We report on the observation of ultrafast photo-enhanced ferromagnetism in
GaMnAs. It is manifested as a transient magnetization increase on a 100-ps time
scale, after an initial sub-ps demagnetization. The dynamic magnetization
enhancement exhibits a maximum below the Curie temperature Tc and dominates the
demagnetization component when approaching Tc. We attribute the observed
ultrafast collective ordering to the p-d exchange interaction between
photoexcited holes and Mn spins, leading to a correlation-induced peak around
20K and a transient increase in Tc.Comment: 4 page

Chemla, D. S.

Cotoros, I.

Dani, K. M.

Furdyna, J. K.

Liu, X.

Wang, J.

English

arXiv

We report on the observation of ultrafast photo-enhanced ferromagnetism in GaMnAs. It is manifested as a transient magnetization increase on a 100-ps time scale, after an initial sub-ps demagnetization. The dynamic magnetization enhancement exhibits a maximum below the Curie temperature {Tc} and dominates the demagnetization component when approaching {Tc}. We attribute the observed ultrafast collective ordering to the p-d exchange interaction between photoexcited holes and Mn spins, leading to a correlation-induced peak around 20K and a transient increase in {Tc}

Dani, K.M.

Furdyna, J.K.

Chemla, D.S.

UNT Digital Library

arXiv:cond-mat/0702439v2   19 Feb 2007Ultrafast Enhancement of Ferromagnetism via Photoexcited Holes in GaMnAsJ. Wang,1† I. Cotoros,1 K. M. Dani,1 X. Liu,2 J. K. Furdyna,2 and D. S. Chemla11Materials Sciences Division, E.O. Lawrence Berkeley National Laboratory and Department of Physics,University of California at Berkeley, Berkeley, California 94720, U.S.A.2Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A.(Dated: February 19, 2007)We report on the observation of ultrafast photo-enhanced ferromagnetism in GaMnAs. It is man-ifested as a transient magnetization increase on a 100-ps time scale, after an initial sub-ps demag-netization. The dynamic magnetization enhancement exhibits a maximum below the Curie temper-ature Tc and dominates the demagnetization component when approaching Tc. We attribute theobserved ultrafast collective ordering to the p-d exchange interaction between photoexcited holesand Mn spins, leading to a correlation-induced peak around 20K and a transient increase in Tc.PACS numbers: 78.20.-e, 78.20.Jq, 42.50.Md, 78.30.Fs, 78.47.+pThere has been long and intense interest in search-ing for possibilities for ultrafast enhancement of collec-tive magnetic order via photoexcitation. Such photoex-citation would lead to fascinating opportunities both forestablishing a transient cooperative phase from an un-correlated ground state and for determining the relevanttime scales for the build-up of order parameters. Pre-vious time-resolved investigations in paramagnetic II-VIsemiconductors provided evidence for collective photoex-citations that led to the formation of magnetic polarons[1]. Substantial recent progress has been made in observ-ing ultrafast spin reorientations, e.g., in antiferromag-netic materials [2, 3]. However, most prior experimentsin magnetically-ordered materials only show an ultrafastdecrease of the magnetization amplitude due to laser in-duced electronic heating [4]. Recently, several experi-ments in strongly correlated manganites and transitionmetal alloys revealed transient photo-induced magneti-zation on ultrafast time scales, but only demagnetizationcould be seen at temperatures away from Tc. The role ofultrafast pumping is most likely a thermal perturbationof competing phases near critical points [5, 6].The discovery of hole-mediated ferromagnetism in III-V ferromagnetic semiconductors (III-V FMSs) such asGaMnAs and InMnAs [7] oﬀers unique opportunities andﬂexibility for nonthermal control of magnetism. Unlikeother types of magnets, the ferromagnetic exchange be-tween localized Mn moments is mediated by free holespins through p-d interaction Hp−d ∼ JpdS · s (Jpd ∼ 1eV), making the magnetic properties a sensitive functionof the hole density. For instance, the trend of experi-mental Tc in GaMnAs is shown to be proportional top1/3J2pd, for a wide range of hole densities p [8]. Recently,hole-density-tuning via external stimuli such as CW lightexcitation [9] and electrical gating [10] has demonstratedclear enhancement of magnetization and increase of Tc,as illustrated in Fig. 1(a). However, no time-resolvedexperiments in III-V FMSs have shown transient photo-induced magnetization, and the time scale for the en-hancement of collective order is completely unknown. Sofar only ultrafast demagnetization and quenching dynam-ics were observed, due in part to the relatively high pumpﬂuences used (∼ 1 mJ/cm2) [11, 12]. Moreover, recenttheory has pointed to the critical role of the Mn-holeexchange correlation in ultrafast, nonthermal manipula-tion of magnetization in GaMnAs [13], but no experi-mental evidence for this has been reported. In additionto their fundamental scientiﬁc interest, III-V FMSs areamong the most promising candidates for future ”multi-functional” devices and for quantum information technol-ogy based on the spin degree of freedom [14]. It is thus ofsigniﬁcance to explore ferromagnetic enhancement in III-V FMSs to technologically important, sub-ns time scales.In this Letter, we report the observation of ultrafastenhancement of ferromagnetism in GaMnAs. Our dataclearly show photo-induced magnetization on a 100-pstime scale after initial sub-ps demagnetization. The dy-namic magnetization enhancement exhibits a maximumbelow Tc and dominates the demagnetization compo-nent when approaching Tc. Our analysis and theoreticalsimulations based on the Hp−d interaction between pho-toexcited holes and Mn spins explain the salient featuresof the experiment showing, in particular, a correlation-induced peak around 20K and a transient increase in Tc.The sample studied in the present work was a GaM-nAs/GaAs heterostructure with a Curie temperature of77 K. The sample was grown by low-temperature molec-ular beam epitaxy (MBE) and consisted of a 73-nmGa0.925Mn0.075As layer deposited on a GaAs buﬀer layerand a semi-insulating GaAs (100) substrate. The back-ground hole density was approximately 3 · 1020 cm−3.Our measurements involved ultraviolet (UV) pump/near-infrared (NIR) magneto-optical Kerr eﬀect (MOKE)spectroscopy. The experimental setup consisted of a fem-tosecond oscillator with 120 fs pulse duration and a BBOcrystal in the pump path for doubling the photon en-ergy. The pump beam was at 3.1 eV and was linearlypolarized, with peak ﬂuences ≃ 10µJ/cm2. Fig. 1(b)illustrates that fs pump pulses create a large density ofholes in the valence band of GaMnAs. A small frac-2840-4  ∆θk (µrad)8006004002000Time Delay (ps)GaMnAs, T = 70K, pump 10 µJ/cm2 Exp Fit(b)Mn, d-likeValance band3.1 eV120 fsEFMn, d-likeBefore external stimuli MpTc ∆∝∆After external stimuliEnhanced FMT(a)(c)Holes, p-likeFIG. 1: (a) Illustration of hole-density-tuning effects via ex-ternal stimuli in III-V FMSs seen in the static experiments[9, 10]. FM: ferromagnetism. △p is hole density change. (b)Schematic diagram of the spin-dependent density of states inGaMnAs. fs pump pulses create a transient population ofholes in the valence band. (c) Time-resolved MOKE dynam-ics at 70K and under 1.0T field. Transient enhancement ofmagnetization, with ∼ 100 ps rise time, is clearly seen afterinitial fast demagnetization. Thick line is the fit described inthe text.tion of the fundamental beam at 1.55 eV was used asa probe, detecting magnetization via the polar MOKEangle θK [15]. The low pump peak ﬂuences and the highpump photon energy minimize spurious eﬀects such astwo-photon absorption and pump scattering. Addition-ally, the ”magnetic origin” of the transient MOKE re-sponse is conﬁrmed by separate measurements showingthe overlap of the pump-induced rotation and ellipticitythrough the entire time scan range [16].A typical temporal proﬁle of transient MOKE changes∆θK at 70K is shown in Fig. 1(c), with a ﬁeld of 1.0Tperpendicular to the sample surface to align the magneti-zation. Two mutually competing dynamic magnetizationprocesses are observed: an initial sub-ps demagnetization(∆θK < 0), followed by a distinct magnetization rise ona 100 ps time scale (∆θK > 0). The two processes clearlyshow diﬀerent temperature dependences, as shown in Fig.2(a)-(b). At elevated lattice temperature, the 200 fs de-magnetization components [inset of Fig. 2(b)] quicklydiminish and nearly disappear above Tc. This is alsoseen in the 600 fs and 3 ps traces in Fig. 2(c). Moreintriguingly, an enhancement of the transient magnetiza-tion begins to dominate the demagnetization componentat high temperatures. For instance, the net magneti-zation changes become positive above 40K at long timedelays, e.g., at 240 ps [Fig. 2(c)]. The photoinduced mag-netization persists above Tc - as is clearly visible in the8004000Time Delay (ps)40 K60 K70 K80 K120 K ∆θk (20 µrad per div.)8004000Time Delay (ps)10 K30 K23 K15 KTc = 77KH = 1T -40-30-20-100  ∆θk (µrad)210Time Delay (ps)T = 15K-60-40-200 ∆θk (µrad)12080400T (K)Tc = 77K 600 fs 3ps 240 ps(c)(a) (b)FIG. 2: (a)-(b) Temporal traces of photoinduced magnetiza-tion changes at different temperatures. All traces are inten-tionally offset for clarity. Inset: the first 2 ps demagnetizationdynamics at 15 K. (c) Temperature dependence of magneti-zation changes at different time delays - 600 fs (squares), 3 ps(diamonds) and 240 ps (circles), respectively.80K trace [Fig. 2(b)] - and gradually vanishes at highertemperatures.MOKE signals, measured with the 1.55 eV probe, arisefrom the macroscopic magnetization M - average local-ized Mn spins - through the coupling of the spin-splitelectronic states near the band edge. The backgroundcarrier spin contribution to M is negligible, and pho-toexcited transient carriers are not spin polarized sincethe pump contains no net angular momentum. Thus thepositive MOKE signals, rising on a 100-ps time scale,clearly indicate an ultrafast alignment of Mn spins andan enhancement of ferromagnetic order. Our results re-veal the ultrafast time scale of this process, not accessiblein previous static measurements [9, 10].We attribute the observed ultrafast photo-enhancedferromagnetism to the transient hole-Mn interaction viathe Hp−d exchange, as follows. At early pump-probe de-lays (△t ∼ 0 fs), the ultrashort laser pulses generate anonequilibrium distribution of spin-unpolarized electron-hole pairs in GaMnAs under a ﬁnite external H ﬁeld.During the ﬁrst ps (△t < 1ps), the photoexcited hotholes will experience eﬃcient spin-ﬂip scattering withthe localized Mn moments, manifesting this as a sub-ps demagnetization component. This results from theoﬀ-diagonal elements of the exchange Hamiltonian Hp−d(∼JpdS± · s∓), which cause the spin polarization of the32520151050 ∆θkm (µrad)12080400T (K)50403020100 − ∆θkd (µrad) 543210M (10-5 emu)1000T (K)H = 1T0.60.40.20.0 ∆M/M0 (%)40200T (K) theory exp(a)(b) Tc = 77KH = 1TFIG. 3: Decomposed demagnetization −△θdk [(a)] and en-hanced magnetization △θmk [(b)] components are plotted asa function of temperature. The static magnetization curveunder 1.0T field is shown as inset in (a). The simulation△M/M0 (thick line, △Tc = 1.1K and the hole-Mn ratio of0.06) and experimental values (circles, normalized by staticθk at 5K) of the photo-enhancement peak ∼ 20K are shownas inset in (b).Mn ions to transfer to the holes within several 100s offs, similar to the fs demagnetization ﬁrst reported in In-MnAs [11]. Meanwhile, the hot hole distribution quicklycools via carrier-phonon scattering (optical phonon en-ergy ∼36 meV), resulting in a rapid termination of de-magnetization (within the ﬁrst ps). At longer pump-probe delays of △t > 1ps, the photoexcited, thermal-ized holes, settling down in the spin-split bands, cannow participate in the process of hole-mediated ferro-magnetic ordering. These extra holes enhance the Mn-Mn exchange correlation and polarize Mn spins via themean-ﬁeld (diagonal) elements of the exchange Hamilto-nian Hp−d (∼JpdSz · sz), thereby increasing the macro-scopic magnetization.In order to elucidate the salient features of the photo-enhanced ferromagnetism, we decompose the transientMOKE changes shown in Fig. 2 into demagnetiza-tion (−△θdk) and enhanced magnetization (△θmk ) compo-nents, based on their diﬀerent time scales. The temporalproﬁle of △θk is well described by △θdk · exp(−t/τd) +△θmk · (1− exp(−t/τm)) · exp(−t/τc). Here −△θdk and τdin the ﬁrst term are the magnitude of demagnetizationand the recovery time determined by the slow heat diﬀu-sion process, respectively. In the second term, △θmk andτm are the magnitude and build-up time of the enhancedmagnetization component, respectively, while τc accountsfor the ﬁnal decay of the magnetization enhancement viahole diﬀusion and recombination. The time constant τcis on the order of a few ns, as seen in the decay of thepositive MOKE signal. As an example, the thick line inFig. 1(c) represents the ﬁt of the MOKE dynamics at70K.Fig. 3 plots the temperature dependence of −△θdk and△θmk . The −△θdk proﬁle resembles the static magnetiza-tion curve of the sample, exhibiting strong deviation fromthe classical mean-ﬁeld convex shape [inset, Fig. 3(a)].This non-classical behavior of magnetization arises fromthe existence of two strongly interacting spin ensembles,Mn and holes, as discussed in [17]. More intriguingly,the magnetization enhancement △θmk in Fig. 3(b) showsa distinctly diﬀerent temperature proﬁle, with a peakof ∼ 0.5% of the saturation magnetization M0 around20K (static θk at 5K ∼ 4 mrad) and a prolonged tailextended to ∼ 120K. The extended proﬁle beyond Tc isexpected as the combined eﬀect of an applied externalﬁeld of 1.0T and of hole-enhanced magnetic susceptibil-ity in the paramagnetic state. The most salient featureof the photo-enhanced ferromagnetism is the peak near20K, which is a manifestation of the Mn-hole correlationHp−d. This can be qualitatively understood as follows:the ferromagnetic molecular ﬁeld acting on the Mn ions(holes) is determined by the average spin polarizations ofthe holes (Mn ions) via the Mn-hole exchange couplingJpd. The eﬀective ﬁeld acting on the holes is much largerthan that acting on the Mn ions, because of the large den-sity of Mn ions compared to the holes. As a consequence,the hole polarization will remain saturated at a temper-ature Th much higher than that needed for saturatingthe Mn magnetization (TMn∼0). As the lattice tempera-ture increases above TMn but less than Th, the Mn spinswith partial alignment begin to be eﬃciently polarizedvia photoexcited holes with near-unity magnetization.However, as the lattice temperature rises higher than Th,because of reduced hole polarization the eﬃciency of thismagnetization enhancement process quickly drops, thusresulting in a magnetization enhancement maximum atsome temperature on the order of Th.Next we present a simple theoretical calculation to sim-ulate the Mn-hole correlation-induced peak around 20K.As we discussed, the hole-enhanced ferromagnetic corre-lation results in an increase of Tc (△Tc > 0). We cal-culate the non-classical magnetization curve [inset, Fig.3(a)] based on a modiﬁed Weiss mean-ﬁeld model to takeinto account the Hp−d correlation [17]:M(T,∆Tc)/M0 = BS [−3Tc +∆TcTγS∗ ×Bs[−3Tc +∆TcTγ−1S∗M(T,∆Tc)M0+ghµBHkBT]−giµBHkBT]where BS,s(x) is the Brillouin function, γ is the squareroot of the hole and Mn density ratio√p/ni, gi(gh) isMn(hole) g factor and S∗ is given by√sS/(s+ 1)(S + 1).The Mn and hole spins, S and s, are 5/2 and 1/2, re-486420 ∆θk (µrad)4 60.12 4 612 4 610Magnetic Field (T)  ∆θk m      −∆θk dFIG. 4: Magnetic field dependence of photo-induced magne-tization enhancement△θmk and demagnetization △θdk at 78K.spectively. At each given △Tc, the magnetization en-hancement △M/M0 is solved self-consistently as a func-tion of lattice temperature. The calculated tempera-ture dependent △M/M0 and experimental △θmk (nor-malized by static θk at 5K) up to 40K are shown inthe inset in Fig. 3 (b) for △Tc = 1.1K. The resultsof the calculation compare well with the experimentalphoto-enhancement peak. In addition, we can also esti-mate△Tc using an analytical expression derived from theZener Model, △Tc =13Tc×△p/p [18]. Knowing the ratioof photoexcited and background hole densities ∼ 2%, weestimate △Tc ∼ 0.5K, in reasonable agreement with thevalue used in the simulation.The photoexcited transient electrons have little eﬀecton ∆θK , because of the short free electron lifetime (< 1ps) [19]. In addition, the standard thermal demagnetiza-tion via heat transfer from phonons, similar to the slowdemagnetization component reported in [11, 12], is alsoseen at temperatures below 15K [Fig. 2(a)], which is notimportant to the physical picture discussed in this paper.So far our discussion has been based on a situationinvolving a ﬁxed magnetic ﬁeld of 1.0T, which is impor-tant at low temperatures in order to eliminate other dis-tractions (such as magnetization reorientation eﬀects),without losing universality. It is worthwhile, however, toconsider the ﬁeld dependence of the magnetization en-hancement at temperatures just above Tc and possibletransient signatures of photo-induced critical phenom-ena, e.g., para- to ferromagnetic phase transition via thepump-induced increase of Tc. Fig. 4 presents the ﬁelddependence of the magnetization enhancement △θmk anddemagnetization −△θdk at 78 K. Here the most interest-ing aspects lie in the fact that △θmk is relatively constantacross a wide ﬁeld range (0.2T - 1T) and only drops oﬀclose to zero T. It is crucial to note that, unlike staticequilibrium measurements, transient pump-induced mag-netization above Tc always reduces to zero at small ex-ternal ﬁeld, even though △Tc > 0. A below-threshold Hﬁeld is not able to activate subsequent growth of mag-netic domains, even though they are nucleated via possi-ble photo-induced long-range ferromagnetic correlation.Therefore, although the 1K increase of △Tc and the sub-stantial transient magnetization enhancement at a smallﬁeld of 0.05T suggest a transient photo-induced para- toferromagnetic phase transition, more studies are neededto further elucidate the details of these transient features.Finally, the decrease (increase) of △θmk (−△θdk) observedfrom 2T to 7T is expected from the larger static magne-tization achieved at higher ﬁelds, resulting in the smallerphoto-induced changes, as indeed shown by the data.In summary, we have observed ultrafast photo-enhanced ferromagnetism in GaMnAs. Our data clearlyshow that the dynamic magnetization build-up occurs ona 100-ps time scale and exhibits a maximum below Tc.Our analysis and theoretical simulations, based on Hp−dinteraction between photoexcited holes and Mn spins, ex-plain the salient features of the experimental observa-tions, demonstrating in particular a correlation-inducedpeak below Tc and a transient increase of Tc. Our mea-surements thus reveal a new transient collective magneticphenomenon, and identify the critical role of non-thermalMn-hole exchange correlation in this photo-induced co-operative behavior. The new functionalities in sub-nstime scales reported here may open future opportunitiesfor high-speed spin-photon-charge integrated devices.This work was supported by the Oﬃce of Basic EnergySciences of the US Department of Energy and by theNational Science Foundation. We thank B. A. Schmid, R.A. Kaindl and  L. Cywin´ski for illuminating discussions.†To whom correspondence should be addressed. 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Ultrafast Enhancement of Ferromagnetism via Photoexcited Holes in GaMnAs

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