Collective magnetization dynamics in ferromagnetic (Ga,Mn)As mediated by photo-excited carriers

0.64 MB·English

by  Hang Li

Collective magnetization dynamics in ferromagnetic (Ga,Mn)As mediated by
photo-excited carriers
Hang Li,1 Xinyu Liu,2 Ying-Yuan Zhou,2,∗ Jacek K. Furdyna,2 and Xinhui Zhang1,†
1State Key Laboratory for Superlattices and Microstructures,
Institute of Semiconductors, Chinese Academy of Sciences, Beijing 100083, China
2Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, USA
We present a study of photo-excited magnetization dynamics in ferromagnetic (Ga,Mn)As films
5 observed by time-resolved magneto-optical measurements. The magnetization precession triggered
1 bylinearlypolarizedopticalpulsesintheabsenceofanexternalfieldshowsastrongdependenceon
0 photonfrequencywhen thephoto-excitation energy approachestheband-edgeof (Ga,Mn)As. This
2 canbeunderstood intermsofmagnetic anisotropymodulation bybothlaserheatingofthesample
n andbyhole-inducednon-thermalpaths. Ourfindingsprovideameansforidentifyingthetransition
a of laser-triggered magnetization dynamics from thermal to non-thermal mechanisms, a result that
J is of importance for ultrafast optical spin manipulation in ferromagnetic materials via non-thermal
9 paths.

]
l I. INTRODUCTION magnetization.8,14,23,24 Although the non-thermal pro-
l
a cessofmodulatingmagneticanisotropyviaphoto-excited
h
carriers has been previously suggested to be the mecha-
- Ultrafastmanipulationofcollectivespinexcitationsin
s nism of magnetization precession in (Ga,Mn)As,5,14–16
ferromagnetic materials has drawn considerable atten-
e the role of such non-thermal manipulation of mag-
m tion both for its relevance to the fundamental physics
netic dynamics with time-resolved magneto-optical ex-
of correlatedspins in non-equilibriumsituations, and for
. periments in this material is still a controversial issue,
t itspotentialforspintronicinformationprocessing.1,2The
a and requires further study. In this paper we present
m ferromagneticsemiconductor(Ga,Mn)Ashasbeenexten-
evidence for the dependence of ultrafast magnetization
sively investigated in this connection, since its magnetic
- dynamics on the photon energy of optical excitation ob-
d functionalitycanbemediatedbyelectricaloropticalcon-
served in (Ga,Mn)As by time-resolved magneto-optical
n trolofitinerantholes.3,4 The interestinultrafastmanip-
Kerr effect (TR-MOKE) experiments. A complex en-
o ulationofmagnetizationinthismaterialhasinturntrig-
c ergy dependence of photo-excited precession frequency
geredintenseresearchontime-resolvedlaserexcitationof
[ of magnetization was observed when the photon energy
coherent magnetization precession.5–17
was tuned in the immediate vicinity of the (Ga,Mn)As
1 It has been shown in earlier studies that optical exci-
band gap. Our results show that such modulation of
v
tation of magnetization precession in ferromagnetic ma-
3 magnetic anisotropy (which we ascribe to photo-excited
terials originates from transient modulation of magnetic
8 holes) constitutes an effective mechanism for controlling
0 anisotropy via thermal effects (i.e., laser heating), which theprecessionfrequencyofmagnetization,thusproviding
2 typically requires optical excitation energy densities of experimental evidence for the possibility of non-thermal
0 up to 1 mJ/cm2.18–21 However, as previously reported
mediation of magnetic dynamics via pulsed laser excita-
. for the case of (Ga,Mn)As films, excitation energy den-
1 tions.
0 sities in the µJ/cm2 range were shown to be adequate
5 for triggering coherent precession of magnetization in
1 this material.5–17 One should note here that magnetic
: anisotropy modulation via photo-induced heating is a II. EXPERIMENT
v
i slow process, not really suitable for ultrafastoptical ma-
X
nipulation of magnetization in ferromagnetic materials. A 97-nm thick Ga Mn As layer deposited on a
0.964 0.036
ar Theoreticalstudies22 suggest,however,thatnon-thermal GaAs (001) substrate was prepared by low-temperature
manipulation of delocalized or weakly localized holes molecular-beam epitaxy (LT-MBE). A piece of the sam-
(e.g.,bychangingtheholedensityofstatesbycircularly- ple was additionally annealed at 250◦C in N for one
2
polarized laser pulses) provides an alternate method for hourto providea companionsample withmodifiedmag-
ultrafast manipulation of magnetization in (Ga,Mn)As. netic and electrical properties. The hole densities p of
Since the influence of transient increase of hole den- theas-grownandannealedsampleswereestimatedtobe,
sity and of local temperature due to laser excitation respectively, ∼2×1020 cm−3 and ∼3×1020 cm−3, with
take place immediately after optical pumping, both ef- Curie temperature T of ∼58 K and ∼79 K as deter-
C
fects contribute to triggering magnetization precession mined by superconducting quantum interference device
in (Ga,Mn)As films. However, in earlier studies differ- (SQUID) measurements. The temperature dependence
ent conclusions were reported regarding the dominant of the magnetization of the specimen is shown in Ap-
effect responsible for the transient modulation of mag- pendix. The TR-MOKE measurements were carried out
netic anisotropy that triggers the observed precession of by employing a Ti:Sapphire laser with a pulse width of
2
150fs and a repetition rateof 80 MHz. The pump beam According to the Landau-Lifshitz-Gilbert equation,
waslinearlypolarized,withexcitationenergytunedfrom the precession frequency of the magnetization is deter-
1.43 eV (865 nm) to 1.81 eV (685 nm). Pump-induced minedbythetotaleffectivemagneticfield,andthusmay
changes of the magneto-optical response of the sam- beafunctionofthephotonenergy,asarguedabove. The-
ples were measured via a time-delayed linearly polarized oretically, the effective field includes the external mag-
probe pulse. The experiments were performedin a Janis neticfield,magneticanisotropyfields,exchangefieldand
subcompact cryostat at various temperatures. No exter- demagnetization field.1 A transient change of this total
nal magnetic field was applied in the experiments. effective field will initialize the precession of the magne-
tization, and will also contribute to the precession fre-
quency. However, the exchange field itself will not affect
III. RESULTS AND ANALYSIS the precession frequency because the hole spin precesses
and relaxes much faster than the Mn spin.26,27 Thus,
Temporal evolution of the TR-MOKE response mea- in the absence of an external magnetic field, the value
sured at 10 K with an optical excitation energy of 1.54 of precessionfrequency is mainly determined by changes
eV is shownin Fig.1(a), showing aninitial pulse-likesig- in the magnetic anisotropy field induced by the optical
nal followed by exponentially damped oscillations. The pulse.
initial pulse-like signal shows no dependence on temper- The dependence of the precession frequency on mag-
ature, persisting even to above Curie temperature, as netic anisotropy fields can be obtained directly from
displayed in Fig.1(b). This temperature dependence, the expression for the ferromagnetic resonance (FMR)
along with its time scale in the range of tens of pi- frequency.24 We recall that for thin compressively-
coseconds, suggests that the pulse-like signal is related strained(Ga,Mn)Asfilmssuchasthesamplesusedinthis
to the non-equilibrium electron-hole pairs in the GaAs paper, the magnetizationlies in the plane of the sample,
substrate,10,25 rather than arising from ultrafast demag- and at low temperatures (where the cubic anisotropy is
netization, which is characterized by a sub-picosecond much stronger than the uniaxial anisotropy) aligns itself
time scale.12,14 with the in-plane cubic easy axes, i.e., with the <100>
We now focus our discussionon the oscillatory partof crystallographicdirections.28 Under these conditions the
Fig.1(a),whichrepresentstheuniformprecessionofmag- precessionfrequencyofthemagnetizationcanbewritten
netizationinthe(Ga,Mn)Asfilm.10 Thedynamicoscilla- as:29
torysignalcanbefittedwellbyanexponentiallydamped
ω H
sine function superimposed on a pulse-like function,17 ( )2 =(H+H )(H+4πM +H + 2k), (2)
γ 4k eff 4k 2
θ =a+be−t/t0 +Ae−t/τDsin(ωt+φ), (1)
k
where γ is the gyromagnetic ratio (γ = 1.7588 Hz/Oe
where A, τD, ω and φ represent, respectively, the am- for g-factor = 2.0023), H is the external magnetic field,
plitude of the oscillation,magnetization relaxationtime, H andH arethecubicanduniaxialanisotropyfields,
4k 2k
oscillationfrequency,andthephaseofthemagnetization respectively, and 4πM is the effective perpendicular
eff
precession; and a is the background offset; and b and t0 uniaxial anisotropy field, 4πMeff = 4πM −H2⊥, where
aretheamplitudeandthedampingtimeofthepulse-like H istheperpendicularuniaxialanisotropyfield. Inthe
2⊥
background in the slow recovery process, respectively. absenceofanexternalmagneticfield,theaboveequation
The magnetization precession frequency obtained by can then be simplified to:
fitting the TR-MOKEdata measuredat different photo-
excitation energies and pumping power densities in the (ω)2 =H (4πM +H + H2k). (3)
absence of an external field are shown in Fig. 2 for both γ 4k eff 4k 2
the as-grown and the annealed (Ga,Mn)As samples. We
see in Fig. 2(a) that the frequency of the magnetization In order to obtain the parameters in Eq. 3, we will
precession of the as-grown sample exhibits a nonmono- use the results of FMR measurements carried out ear-
tonicdependence whentheexcitationenergyvariesfrom lier on the same samples at a series of temperatures (see
1.43 eV to 1.81 eV: as the excitation energy increases, Appendix).29 The values of 4πM , H and H ob-
eff 4k 2k
the precessionfrequency firstdecreasesrapidlyto amin- tained by fitting the FMR results are shown in Fig. 3.
imum at 1.56 eV, then increases monotonically to about It is seen in the figure that, the in-plane magnetocrys-
1.60 eV, and eventually levels off. It is known that the tallineanisotropyfieldsH andH decreasemonotoni-
4k 2k
photo-excitation can cause momentary changes in both callywithincreasingtemperature,whilethetemperature
the carrier density and the sample temperature, which dependence of the 4πM shows a non-monotonic vari-
eff
can then result in transient changes of the internal mag- ation. The temperature dependence of the precession
netic fields (and thus of the magnetization) in the ma- frequency can thus be directly obtained from the tem-
terial. Furthermore, all these changes are expected to perature dependence of the magnetic anisotropy fields.
depend on the photon energy of the optical pulse due to As seen in Fig. 4, calculations based on Eq. 3 and the
thevariationoftheabsorptioncoefficient,especiallynear FMR results shows that the precession frequency of the
the bandgap.15,24 magnetization decreases monotonically with increasing
3
temperature. This analysisclearlysuggeststhatthe pre- role in determining the precession frequency.
cession frequency is inversely proportional to the local One should note, of course, that the effects of laser
temperature.26,29–32 From this we conclude that, when heating and of photo-excited carriers affect magnetiza-
thermal effects dominate the precession process, a tran- tiondynamics simultaneously but in opposite directions.
sientincreaseofthelocaltemperature∆T inducedbythe Thus they may compensate in certain regions, resulting
absorption of an optical pulse will lead to a decrease of in a relatively constant precession frequency, as seen in
the precessionfrequency.5–16 Consistentwith this expec- Fig. 2(a) for excitation energies above 1.62 eV for the
tation,inFig. 2(a)weseeinthatfortheas-grownsample as-grown sample. For completeness, we note that an-
theprecessionfrequencyindeeddecreaseswithincreasing other possible reason for the observed leveling-off of the
laser energy (i.e., with increase in laser-inducedheating) precession frequency at high photon excitation energies
at excitation energies below 1.56 eV, i.e., the band gap may arise as follows. It is known that the electron-hole
of (Ga,Mn)As,33,34 thus implying that photo-excitation- density of states undergoes a dramatic increase between
induced modulation of the precession frequency below 1.56 eV and 1.62 eV near the Γ point, but when the
the (Ga,Mn)As bandgapcan be ascribedmainly to laser photo-excitation energy exceeds 1.62 eV, the electron-
heating. hole density of states quickly reaches a plateau.37 This
However, for excitation energies between 1.56 eV to will eventually lead to a saturation of the photo-excited
1.62 eV the precessionfrequency in the as-grownsample carrier density, and thus to a leveling off of the preces-
is clearly observed to increase with photon energy. This sion frequency at excitation energies above 1.62 eV seen
contrastssharplywiththebehaviorinducedbymagnetic in Fig. 2(a).
anisotropymodulationviathermaleffectsjustdiscussed. Figure 2(b) shows the dependence of precession fre-
Themajordifferencebetweenbelow-andabove-bandgap quencyonphoto-excitationenergyfora higherpumpin-
photo-excitations is, of course, the creationof holes, and tensity. The figure clearly shows that for the as-grown
weascribetheobserveddifferenceinthebehaviorofmag- (Ga,Mn)As samplea criticalturning point ofthe preces-
netization precession to that latter effect. Indeed, it has sion frequency variation also occurs near the band-edge.
been theoretically predicted that a change of hole den- Below the band-edge, the increased laser heating at the
sity will lead to changes in magnetic anisotropy fields in pump intensity of1.33µJ/cm2 causes a quickerdecrease
(Ga,Mn)As.35,36 Furthermore, it has also been experi- of the precession frequency, compared to the excitation
mentally demonstrated that an increase in the hole den- at 0.44 µJ/cm2 seen in Fig. 2(a). However, in contrast
sity leads to an increase in the 4πMeff parameter. Al- withthelow-intensityresults,whentheexcitationenergy
though the increase of the hole population also reduces exceedstheband-edge,theprecessionfrequencylevelsoff
the in-plane cubic anisotropy fields H4k and H2k, it has atabout1.54eV.Wesuggestthatatthishighexcitation
been shown that the latter effect is weaker.30 This can intensity the increased laser heating may be sufficient to
indeedbeseeninFig. 3where,forthemoderateMncon- compensatetheeffectofoptically-pumpedholes,thusre-
centration of ∼3.6% of our samples, the in-plane mag- sulting in a relatively flat precession frequency.
netic anisotropy fields H and H exhibit a decrease
4k 2k Inordertofurtherunderstandthedependenceofmag-
with the increase of hole density due to annealing, while
netizationprecessionfrequencyontheholedensity,mea-
4πM undergoes a noticeable increase. The striking
eff surements were also carriedout on the annealed sample,
dependenceofmagneticanisotropyfieldsontheholeden-
which has a significantly higher hole density than the
sity shown in Fig. 3 strongly suggests that the increase
as-grown specimen. Experimentally, we found that it is
of hole density due to ultrafast laser-excitation leads to
harder to excite the magnetization precession in the an-
a similar variation of magnetic anisotropy field.
nealed sample than in the as-grown sample below the
A quantitative look at the anisotropy fields obtained band gap. In this case one sees that at the low pumping
from fitting the FMR data in Fig. 4 shows that at 10 K, intensity of 0.44 µJ/cm2 the annealing leads to a very
fortheas-grownsamplethein-planemagneticanisotropy different scenario; i.e., as shown in Fig. 2(a), the pre-
fieldH4k istwotimessmallerthan4πMeff,whileforthe cession frequency remains basically unchanged through-
annealed sample H4k is six times smaller than 4πMeff. out the entire photon energy range used in this study.
From this we conclude that, based on Eq. 3, when the From this we conclude that in this case the effects of
change of 4πMeff due to laser-induced hole density is H4k and4πMeff duetotheincreasedholeconcentration
much stronger than that of H4k, which is expected for compensate each other. At the higher pump intensity of
the sample with a higher hole density,30 the variation of 1.33 µJ/cm2, however, the precession frequency in the
precession frequency is expected to be determined pri- annealed sample shows a continuous increase with exci-
marily by the trend of 4πM . One can thus readily tation energy, as shown in Fig. 2(b). For the excitation
eff
concludethattheenhancementofthe4πM parameter of pumping intensity of 1.33 µJ/cm2, since the laser-
eff
by photo-induced increase of hole density leads to an in- heating-induced ∆T is now higher than that of lower-
crease of precession frequency. This trend is indeed seen densityexcitation,the precessionfrequency ω at1.51eV
in Fig. 2(a) for the as-grownsample at above band-edge drops to 19.8 GHz due to the dominance of thermal ef-
excitations (from 1.56 eV to 1.62 eV), suggesting that fects. However, the frequency now shows a continuous
the concentration of photo-excited holes plays a critical increase with photo-excitation energy from 1.52 eV to
4
1.81 eV. According to the discussion above, we suggest backgroundhole density can suppresses the Bir-Aronov-
thatinthiscasetheenhancedvalueof4πM causedby Pikus(BAP)spinrelaxationmechanismviareducingthe
eff
the higher hole density, which continues to increase with magnetic disorder.39–41 Thus, the magnetic relaxation
increasingphoto-excitationenergy,isresponsibleforthis time ofthe annealedsample substantiallyincreasescom-
behavior, thus revealing the importance of non-thermal paring with that of the as-grown sample. In addition, it
mechanism in the annealed sample. should be mentioned that the relaxation time τ of the
D
In order to further illustrate the behavior of non- magnetizationprecessionisalsoinverselyproportionalto
thermaleffectsonmagnetizationprecession,inFig. 5we the anisotropyfields.24 As shown in figure, the magnetic
compare the photo-excitation energy dependence of the relaxation times for both samples exhibit negligible de-
precession frequency measured at two different temper- pendence on the excitation energy above band gap of
atures for the annealed sample. At 25 K the precession (Ga,Mn)As. Such result indicates that the variances of
frequency has shown strong proportional dependence on 4πM and H as function ofphoton energyare in op-
eff 4k
the excitation energy with lower photo-excitation inten- position directions and compensate each other when the
sity of 0.44 µJ/cm2. Above T = 25 K, since the temper- photon energy is above the (Ga,Mn)As band gap, which
ature dependence of the in-plane anisotropy fields H is consistent with the results shown in Fig. 2.
4k
becomes not obvious as shown in Fig. 3, the influence
of 4πM is more significant in the frequency analysis.
eff
As seen in Fig. 5, because of the strong enhancement
IV. CONCLUSIONS
of 4πM by the increase in hole density upon photo-
eff
excitation above the band-edge, the measured frequency
shows a continuous increase, which is even higher than In conclusion, we have studied photo-induced
theessentialvalueatT =25KcalculatedfromtheFMR magnetization dynamics in as-grown and annealed
result. Nevertheless,asshowninFig. 2(b), atT =10K, Ga Mn Asfilmsbytime-resolvedmagneto-optical
0.964 0.036
the optical pumping intensity must be increased to 1.33 spectroscopy. The results suggest that at photo-
µJ/cm2tosaturatethevarianceofH ,sotoobservethe excitation energies below the band-edge of (Ga,Mn)As
4k
similartrend: the precessionfrequencyincreaseswithan the observed changes in the precession frequency arise
increasing excitation energy. from changes in the magnetic anisotropy fields induced
The impact of photo-excited carriers is also reflected throughlaserheating. Fortheregimeofabove-band-edge
in the relaxation time τ of the magnetization preces- excitation, on the other hand, photo-excitation induces
D
sion, which is connected to the Gilbert damping coeffi- non-thermal effects that result from photo-excitated
cient by the anisotropy fields.24 For completeness, Fig. holes in the material. Our results reveal the competing
6 shows the relaxation time τ for both as-grown and role ofthese two distinct contributions in controllingthe
D
annealed samples measured at 10 K at different optical collective magnetization precession in (Ga,Mn)As, pro-
pump intensities. As seen in Fig. 6(a), below the en- viding direct experimental evidence for the possibility of
ergy gap, the magnetic relaxationtime is observedto be ultrafastnon-thermalmanipulationofmagnetizationdy-
quitestronglyinfluencedbythephotonenergyfortheas- namicsinferromagnetic(Ga,Mn)Asbylinearlypolarized
grown sample. Below the band gap, various scattering optical pulse excitation.
processes such as hole-phonon, hole-disorder and hole-
hole scatterings will be greatly reduced, since there are
no spatial and temporal fluctuations created by photo-
generated carriers.12,14,24 When the excitation energy is Acknowledgments
above 1.56 eV, however, the extrinsic dephasing effects
due to the fluctuations created by photo-generated car- This work was supported by the National Ba-
riers are greatly enhanced. Thus, the relaxation time sic Research Program of China (Nos.2011CB922200,
showsacleardrop,withamoreobviouschangeathigher 2013CB922303),andtheNationalNaturalScienceFoun-
pumpingintensity. Fortheannealedsample,theremoval dationofChina(No.10974195). TheworkatNotreDame
of the interstitial Mn efficiently reduces the amount wassupportedbytheNationalScienceFoundationGrant
of scattering source,24,38 and meanwhile, the increased DMR14-00432.
∗ Currentaddress: ShanghaiResearchCenterofEngineering delberg New York,2002).
and Technology for Solid-State Lighting, Shanhai, China 3 T. Dietl, Nat.Mater. 9, 965 (2010).
† Electronic address: [email protected] 4 T. Jungwirth, J. Sinova, J. Maˇsek, J. Kuˇcera, and A. H.
1 A.Kirilyuk,A.V.Kimel,andT.Rasing,Rev.Mod.Phys. MacDonald, Rev.Mod. Phys.78, 809 (2006).
82, 2731 (2010). 5 A.Oiwa,H.Takechi,andH.Munekata,J.Supercond.18,
2 B. Hillebrandsand K.Ounadjela, Spin Dynamics in Con- 9 (2005).
fined Magnetic Structures I (Springer Verlag, Berlin Hei- 6 D.M.Wang,Y.H.Ren,X.Liu,J.K.Furdyna,M.Grims-
5
ditch, and R.Merlin, Phys. Rev.B 75, 233308 (2007). Phys. Rev.B 76, 035327 (2007).
7 H. Takechi, A. Oiwa, K. Nomura, T. Kondo, and 33 T. deBoer, A.Gamouras, S.March, V.Nova´k,andK.C.
H. Munekata,physica status solidi (c) 3, 4267 (2006). Hall, Phys.Rev.B 85, 033202 (2012).
8 J. Qi,Y.Xu,N.H.Tolk,X.Liu,J. K.Furdyna,and I.E. 34 N. Tesaˇrova´, T. Ostatnicky´, V. Nova´k, K. Olejn´ık,
Perakis, Appl.Phys. Lett. 91, 112506 (2007). J. Sˇubrt, H. Reichlova´, C. T. Ellis, A. Mukherjee, J. Lee,
9 O.Yastrubchak,J.Z˙uk,H.Krzyz˙anowska,J.Z.Domagala, G. M. Sipahi, et al., Phys. Rev.B 89, 085203 (2014).
T.Andrearczyk,J.Sadowski,andT.Wosinski,Phys.Rev. 35 T. Dietl, H. Ohno, and F. Matsukura, Phys. Rev. B 63,
B 83, 245201 (2011). 195205 (2001).
10 E. Rozkotova´, P. Nˇemec, P. Horodysk´a, D. Sprinzl, 36 J. Zemen,J.Kuˇcera, K.Olejn´ık, and T.Jungwirth, Phys.
F. Troj´anek, P. Maly´, V. Nova´k, K. Olejn´ık, M. Cukr, Rev.B 80, 155203 (2009).
and T. Jungwirth, Appl. Phys.Lett. 92, 122507 (2008). 37 M. D. Kapetanakis, J. Wang, and I. E. Perakis, J. Opt.
11 E.Rozkotova´,P.Nˇemec,N.Tesaˇrova´, P.Maly´,V.Nova´k, Soc. Am. B 29, A95 (2012).
K.Olejn´ık, M.Cukr,andT.Jungwirth,Appl.Phys.Lett. 38 T. Dietl, D. D. Awschalom, M. Kaminska, and H. Ohno,
93, 232505 (2008). Spintronics (Elsevier, Amsterdam, 2008).
12 J. Wang, C. Sun, Y. Hashimoto, J. Kono, G. A. Khoda- 39 G. V. Astakhov, R. I. Dzhioev, K. V. Kavokin, V. L. Ko-
parast, L. Cywin´ski, L. J. Sham, G. D. Sanders, C. J. renev, M. V. Lazarev, M. N. Tkachuk, Y. G. Kusrayev,
Stanton,andH.Munekata,J.Phys.: Condens.Matter18, T.Kiessling,W.Ossau,andL.W.Molenkamp,Phys.Rev.
R501 (2006). Lett. 101, 076602 (2008).
13 Y. Hashimoto and H. Munekata, Appl. Phys. Lett. 93, 40 G.L.Bir,A.G.Aronov,andG.E.Pikus,Zh.Eksp.Teor.
202506 (2008). Fiz. 69, 1382 (1975).
14 J. Wang, I. Cotoros, K. M. Dani, X. Liu, J. K. Furdyna, 41 G.L.Bir,A.G.Aronov,andG.E.Pikus,Sov.Phys.JETP
and D.S. Chemla, Phys.Rev.Lett. 98, 217401 (2007). 42, 705 (1976).
15 Y.Hashimoto,S.Kobayashi,andH.Munekata,Phys.Rev.
Lett. 100, 067202 (2008).
16 S. Kobayashi, K. Suda, J. Aoyama, D. Nakahara, and
H. Munekata,IEEE Trans. Magn. 46, 2470 (2010).
17 P. Nˇemec, E. Rozkotova´, N. Tesaˇrova´, F. Troj´anek,
E. De Ranieri, K. Olejn´ık, J. Zemen, V. Nova´k, M. Cukr,
P. Maly´, et al., Nat. Phys. 8, 411 (2012).
18 E. Beaurepaire, J.-C. Merle, A. Daunois, and J.-Y. Bigot,
Phys. Rev.Lett. 76, 4250 (1996).
19 L. Guidoni, E. Beaurepaire, and J.-Y. Bigot, Phys. Rev.
Lett. 89, 017401 (2002).
20 C. Stamm, T. Kachel, N. Pontius, R. Mitzner, T. Quast,
K.Holldack, S.Khan,C. Lupulescu,E.F.Aziz, M.Wiet-
struk, et al., Nat. Mater. 6, 740 (2007).
21 G. M. Mu¨ller, J. Walowski, M. Djordjevic, G.-X. Miao,
A. Gupta, A. V. Ramos, K. Gehrke, V. Moshnyaga,
K. Samwer, J. Schmalhorst, et al., Nat. Mater. 8, 56
(2009).
22 M. D. Kapetanakis, I. E. Perakis, K. J. Wickey, C. Pier-
marocchi, and J. Wang, Phys. Rev. Lett. 103, 047404
(2009).
23 K.Hamaya,T.Watanabe,T.Taniyama,A.Oiwa,Y.Kita-
moto, and Y. Yamazaki, Phys. Rev.B 74, 045201 (2006).
24 J. Qi, Y. Xu, A. Steigerwald, X. Liu, J. K. Furdyna, I. E.
Perakis, and N. H.Tolk, Phys.Rev.B 79, 085304 (2009).
25 A.J.Lochtefeld,M.R.Melloch, J.C.P.Chang,andE.S.
Harmon, Appl.Phys. Lett. 69, 1465 (1996).
26 J. Qi, Y. Xu, X. Liu, J. K. Furdyna, I. E. Perakis, and
N. H.Tolk, Phys.StatusSolidi (c) 5, 2637 (2008).
27 N. Tesaˇrova´, P. checkemec, E. Rozkotova´, J. Zemen,
T. Janda, D. Butkoviˇcova´, F. Troj´anek, K. Olejn´ık,
V. Nova´k,P. Maly´, et al., Nat. Photon. 7, 492 (2013).
28 U.Welp,V.K.Vlasko-Vlasov,X.Liu,J.K.Furdyna,and
T. Wojtowicz, Phys. Rev.Lett. 90, 167206 (2003).
29 X. Liu, Y. Sasaki, and J. K. Furdyna, Phys. Rev. B 67,
205204 (2003).
30 X. Liu, W. L. Lim, M. Dobrowolska, J. K. Furdyna, and
T. Wojtowicz, Phys. Rev.B 71, 035307 (2005).
31 K.Hamaya,T.Watanabe,T.Taniyama,A.Oiwa,Y.Kita-
moto, and Y. Yamazaki, Phys. Rev.B 74, 045201 (2006).
32 D.Y.Shin,S.J.Chung,S.Lee,X.Liu,andJ.K.Furdyna,
6

Tc 80K
T = 10K
T = 80K
Kerr rotation (a.u.) Kerr rotation (a.u.) TTT === 534000KKK
1.54eV
T = 20K
Fit
(a) (b)
0 500 1000 1500 0 400 800 1200
Time delay (ps) Time delay (ps)
FIG. 1: (Color online) (a) Temporal profile of Kerr rotation
measured at 10 K for linearly- polarized pumpingat 1.54 eV
fortheannealed(Ga,Mn)Assample. Thesolidline(redcolor)
shows the best fit. (b) Time-resolved Kerr rotations excited
atdifferentambienttemperatures. Thecrosshatchshowsthat
the pulse-like signal has no noticeable temperature depen-
dence, even at temperatures aboveTc.
7

36 FMR 36
)
Hz 34 GaMnAs (b) 34
(G Eg
32 2 32
y 1.33 J/cm
nc 30 30
e
u
q 28 28
e
n fr 26 26
o
si 24 24
s 2
e 0.44 J/cm as-grown
Prec 22 annealed 22
20 20
(a)
18 18
1.4 1.5 1.6 1.7 1.8 1.4 1.5 1.6 1.7 1.8
Photon energy (eV)
FIG. 2: (Color online) Extracted precession frequencies as a
function of excitation photon energy measured at 10 K with
optical pumpingbylinearly polarized light. Noexternalfield
isapplied. (a) Dependenceofprecession frequencyon photo-
excitation energy for theas-grown sample (upper panel) and
the annealed sample (lower panel). The black arrow repre-
sents the band edge of (Ga,Mn)As. The optical pumping
intensity is 0.44 µJ/cm2. (b) Dependence of precession fre-
quencies on photo-excitation energy measured with pump-
ing intensity of 1.33 µJ/cm2. The lines in the middle of fig-
urerepresenttheprecession frequencyvaluescalculatedfrom
the FMR results for the as-grown (blue) and annealed (red)
samples,respectively. Thecolor-codedregimescorrespondto
different dominant mechanisms responsible for the manipu-
lation of magnetization precession as discussed in the text:
the thermal effect due to laser heating (yellow regime); the
nearly constant frequency resulting from the competing role
between the thermal and non-thermal effects with high den-
sity of photo-excited holes (cyan regime); the enhanced non-
thermal effect due to photo-excitated holes in (Ga, Mn)As
film (grey regime).
8

As-grown Annealed
4 (a) (b)
e)
O
K
d ( 3
el
py fi 4 Meff
o 2
otr H4||
s
ni H2||
A
1
0
0 10 20 30 40 50 0 10 20 30 40 50
Temperature (K)
FIG.3: (Coloronline)Extractedmagneticanisotropyparam-
eters for both the as-grown and annealed samples, including
4πMeff and thein-planemagnetic anisotropy fields H4k and
H2k. When the temperature is above 25 K, the variation of
thein-planeanisotropyfieldswithtemperatureisnotobvious.

)
z
H
G
40
(

As-grown
y
c Annealed
n 30
e
u
q
e
n fr 20
o
si
s
e 10
c
e
r
P
0
0 10 20 30 40 50
Temperature (K)
FIG. 4: Calculated magnetization precession frequency as a
functionoftemperatureforbothas-grownandannealedsam-
ples. The calculation shows that the increase in the sample
temperature decreases theprecession frequency.
9

) 28
z
H
G
(
26
y
c
n
ue 24 10K 0.44 J/cm2
q
e 2
r 25K 0.44 J/cm
n f 22
o
si
s
e
c 20
e
Pr FMR Annealed
18
1.4 1.5 1.6 1.7 1.8
Photon energy (eV)
FIG. 5: (Color online) Precession frequency triggered by the
laserpulseasafunctionofphoto-excitationenergymeasured
at two temperatures at the 0.44 µJ/cm2 pump intensity for
the annealed (Ga,Mn)As sample. The arrows represent the
valuescalculatedfromtheFMRresultsfor10K(red)and25
K (black), respectively.

600 2
1.33 J/cm
2
0.44 J/cm
500
s) 400
p
(
D300
200
100
(a) As-grown (b) Annealed
0
1.4 1.5 1.6 1.7 1.8 1.4 1.5 1.6 1.7 1.8
Photon energy (eV)
FIG.6: (Coloronline)(a)Themagnetizationrelaxationtime
τD as function of photo-excitation energy measured at 10 K
with linearly polarized pumppulsesat 0.44 µJ/cm2 and 1.33
µJ/cm2 intensities for the as-grown sample. (b) The mag-
netization relaxation time τD as function of photo-excitation
energymeasuredat10Kwithlinearlypolarizedpumppulses
at 0.44 µJ/cm2 and 1.33 µJ/cm2 for theannealed sample.
10
Appendix

16
3 )m 14 As-grown
c
u/ 12 Annealed
m
e 10
(n
atio 8
z
eti 6
n
g
a 4
M
2
0
0 10 20 30 40 50 60 70 80 90 100
Temperature (K)
FIG.A1: M-Tcurvesfortheas-grownandannealedsamples.
TheexperimentsshowtheCurietemperaturesofthesamples
are 58 K and 79K, respectively.

[001] [001] [010] [010]
7
e) H||(110) H||(001)
O 6
k
(
d 5
el
e fi 4 [110] [110]
c
n
a 3 [110]
n
o
s 2
e
R
1
(a) (b) [100]
0
0 45 90 135 1800 45 90 135 180

H H
FIG. A2: FMR results for the as-grown sample at T = 4 K.
Redsolidlinesrepresentbestfitresults,fromwhichthevalues
of anisotropy fieldsare extracted for the as-grown specimen.