-plane and out-of-plane magnetic anisotropy The extracted oscillation amplitude presents the change of amplitude with Hz and Hx-y in opposite fields. The extracted oscillation amplitude presents the change of amplitude with Hz and Hx-y in directions, as shown in Figure6. When pump intensity increases from 1.8 µJ/cm2 to 28 µJ/cm2, opposite directions, as shown in Figure 6. When pump intensity increases from 1.8 μJ/cm2 to 28 the decrease of in-plane magnetic anisotropy field is accompanied by a linear increase in precession μJ/cm2, the decrease of in-plane magnetic anisotropy field is accompanied by a linear increase in amplitude. Thus, the nonlinear variation of precession amplitude seen in Figure2 cannot be ascribed precession amplitude. Thus, the nonlinear variation of precession amplitude seen in Figure 2 cannot only to the change of in-plane magnetic anisotropy field. Recall that the increase of pump intensity be ascribed only to the change of in-plane magnetic anisotropy field. Recall that the increase of decreases the out-of-plane magnetic anisotropy field through laser heating, but increases it through pump intensity decreases the out-of-plane magnetic anisotropy field through laser heating, but the increase of carrier concentration. In addition to the calculated results in Figure6, only the increase increases it through the increase of carrier concentration. In addition to the calculated results in of out-of-plane magnetic anisotropy field can lead to an increase of the oscillation amplitude. Thus, Figure 6, only the increase of out-of-plane magnetic anisotropy field can lead to an increase of the the accelerated increase of precession amplitude shown in Figure2 can result from the increase of oscillation amplitude. Thus, the accelerated increase of precession amplitude shown in Figure 2 can the out-of-plane magnetic anisotropy field. It is therefore suggested that non-thermal effects have result from the increase of the out-of-plane magnetic anisotropy field. It is therefore suggested that the distinct advantage over thermal effects for manipulating the out-of-plane magnetic anisotropy non-thermal effects have the distinct advantage over thermal effects for manipulating the field through pump intensity variation. This conclusion also supports our analysis above, i.e., out-of-plane magnetic anisotropy field through pump intensity variation. This conclusion also that non-thermal effects due to photo-carrier excitation could effectively influence magnetization supports our analysis above, i.e., that non-thermal effects due to photo-carrier excitation could precession by their effect on the out-of-plane magnetic anisotropy field. effectively influence magnetization precession by their effect on the out-of-plane magnetic anisotropy field. Appl. Sci. 2018, 8, 1880 8 of 10 Appl. Sci. 2018, 8, x FOR PEER REVIEW 8 of 10

Figure 6.6.(Color (Color online) online) Oscillation Oscillation amplitude amplitude of magnetization of magnetization precession precession as a function as a offunction modulated of modulatedvalue of out-of-plane value of out-of-plane (a) and in-plane (a) and (b) magneticin-plane ( anisotropyb) magnetic fields anisotropy for the annealed fields for and the compressivelyannealed and compressivelystrained (Ga, Mn)As strained thin (Ga, film, Mn)As obtained thin byfilm, LLG obtained simulation. by LLG simulation. 5. Conclusions 5. Conclusions We report a study of photoinduced collective spin excitation and their dynamics in ferromagnetic We report a study of photoinduced collective spin excitation and their dynamics in (Ga,Mn)As using time-resolved magneto-optical spectroscopy. Our observations indicate the effectiveness ferromagnetic (Ga,Mn)As using time-resolved magneto-optical spectroscopy. Our observations of non-thermal photo-carrier excitation via its effect on magnetization precession. For the (Ga,Mn)As indicate the effectiveness of non-thermal photo-carrier excitation via its effect on magnetization films with in-plane compressive strain, the non-thermal modulation arising through out-of-plane precession. For the (Ga,Mn)As films with in-plane compressive strain, the non-thermal modulation magnetic anisotropy field causes a nonlinear influence on precession frequency and precession arising through out-of-plane magnetic anisotropy field causes a nonlinear influence on precession amplitude. Our results reveal the existence of a competing path of non-thermal effects occurring via frequency and precession amplitude. Our results reveal the existence of a competing path of out-of-plane magnetic anisotropy field, providing direct experimental evidence for the possibility of non-thermal effects occurring via out-of-plane magnetic anisotropy field, providing direct ultrafast nonthermal manipulation of magnetization dynamics in ferromagnetic (Ga,Mn)As by linearly experimental evidence for the possibility of ultrafast nonthermal manipulation of magnetization polarized optical pulse excitation. dynamics in ferromagnetic (Ga,Mn)As by linearly polarized optical pulse excitation. Author Contributions: H.L., X.Z. and X.L. conceived and designed this work. X.L., M.D. and J.F. prepared and Authorcharacterized Contributions: the sample. H.L., H.L. X.Z. performed and X.L. the conceived experiment and anddesigned analyzed this thework. results. X.L., H.L., M.D. X.Z. andand J.F. X.L.prepared wrote and the characterizedmanuscript. All the authors sample. have H.L. reviewed performed and the commented experiment on and the manuscript.analyzed the results. H.L., X.Z. and X.L. wrote theFunding: manuscript.This workAll authors was supportedhave reviewed by the and National commented Key on R&D the manuscript. Program of China (No. 2017YFB0405700), the National Natural Science Foundation of China (No. 81601855), and Foundation of Liaoning Educational Funding: This work was supported by the National Key R&D Program of China (No. 2017YFB0405700), the Committee (No. L2016036). The work at Notre Dame was supported by the NSF Grant DMR14-00432. National Natural Science Foundation of China (No. 81601855), and Foundation of Liaoning Educational CommitteeAcknowledgments: (No. L2016036).We acknowledge The work T.at MatsudaNotre Dame and was H. Munekata supported for by their the guidanceNSF Grant in DMR14-00432. analyzing magnetization precession data with LLG-2MO simulation. Acknowledgments: We acknowledge T. Matsuda and H. Munekata for their guidance in analyzing Conflicts of Interest: The authors declare no conflict of interest. magnetization precession data with LLG-2MO simulation. ConflictsReferences of Interest: The authors declare no conflict of interest.

References1. Hillebrands, B.; Ounadjela, K. Spin Dynamics in Confined Magnetic Structures I; Springer: Berlin/Heidelberg, Germany, 2002; ISBN 978-3-540-40907-6. 1.2. Hillebrands,Ramsay, A.J.; B.; Roy, Ounadjela, P.E.; Haigh, K. Spin J.A.; Dynamics Otxoa, R.M.;in Confined Irvine, Magnetic A.C.; Janda, Structures T.; Campion, I; Springer: R.P.; Berlin/Heidelberg, Gallagher, B.L.; Germany,Wunderlich, 2002; J. Optical ISBN 978-3-540-40907-6. Spin-Transfer-Torque-Driven Domain-Wall Motion in a Ferromagnetic Semiconductor. 2. Ramsay,Phys. Rev. A.J.; Lett. Roy,2015 P.E.;, 114 ,Haigh, 067202. J.A.; [CrossRef Otxoa,][ R.M.;PubMed Irvine,] A.C.; Janda, T.; Campion, R.P.; Gallagher, B.L.; 3. Wunderlich,Muneta, I.; Kanaki,J. Optical T.; Ohya,Spin-Transfer-Torque-D S.; Tanaka, M. Artificialriven Domain-Wall control of theMotion bias-voltage in a dependenceFerromagnetic of Semiconductor.tunnelling-anisotropic Phys. Rev. magnetoresistance Lett. 2015, 114, 067202, using quantization doi:10.1103/PhysRevLett.114.067202. in a single-crystal ferromagnet. Nat. Commun. 3. Muneta,2017, 8, 15387.I.; Kanaki, [CrossRef T.; ][Ohya,PubMed S.;] Tanaka, M. Artificial control of the bias-voltage dependence of 4. tunnelling-anisotropicKirilyuk, A.; Kimel, A.V.; magnetoresistance Rasing, T. Ultrafast using optical quantization manipulation in of magnetica single-crystal order. Rev. ferromagnet. Mod. Phys. 2010Nat., Commun.82, 2731–2784. 2017, [8CrossRef, 15387, doi:10.1038/ncomms15387.] 4. Kirilyuk, A.; Kimel, A.V.; Rasing, T. Ultrafast optical manipulation of magnetic order. Rev. Mod. Phys. 2010, 82, 2731–2784, doi:10.1103/RevModPhys.82.2731. Appl. Sci. 2018, 8, 1880 9 of 10

5. Lao, Y.F.; Perera, A.G.U.; Wang, H.L.; Zhao, J.H.; Jin, Y.J.; Zhang, D.H. Optical characteristics of p-type GaAs-based semiconductors towards applications in photoemission infrared detectors. J. Appl. Phys. 2016, 119, 105304. [CrossRef] 6. Luo, J.; Xiang, G.; Gu, G.; Zhang, X.; Wang, H.; Zhao, J. Li(Zn,Mn)As as a new generation ferromagnet based on a I–II–V semiconductor. J. Magn. Magn. Mater. 2017, 422, 124. [CrossRef] 7. Jungwirth, T.; Sinova, J.; Mašek, J.; Kuˇcera, J.; MacDonald, A.H. Theory of ferromagnetic (III,Mn)V semiconductors. Rev. Mod. Phys. 2006, 78, 809. [CrossRef] 8. Dietl, T. A ten-year perspective on dilute magnetic semiconductors and oxides. Nat. Mater. 2010, 9, 965–974. [CrossRef][PubMed] 9. Li, H.; Zhang, X.; Liu, X.; Furdyna, J.K. The observation of phase reversal in photo-induced coherent spin dynamics in ferromagnetic semiconductor (Ga,Mn)As thin film. Solid State Commun. 2015, 221, 45. [CrossRef] 10. Nˇemec,P.; Rozkotová, E.; Tesaˇrová, N.; Trojánek, F.; DeRanieri, E.; Olejník, K.; Zemen, J.; Novák, V.; Cukr, M.; Malý, P.; et al. Experimental observation of the optical spin transfer torque. Nat. Phys. 2012, 8, 411. [CrossRef] 11. Qi, J.; Xu, Y.; Tolk, N.H.; Liu, X.; Furdyna, J.K.; Perakis, I.E. Coherent magnetization precession in GaMnAs induced by ultrafast optical excitation. Appl. Phys. Lett. 2007, 91, 112506. [CrossRef] 12. Rozkotová, E.; Nˇemec,P.; Horodyská, P.; Sprinzl, D.; Trojánek, F.; Malý, P.; Novák, V.; Olejník, K.; Cukr, M.; Jungwirth, T. Light-induced magnetization precession in GaMnAs. Appl. Phys. Lett. 2008, 92, 122507. [CrossRef] 13. Hashimoto, Y.; Kobayashi, S.; Munekata, H. Photoinduced Precession of Magnetization in Ferromagnetic (Ga,Mn)As. Phys. Rev. Lett. 2008, 100, 067202. [CrossRef][PubMed] 14. Qi, J.; Xu, Y.; Steigerwald, A.; Liu, X.; Furdyna, J.K.; Perakis, I.E.; Tolk, N.H. Ultrafast laser-induced coherent

spin dynamics in ferromagnetic Ga1−xMnxAs/GaAs structures. Phys. Rev. B 2009, 79, 085304. [CrossRef] 15. Guidoni, L.; Beaurepaire, E.; Bigot, J.-Y. Magneto-optics in the Ultrafast Regime: Thermalization of Spin Populations in Ferromagnetic Films. Phys. Rev. Lett. 2002, 89, 017401. [CrossRef][PubMed] 16. Stamm, C.; Kachel, T.; Pontius, N.; Mitzner, R.; Quast, T.; Holldack, K.; Khan, S.; Lupulescu, C.; Aziz, E.F.; Wietstruk, M.; et al. Femtosecond modification of electron localization and transfer of angular momentum in nickel. Nat. Mater. 2007, 6, 740–743. [CrossRef][PubMed] 17. Müller, G.M.; Walowski, J.; Djordjevic, M.; Miao, G.-X.; Gupta, A.; Ramos, A.V.; Gehrke, K.; Moshnyaga, V.; Samwer, K.; Schmalhorst, J.; et al. Spin polarization in half-metals probed by femtosecond spin excitation. Nat. Mater. 2009, 8, 56–61. [CrossRef][PubMed] 18. Kapetanakis, M.D.; Perakis, I.E.; Wickey, K.J.; Piermarocchi, C.; Wang, J. Femtosecond Coherent Control of Spins in (Ga,Mn)As Ferromagnetic Semiconductors Using Light. Phys. Rev. Lett. 2009, 103, 047404. [CrossRef][PubMed] 19. Tesaˇrová, N.; Nˇemec,P.; Rozkotová, E.; Zemen, J.; Janda, T.; Butkoviˇcová, D.; Trojánek, F.; Olejník, K.; Novák, V.; Malý, P.; et al. Experimental observation of the optical spin–orbit torque. Nat. Photon. 2013, 7, 492–498. [CrossRef] 20. Lingos, P.C.; Wang, J.; Perakis, I.E. Manipulating femtosecond spin-orbit torques with laser pulse sequences to control magnetic memory states and ringing. Phys. Rev. B 2015, 91, 195203. [CrossRef] 21. Li, H.; Liu, X.; Zhou, Y.; Furdyna, J.K.; Zhang, X. Collective magnetization dynamics in ferromagnetic (Ga,Mn)As mediated by photoexcited carriers. Phys. Rev. B 2015, 91, 195204. [CrossRef] 22. Hashimoto, Y.; Munekata, H. Coherent manipulation of magnetization precession in ferromagnetic semiconductor (Ga,Mn)As with successive optical pumping. Appl. Phys. Lett. 2008, 93, 202506. [CrossRef] 23. Matsuda, T.; Munekata, H. Mechanism of photoexcited precession of magnetization in (Ga,Mn)As on the basis of time-resolved spectroscopy. Phys. Rev. B 2016, 93, 075202. [CrossRef] 24. Hamaya, K.; Watanabe, T.; Taniyama, T.; Oiwa, A.; Kitamoto, Y.; Yamazaki, Y. Magnetic anisotropy switching in (Ga,Mn)As with increasing hole concentration. Phys. Rev. B 2006, 74, 045201. [CrossRef] 25. Oiwa, A.; Takechi, H.; Munekata, H. Photoinduced Magnetization Rotation and Precessional Motion of Magnetization in Ferromagnetic (Ga,Mn)As. J. Supercond. 2005, 18, 9. [CrossRef] 26. Takechi, H.; Oiwa, A.; Nomura, K.; Kondo, T.; Munekata, H. Light-induced precession of ferromagnetically coupled Mn spins in ferromagnetic (Ga,Mn)As. Phys. Status Solidi C 2006, 3, 4267–4270. [CrossRef] 27. Wang, J.; Cotoros, I.; Dani, K.M.; Liu, X.; Furdyna, J.K.; Chemla, D.S. Ultrafast Enhancement of Ferromagnetism via Photoexcited Holes in GaMnAs. Phys. Rev. Lett. 2007, 98, 217401. [CrossRef][PubMed] Appl. Sci. 2018, 8, 1880 10 of 10

28. Chovan, J.; Perakis, I.E. Femtosecond control of the magnetization in ferromagnetic semiconductors. Phys. Rev. B 2008, 77, 085321. [CrossRef] 29. Qi, J.; Xu, Y.; Liu, X.; Furdyna, J.K.; Perakis, I.E.; Tolk, N.H. Control of coherent magnetization precession in GaMnAs by ultrafast optical excitation. Phys. Status Solidi C 2008, 5, 2637–2640. [CrossRef] 30. Lochtefeld, A.J.; Melloch, M.R.; Chang, J.C.P.; Harmon, E.S. The role of point defects and arsenic precipitates in carrier trapping and recombination in low-temperature grown GaAs. Appl. Phys. Lett. 1996, 69, 1465. [CrossRef] 31. Wang, J.; Sun, C.; Hashimoto, Y.; Kono, J.; Khodaparast, G.A.; Cywinski, L.; Sham, L.J.; Sanders, G.D.; Stanton, C.J.; Munekata, H. Ultrafast magneto-optics in ferromagnetic III–V semiconductors. J. Phys. Condens. Matter 2006, 18, R501. [CrossRef] 32. Welp, U.; Vlasko-Vlasov, V.K.; Liu, X.; Furdyna, J.K.; Wojtowicz, T. Magnetic Domain Structure and Magnetic

Anisotropy in Ga1−xMnxAs. Phys. Rev. Lett. 2003, 90, 167206. [CrossRef][PubMed] 33. Ohno, H.; Shen, A.; Matsukara, F.; Oiwa, A.; Endo, A.; Katsumoto, S.; Iye, Y. (Ga,Mn)As: A new diluted magnetic semiconductor based on GaAs. Appl. Phys. Lett. 1996, 69, 363. [CrossRef]

34. Liu, X.; Sasaki, Y.; Furdyna, J.K. Ferromagnetic resonance in Ga1−xMnxAs: Effects of magnetic anisotropy. Phys. Rev. B 2003, 67, 205204. [CrossRef] 35. Tserkovnyak, Y.; Fiete, G.A.; Halperin, B.I. Mean-field magnetization relaxation in conducting ferromagnets. Appl. Phys. Lett. 2004, 84, 5234. [CrossRef] 36. Tesaˇrová, N.; Nˇemec,P.; Rozkotová, E.; Šubrt, J.; Reichlová, H.; Butkoviˇcová, D.; Trojánek, F.; Malý, P.; Novák, V.; Jungwirth, T. Direct measurement of the three-dimensional magnetization vector trajectory in GaMnAs by a magneto-optical pump-and-probe method. Appl. Phys. Lett. 2012, 100, 102403. [CrossRef] 37. Kimel, A.V.; Astakhov, G.V.; Kirilyuk, A.; Schott, G.M.; Karczewski, G.; Ossau, W.; Schmidt, G.; Molenkamp, L.W.; Rasing, T. Observation of Giant Magnetic Linear Dichroism in (Ga,Mn)As. Phys. Rev. Lett. 2005, 94, 227203. [CrossRef][PubMed] 38. Tesaˇrová, N.; Šubrt, J.; Malý, P.; Nˇemec,P.; Ellis, C.T.; Mukherjee, A.; Cerne, J. High precision magnetic linear dichroism measurements in (Ga,Mn)As. Rev. Sci. Instrum. 2012, 83, 123108. [CrossRef][PubMed] 39. Al-Qadi, B.; Nishizawa, N.; Nishibayashi, K.; Kaneko, M.; Munekata, H. Thickness dependence of magneto-optical effects in (Ga,Mn)As epitaxial layers. Appl. Phys. Lett. 2012, 100, 222410. [CrossRef]

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