Fast optical control of spin in semiconductor interfacial structures
L. Nádvorník, M. Surýnek, K. Olejník, V. Novák, J. Wunderlich, F. Trojánek, T. Jungwirth, P. N?mec
aa r X i v : . [ c ond - m a t . o t h e r] M a y Fast optical control of spin in semiconductor interfacial structures
L. N´advorn´ık,
1, 2, ∗ M. Sur´ynek, K. Olejn´ık, V. Nov´ak, J. Wunderlich,
1, 4
F. Troj´anek, T. Jungwirth,
1, 5 and P. Nˇemec Institute of Physics ASCR, v.v.i., Cukrovarnick´a 10, 16253 Praha 6, Czech Republic Department of Physical Chemistry, Fritz Haber Institute of the Max Planck Society, 14195 Berlin, Germany Faculty of Mathematics and Physics, Charles University, Ke Karlovu 3, 12116 Praha 2, Czech Republic Hitachi Cambridge Laboratory, J. J. Thomson Avenue, CB3 0HE Cambridge, UK School of Physics and Astronomy, University of Nottingham, Nottingham NG7 2RD, UK (Dated: October 20, 2018)We report on a picosecond-fast optical removal of spin polarization from a self-confined photo-carrier system at an undoped GaAs/AlGaAs interface possessing superior long-range and high-speedspin transport properties. We employed a modified resonant spin amplification technique withunequal intensities of subsequent pump pulses to experimentally distinguish the evolution of spinpopulations originating from different excitation laser pulses. We demonstrate that the density ofspins, which is injected into the system by means of the optical orientation, can be controlled byreducing the electrostatic confinement of the system using an additional generation of photocarriers.It is also shown that the disturbed confinement recovers within hundreds of picoseconds after whichspins can be again photo-injected into the system.
PACS numbers: 72.25.Dc, 72.25.FeKeywords: optical excitation, electron spin, resonant spin amplification, degree of spin polarization
I. INTRODUCTION
Magnetic random access memory (MRAM) bits andspin Hall effect transistors are examples of two differentconceptual approaches to spintronic devices whose func-tionality requires different spin-conserving length-scales.The operation of MRAM bits is based on a vertical trans-fer of spins through a nm-thin layer in a “sandwich-like” layered structure. In spin-logic devices, however,spins have to be manipulated (by electric gates, for in-stance) before they reach the drain electrode which callsfor a lateral design rather than the vertical geometry.
Orders of magnitude larger spin-conserving length-scaleis, therefore, needed in the spin-logic devices due to thetypical dimensions of the order of a µ m of lateral struc-tures fabricated by the electron-beam lithography. The desired high-rate operation of the devices impliesan additional requirement on a fast spin transport overthis length scale. The criteria for the simultaneouslylong-range and high-speed spin transport are not sat-isfied in a majority of standard systems, including n -doped bulk semiconductors or (001)-grown quantumwells , due to their limited spin mobility or spin lifetime, respectively. Another critical parameter which lim-its the operation rate of a spin-logic device is the speed ofspin manipulation. While the spin injection and detec-tion can be a fast process (for instance by means of theoptical orientation and magneto-optical probing ),a fast removal of the spin polarization from the systemis a much more challenging task.In this paper, we show experimentally that the elec-tronic spin polarization can be removed from a transportchannel of a self-confined system in a picosecond time-scale using a control optical pulse which reduces the levelof its confinement. We demonstrate this novel functional- ity in an optically generated self-confined system formedat an undoped GaAs/Al x Ga − x As heterointerface wherethe spin transport meets the other key requirements ofhigh speed and long range, as reported recently in Ref. 16.In addition, we show that the confinement of the trans-port layer is recovered after the removal of the spin po-larization within a few hundreds of picosecond. Combin-ing all these favorable characteristics, we obtain a uniquecandidate system for the development of the spin logicconcept in semiconductors.Our study was performed by a modified resonant spinamplification (RSA) technique using unequal intensi-ties of neighbouring pump pulses which enables us toprobe simultaneously the time evolution of mixed spinpopulations created at different time instants. Thisscheme also allows us to generate the spin polarizationby a lower intensity pulse in a well controlled way with-out disturbing the confinement, then to reduce it by ahigh intensity pulse, and eventually to read it by a probepulse.The paper is organized as follows: First, we describethe studied structure and explain the mechanism of thecreation of the long-lived electronic spin sub-system andshow its fingerprint in a magneto-optical (MO) signal.Then we describe the modified RSA technique with un-equal intensities of subsequent pump pulses. In thefollowing sections, we discuss our experimental resultsdemonstrating the fast optical control of spin polariza-tion. Finally, in appendices, we provide additional infor-mation on our experimental setup and an estimate of theimpact of the disturbed confinement on the spin polar-ization. II. STUDIED SYSTEMA. Sample composition
The studied long-lived and highly mobile electron spin-system is self-confined near the upper GaAs/Al x Ga − x Asinterface in an undoped heterostructure. This spin sys-tem is formed in a wide range of x -composition and layerthicknesses as a consequence of the spatial separation ofoptically generated electron-hole pairs in a built-in elec-tric field due to surface states. In this paper, we use theoptimal Al composition, x = 0 .
4, and the most simplelayer composition shown in Fig. 1(a). A 100 nm thickundoped Al . Ga . As barrier was deposited by a molec-ular beam epitaxy on a top of an insulating GaAs bufferand a GaAs substrate. The barrier was then covered byanother undoped 800 nm thick GaAs layer where the con-fined electron sub-system is formed, as explained below.
B. Creation of electronic sub-system
The process which usually limits the spin lifetime τ s inundoped structures is the electron-hole recombination. The origin of the unusually long τ s measured in our un-doped sample is the suppression of the recombinationspin decay channel due to the presence of a long-livedsub-system of photo-generated excess electrons. This ef-fective optically generated doping is possible due to thespatial separation of photo-generated electrons and holesin the built-in electric field. If we consider our structurein dark, charged residual bulk and surface states pin theFermi level near the valence band which causes a bandbending and, thus, an electric field across the structure– see Fig. 1(b), solid curves. When the sample is illumi-nated from the surface side, photo-electrons and photo-holes are generated. If the structure did not contain thebarrier, the photo-carriers would migrate in the built-inelectric field, fill all the charged states and compensatefully the electric field. However, because of the AlGaAsbarrier, the free migration between the layers above andbelow the barrier is obstructed and the full compensationof the field is not possible (dotted curves). The residualbuilt-in electric field leads to a formation of a steady-state optically excited electronic system near the up-per GaAs/AlGaAs interface, depicted by the quasi-Fermilevel in Fig. 1(b). Due to the minimal spatial overlap be-tween electrons and holes, the carrier recombination issuppressed. The long-lived system created this way canbe viewed as an effective (optically generated) local n -doping which suppresses the spin decay channel via thecarrier recombination and allows for the observed long τ s ,similarly as in n -doped GaAs samples . The processis described explicitly in Sec. V; a more detailed discus-sion with its experimental confirmation can be found inRef. 16 and its Supplementary information. GaAs Al Ga AsGaAs E F valence bandconduction band e h h (cid:1) + - + + + + + E QF
800 nm > 0.5 mm100 nm (a)(b)(c) h (cid:0) s u r f a c e K e rr r o t a t i on ( m r ad ) ∆ t (ns)sample with AlGaAs barrier÷ 20 D i ff. r e f l e c t i v i t y ( - ) ∆ t (ps) τ = 70 ps sample with Ale with AlGaAs barrier FIG. 1. (Color online) (a) The layer structure of the stud-ied sample (the sample surface, on which the light is inci-dent, is on the left side). (b) The energetic diagram of theconduction and valence bands before (solid curves) and af-ter the illumination (dotted curves). The Fermi level E F ispinned to the edge of the valence band due to the negativelycharged surface states (the square with the minus sign) andionized unintentional bulk impurity states (squares with theplus sign) and the band banding results in a built-in elec-tric field. After the illumination by light with photon energy hν = 1 .
52 eV, the photo-created electrons (circle with the let-ter e ) and holes (circle with h ) are driven by the built-in elec-tric field and spatially separated (arrows). This process com-pensates partially the electric field and leads to a formationof a steady-state long-lived electron sub-system near the up-per GaAs/AlGaAs interface, depicted by the quasi-Fermi level E QF . The electron-hole overlap is minimal in the sub-systemwhich suppresses the recombination and allows for long spinlifetime τ s . (c) The measured dynamics of magneto-opticalKerr signal (points) with fits by Eq. 1 (solid curves). The datameasured in the corresponding samples at 10 K, B = 500 mT, hν = 1 .
52 eV, and 14 µ J · cm − were multiplied or divided bythe indicated factors and vertically shifted for clarity. Thenon-zero signal for ∆ t < τ s in the electron sub-system ex-ceeds the time spacing between the neighbouring pump laserpulses t , which is 12.5 ns in this particular case. Inset: Themeasured dynamics of the differential reflectivity (points) forthe sample with the AlGaAs barrier. The depicted recombi-nation time τ was inferred from an exponential fit (curve). C. Time-resolved magneto-optical detection
The presence of the steady-state long-lived electronicspin system in the studied sample is revealed by themagneto-optical (MO) pump-and-probe experiment; weuse the optical orientation and the MO Kerr effect forspin injection and detection, respectively, as describedin detail in Appendix A and Fig. 5. In Fig. 1(c) weshow the data measured in the sample with the localizedelectronic sub-system and in two reference samples us-ing laser pulses with a repetition frequency of 80 MHz,i.e., a time-spacing between neighbouring laser pulses t = 12 . t (i.e., the fact that the spin signal inducedby a previous pump pulse did not decay to zero beforethe impact of an another pump pulse) immediately in-dicates that τ s > ∼ t = 12 . τ is of the order of hundredsof picosecond in the undoped GaAs.The fitting of the data provides a more precise deter-mination of τ s as shown in Fig. 1(c). By applying themodel for the total MO signal presented in Ref. 16 (i.e.,Eq. 1 for m = 0 , A = A = A below) on the data[solid curves in Fig. 1(c)] we deduced τ s ≈
16 ns which is,indeed, more than two orders of magnitude larger thanthe carrier recombination time τ ≈
70 ps, inferred fromthe dynamics of the differential reflectivity measured inthis sample. From the dependence of the fitted oscil-latory (Larmor) frequency on applied magnetic field weinferred the g -factor of magnitude 0 . ± .
01, confirm-ing that the spin-carriers are free electrons. In the bareGaAs substrate and the undoped epitaxial GaAs on thesubstrate, the spin lifetimes are more than two orders ofmagnitudes shorter – 350 ps and 70 ps for the substrateand epitaxial GaAs, respectively. This agrees well withthe observed τ in the sample with the barrier and withtypical values reported for undoped bulk GaAs where thespin lifetime of spin-polarized photo-carriers is limited bytheir recombination time and where τ is typically at thetime-scale of 100’s of ps are reported. We point out that the MO detection technique enablesus to separate signals coming from different parts of thestudied sample. In particular, a proper selection of theprobe detection wavelength enhances the sensitivity tothe detected MO signals originating from the localizedelectronic sub-system (see Appendix A, Ref. 16 and itsSupplementary information for more details). Thanks tothis, the measured MO dynamics is not dominated bycontributions of short-lived spins generated in the bulkdespite their much a higher density [see Fig. 1(c)].
III. RSA TECHNIQUE WITH UNEQUALINTENSITIES OF SUBSEQUENT LASER PULSES
In our case, when the electron spin lifetime is longerthan the time separation between adjacent pump laserpulses, the measured MO signal is a sum of signals com-ing from spin populations photoinjected by pump laserpulses at different times. The separation of these signals,which is difficult to infer from a time domain measure-ment, can be performed straightforwardly by the RSAtechnique that is schematically depicted in Fig. 2(a).The total Kerr signal S (∆ t, B ) can be expressed as S (∆ t, B ) = P m Θ (∆ t + mt ) A m e − (∆ t + mt ) /τ s × cos [ gµ B B (∆ t + mt ) / ¯ h ] , (1)where Θ( x ) is the Heaviside function that guarantees thatonly the previous pulses contribute to the total signal and m = 0 , , . . . is the index of the m -th preceding excita-tion pulse. A m is the initial amplitude of the Kerr signalat the instant of creation of the respective spin popula-tion by the m -th pulse (for equal intensities of all exci-tation laser pulses, A m = A is the same for all m ). Theterm gµ B B/ ¯ h is the Larmor frequency due to the exter-nal magnetic field B applied in the sample plane where g , µ B and ¯ h are the g -factor corresponding to the stud-ied system, Bohr magneton and reduced Planck constant,respectively.As follows from Eq. 1, if ∆ t is fixed and B is variedinstead, two spin populations created by two subsequentexcitation pulses contribute to the total Kerr signal withdifferent oscillatory frequencies. This is due to a dif-ferent time elapsed from the instant of the photoinjec-tion of the corresponding spin populations [see Fig. 2(a)].Consequently, the signal amplitudes corresponding to thedifferent modulation frequencies are connected with thenumber of spins in these two populations. Therefore,one can probe simultaneously the time evolution of manymixed spin populations created at different instants bymeasuring the RSA curves at several ∆ t .The standard implementation of the RSA techniqueis based on an utilization of a train of laser pulses withequal intensities. Here, on the contrary, we use a trainof laser pulses where each second laser pulse has a sig-nificantly lower intensity using a non-ideally workingpulse picker - see Fig. 2(b) and Appendix A. The lower-intensity laser pulses create a localized spin population atthe GaAs/AlGaAs interface without disturbing the self-confinement, as discussed in Section II B. A spin popu-lation created in such a way is already saturated withrespect to the laser fluence, as can be seen in the insetin Fig. 4(a). This spin population serves as a probe ofthe influence of the much stronger (unattenuated) laserpulse which is incident on the sample at ∆ t = 0 ps. Wenote that this modified RSA technique with unequal in-tensities of neighbouring laser pulses is, in certain sense,using the same idea as ordinary pump-probe experimentwhere a weak probe pulse is used to measure the changesinduced in the sample by a strong pump pulse. time divider ratio 2 (b) Laser intensity (a)
Kerr signal + Kerr signal at (cid:2) xed = FIG. 2. (Color online) (a) A schematic depiction of the reso-nant spin amplification technique (RSA). If the decay of spinpopulation exceeds the time-spacing between neighbouringlaser pulses, the MO signal measured for a given value ofa time delay ∆ t is a sum of (at least) two signals. Inset: De-pendence of MO signal for a fixed value of ∆ t on externalmagnetic field B . (b) A schematic illustration of the trainof femtosecond laser pulses where each second laser pulse hasa significantly lower intensity (in our case at least 30-times)due to the non-ideally working pulse picker which does notremove completely the laser pulse depicted by a dotted line(see Appendix A for more details). IV. RESULTS
In Fig. 3 we show the results of our modified RSA tech-nique for several values of time delays measured on thestudied sample (see Sec. II A). For ∆ t = 500 and 150 ps,we can identify two signals with distinct frequencies - thelarger signal oscillating with a smaller frequency corre-sponds to the spin population photoinjected by an unat-tenuated pulse at ∆ t = 0 and the smaller signal oscillat-ing with a larger frequency corresponds to the spin popu-lation photoinjected by a reduced-intensity pulse at ∆ t = t = − . t = −
400 ps[Fig. 3(e) and (f)] we see only one precession frequencybecause only the spin-population photoinjected by thereduced-intensity pulse is present in the sample for thistime delay, which is in agreement with the deduced valueof the spin lifetime τ s ∼
16 ns < t = 25 ns. Moreover,a strong reduction of the spin-population photoinjectedby the reduced-intensity pulse due to the impact of theunattenuated pulse is immediately apparent from a com-parison of the oscillation amplitudes in Fig. 3(f) and (d).To visualize this effect more clearly, we have fitted themeasured data (see Fig. 3) by Eq. 1 for m = 0 and 1.If there were no disturbing effects of the incident laserpulses, the time delay-dependent amplitudes A m (∆ t )should follow the exponential decay due to the electronspin relaxation A m (∆ t ) = A m e − (∆ t + mt ) /τ s (2) -0.50.00.51.0 (e) (d)(c) (b) K e rr r o t a t i on ( a r b . u . ) (a) -0.50.00.51.00 100 200 300 400-0.250.000.250.50 B (mT) -0.6-0.4-0.2 t = 500 ps experimental data fit t = 150 ps
100 150 200-0.250.000.250.50 t = -400 ps (f) K e rr r o t a t i on ( a r b . u . ) B (mT)
FIG. 3. (Color online) Results obtained by the RSA tech-nique using a train of laser pulses where each second laserpulse has a significantly lower intensity. The experimentallymeasured data (black lines) were measured at ∆ t = 500 ps(a,b), 150 ps (c,d) and −
400 ps (e,f); the right column showzoom views of the data marked by grey rectangles in the leftcolumn. The fits of the data by Eq. 1 for m = 0 and 1 areplotted by the green (grey) curves. All data were measuredat 10 K using laser fluence 140 µ J · cm − and time separationof unattenuated pulses of 2 t = 25 ns. for m = 0 and 1 according to Eq. 1. However, as illus-trated in Fig. 4(b), A (∆ t ) does not follow the depen-dence expected from Eq. 2, which is shown by the reddotted curve in Fig. 4(b). Instead, the impact of theunattenuated pulse reduces it almost instantly, within∆ t < A then slows down and it saturates at ∼ / ∼ A (∆ t ) is zero for ∆ t < B n gen-erated by spin polarized nuclei which adds to the exter-nal magnetic field. We used B n of completely saturated FIG. 4. (Color online) Time evolution of spin populationsphotoinjected by laser pulses. (a) Amplitude A (∆ t ) gener-ated by the unattenuated pulse at ∆ t = 0 ps. (b) Amplitude A (∆ t ) generated by the diminished pulse at ∆ t = − . A on thefluence measured at ∆ t = −
250 ps. Due to a very weak (andnot known precisely) intensity of the suppressed laser pulses,the x-scale is expressed in terms of the intensity of the unat-tenuated laser pulses, which is used to label the excitationconditions throughout the paper. (b) A zoom of data forsmall time delays with a calculated decay of spin populationwhich would correspond to the electron-hole recombinationwith τ ≈
70 ps (black dashed curve). The experiment wasperformed at 10 K using laser fluence 140 µ J · cm − and timeseparation of unattenuated pulses of 2 t = 25 ns. nuclei to estimate the time-average degree of spin po-larization of electrons P e = ( n + − n − ) / ( n + + n − ) withrespect to the average density n + or n − of electrons withtheir spin oriented parallel or antiparallel to the propaga-tion vector of excitation light, respectively. We inferred P e ≈
18 % and nuclei charging time ≈
60 minutes.
V. DISCUSSION
In the previous section we have shown experimentaldata demonstrating that a strong excitation pulse trig-gers a very fast reduction of the existing spin population A . In the following text we discuss possible mechanismsthat can be responsible for this observation. First, we describe the processes which take place if atrain of circularly polarized laser pulses is absorbed inan n -type doped bulk semiconductor. Due to the opti-cal orientation, each laser pulse excites a non-equilibriumpopulation of spin-polarized electrons and holes which re-combine with a time constant τ . Thanks to the presenceof equilibrium electrons in the conduction band, whichare provided by the doping, a certain fraction of thephoto-injected holes recombines with these pre-existingelectrons. Consequently, the remaining photo-injectedspin-polarized electrons can maintain their spin for time τ s significantly exceeding τ . For τ s larger than thespacing between the adjacent laser pulses t , the result-ing electronic spin population is always partially reducedby an impact of the following laser pulse due to a recombi-nation with photo-injected holes and new spin-polarizedelectrons are added, which is leading to a periodic spinrenewal.In our sample, the observed fast reduction of thespin population A [to ≈
50% of the initial value intime < τ = 70 ps [see the in-set in Fig. 1(c) for the transient reflectivity decay mea-surement], a value consistent with the literature .Moreover, a recombination of electrons would free somestates in the studied self-confined sub-system, which arenearly fully occupied by electrons for our experimentalconditions [see the saturation behavior of the MO signalwith the pump intensity in the inset in Fig. 4(a)]. Con-sequently, the fast reduction of A due to a recombina-tion of electrons should be accompanied by an increase ofnewly injected population A into the sub-system, whichis not the case (see Fig. 4(a) where A ≈ t = 6 ps).Another possible mechanism, which could in principlereduce A without a decay of the electron concentration,is the spin relaxation process. The most efficient mecha-nism in GaAs at low temperatures, especially in confinedsystems, is the Dyakonov-Perel (DP) spin dephasing. Indeed, the DP mechanism can be the origin of a fastspin relaxation with τ s of tens or even units of ps in sys-tems with a strong confinement such as remote-doped Al-GaAs/GaAs heterointefaces or quantum wells (see, e. g.,Ref. 13 and references herein). However, we observe ex-ceptionally long τ s ≈
16 ns which is a signature of a weakconfinement and an inefficient DP dephasing in the stud-ied sample. The photoexcitation of carriers due to theabsorption of an intense excitation pulse can be expectedto weaken the confinement [see Fig. 1(b)]. Moreover, theeventual pump-induced fluctuations of the confinementwould lead to a further decrease of the DP efficiency dueto the motional narrowing and, thus, it would leadto a further increase of τ s . Overall, this rules out the DPand other less efficient spin-relaxation mechanisms as acause of the fast decay of A .We attribute the observed phenomenon to a removalof the spin-polarized electrons from the self-confined elec-tron sub-system. This is due to the pump-induced dis-turbance of the confining potential and, thus, to a reduc-tion of the density of available states in the sub-system.The confinement is a self-consistent process which de-pends strongly on boundary conditions and local chargedistribution and can be disturbed by a high density ofphoto-injected charges. When the confining potentialis modified by the additional carriers in the bulk GaAs,the excess electrons move from the sub-system to the bulk[see Fig. 1(b)]. Therefore, they do not contribute signifi-cantly to the measured MO signals, which were optimizedfor the sub-system detection as discussed in Sec. II C andin more details in App. A. In the following tens and hun-dreds of picoseconds, the electrostatic confinement startsto recover due to a continuous decay of photo-carriers inthe bulk via their recombination and, consequently, addi-tional states become available in the sub-system. Thesenew states and the states made available by a partialrecombination of A electrons with the photo-injectedholes are subsequently filled by spin-polarized electronsfrom the bulk. This results in an increase of the spin-polarized population A within ≈
300 ps (see Fig. 4).To sum up, this experiment revealed that the spin po-larization can be periodically “erased” from the superiorhighly mobile spin-transport layer in times < A and other possible perturbations of the spin system. Thisleads to a decrease of the degree of spin polarization P e which is practically achievable in the sub-system. Ideally,each absorbed laser pulse should generate P e ≈
50% atthe instant of absorption . If a material with τ s ≈
16 nsis excited by a train of circularly polarized laser pulseswith a repetition rate of 80 MHz it should lead to time-average P e ≈
36% when this unideal renewal is not con-sidered. Experimentally, we obtained P e ≈
18% thatshows, indeed, a visible but not dramatic reduction ofthe spin polarization.
VI. CONCLUSION
Long-range and high-speed spin transport togetherwith fast spin manipulation are the keystones of high-operation-rate spin-logic devices. In this paper weshow that the fast spin removal functionality can beadded to a superior spin-transport channel in undopedGaAs/Al x Ga − x As heterointerfaces using absorption ofoptical pulses. By employing a modified resonant spinamplification technique with unequal intensities of neigh-bouring laser pulses we demonstrated that spins can beremoved from the high-performance self-confined systemin a picosecond timescale by optical manipulation of thedensities of carriers in the system. This is achieved byreducing the degree of confinement due to the photo- injection of carriers in this region. It was also observedthat the recovery of the confinement occurs in a few hun-dreds of picoseconds. The demonstrated functionalitywhich allows for a fast periodic erasing and regeneratingof the electronic spin polarization in a long-range andhigh-speed spin-transport layer makes the system an ex-cellent candidate for fast spin-logic devices. Since thesesuperior properties should be, in principle, common for alarger variety of self-confined semiconductor structures,the present finding can open new perspectives for spin-logic applications.
ACKNOWLEDGMENTS
We acknowledge support from the European ResearchCouncil (ERC) Advanced Grant No. 268066, from Eu-ropean Metrology Research Programme within the JointResearch Project EXL04 (SpinCal), from the Ministry ofEducation of the Czech Republic Grant No. LM2015087,from the Czech Science Foundation Grant No. 14-37427G, from the Charles University Grants No. 1582417and No. SVV-2015-260216.
Appendix A: Experimental setup
The used time-resolved spin-injection and de-tection method relies on the pump-probe (P&P)technique . The spin-injection is realized using the op-tical orientation by the circularly polarized excitationlaser pulse and the spin-detection is done by measuringthe polarization rotation of the linearly polarized probepulse via the magneto-optical polar Kerr effect .A schematics of the experimental setup is shown inFig. 5. A mode-locked Ti:sapphire laser (Mai Tai,Spectra Physics) with a repetition rate 80 MHz (i.e.a time separation between neighbouring laser pulses t =12 . λ = 815 nm, close to thebandgap of GaAs at low temperatures. The generated ∼
100 fs laser pulses were splitted to pump and probepulses and their fluence was adjusted by neutral densityfilters (their intensity ratio at the sample was typically10:1). A time delay between pump and probe pulses ∆ t was controlled by a delay line from -0.5 ns to 3.5 ns. Thelaser pulses were focused by a converging 10D lens onthe sample to ∼ µ m-sized overlapped spots. Unlessexplicitly mentioned otherwise, the angles of incidence tothe sample surface were < ◦ and ≈ ◦ for the pump andprobe beams, respectively. The sample was mounted inan optical cryostat at temperature of 10 K and placedbetween the poles of an electromagnet that provided in-plane magnetic field up to B = 500 mT oriented in theplane of light incidence. The MO signal correspondingto the probe polarization rotation and the differential re-flectivity were measured as a difference and sum signalin the optical bridge, respectively. A pulse picker (PP) can be inserted to the setup at theposition marked by “PP” in Fig. 5. A PP is essentiallyan electrically controlled acousto-optical modulator thattransmit only certain pulses and block all the others. ThePP in MO experiments usually used in order to deter-mine precisely the spin lifetime from MO time-resolvedsignals in systems where the spin polarization decay timeexceeds the time separation t between the neighbouringlaser pulses. The dilution of laser pulses achieved by thePP is characterized by a so-called divider ratio n whichdescribes that the time separation between neighbouringpulses is increased to nt . However, in the case of ourexperiments, we employed the PP in order to modulatethe intensity of pulse train instead of the selection of ev-ery n -th pulse. This is possible thanks to the unidealefficiency of the pulse suppression by the PP. We veri-fied experimentally, that the diminished laser pulses hasintensity suppressed at lest 30-times, which is the detec-tion limit given by the noise level in our measurementwith a fast photodiode, with respect to that of the unat-tenuated ones. The diminished laser pulses create thespin-polarized population in the sub-system which is al-ready saturated with respect to the laser fluence [see theinset in Fig. 4(a)]. This means that all states which areavailable in the confined system are already filled by thediminished excitation pulse.The polar Kerr efect, which is the origin of the detectedprobe polarization rotation in our sample, changes a signaround the semiconductor bandgap - see inset in Fig. 1 inRef. 25. Consequently, if spectrally broad laser pulses areused, which is the case for our ∼
100 fs long laser pulses(with a spectral bandwidth of ∼
10 nm), the measuredMO signals can be positive, negative or even close to zerodepending of the mutual spectral position of the laserpulse and the MO spectrum. If more than one MO-activesystem with a distinct MO spectrum is present in thesample, the fine tuning of the probe pulses can be usedto enhance or suppress the sensitivity of the detected MOsignal to the system of interest. This is the reason whythe spins photoinjected to the bulk region outside theconfined sub-system, which are rather short-lived, do notsignificantly contribute to the MO signals shown in thispaper, which were optimized with respect to the confinedelectron sub-system - see Fig. 1(c) and Fig. 4(a). Morediscussion about this can be found in the Supplementaryinformation in Ref. 16.
Appendix B: Estimate of degree of electronspin-polarization from nuclear polarizationmeasurements
In semiconductors whose nuclei carry a magnetic mo-ment, like GaAs, the degree of spin-polarization of elec-trons, P e , can be transferred from electrons to nuclei viathe hyperfine interaction. The evolution of the degree ofpolarization of nuclei P n in the laboratory time t follows D(cid:3) B S L(cid:4)
EMlaserpumpprobe PCH fPP PGL
FIG. 5. (Color online) A Schematic depiction of the usedP&P magneto-optical setup. Femtosecond laser pulses weresplitted by a beam splitter (BS) to pump and probe pulseswith a delay line (DL) controlled mutual time delay (∆ t ). Therequired polarization state of laser pulses was set using a com-bination of polarizers (P) and waveplates ( λ/ λ/
4) andthey were focused by a single lens (L) on the sample (S) placedin a cryostat. The reflected probe pulses were collimated byanother lens and their polarization rotation was measured byan optical bridge based on a Glan-Laser (GL) polarizer ana pair silicon photo-diode detectors. The difference electricalsignal was processed by a lock-in amplifier at a modulationfrequency f of the optical chopper (CH). External magneticfield B was applied in the sample plane by an electromag-net (EM). Optionally, the pulse-picker (PP) can be used toincrease a time separation between neighbouring laser pulses. the exponential function P n ( t ) ∝ P e (cid:16) − e − t/T n (cid:17) , (B1)where T n is the characteristic time of the electron-nuclearhyperfine coupling, which is usually of the order ofminutes (i.e., much longer that the electron spin re-laxation time). Consistently with the main text, we usethe standard definition of the degree of polarization, P = ( n + − n − ) / ( n + + n − ), with respect to the density n + or n − of spin-carriers with a spin oriented parallel orantiparallel to the quantization axis (propagation vectorof the circularly polarized excitation beam).As the nuclei are getting polarized, they generate anuclear magnetic field, B n = b n h P n i , that adds to theexternal magnetic field B . Here, b n = − . P n = P n ˆI is the vector of nuclearspin-polarization oriented along the unit vector of the nu-clear spin ˆI . When P n achieves its saturation value for t ≫ T n , B n can be expressed using P e as B n = f b ∗ n B · P e B B , (B2)where the vector P e = P e ˆs is oriented along the unit vec-tor of the electronic spin ˆs ( P e = 1 for fully spin-polarizedelectronic system), b ∗ n = − . B t o t ( m T ) t (min) σ (cid:5) σ + 2B n (a)(b)
58 min43 min28 min13 min K e rr r o t a t i on ( a r b . u . ) ∆ t (ns) FIG. 6. (Color online) (a) Time-resolved MO signal mea-sured on the sample whose nuclei have been spin-polarizedby a long term exposure to light with the helicity σ + . Thecurves and the corresponding labels indicate the laboratorytime during which the sample was illuminated by light withthe helicity σ − ; the curves were vertically shifted for clar-ity. The vertical lines emphasize the variation of the pre-cession frequency due to the varying nuclear magnetic field.Data were measured for the time separation between neigh-bouring pulses nt = 12 . µ J · cm − ,sample temperature T = 10 K, and external magnetic field B = 500 mT. (b) The dependence of B tot = B + B n on lab-oratory time for excitation by helicities σ − (open symbols)and σ + (closed symbols) measured on the sample whose nu-clei have been spin-polarized by a long term exposure to lightwith the opposite helicity. The curves are the fits by Eq. B3.The vertical arrow depicts the saturated value of 2 B n . field generated by a spin-polarized nuclei and f ≤ that takes into ac-count possible processes of nuclear spin-relaxation otherthan the hyperfine coupling with electrons. Usually, itis reported f b ∗ n ≈ − .
85 T.
Eq. B2 holds for B ≫ B and P e is known, the value of P e can be inferred from the measured value of B n .In our experimental setup, the angles of incidence tothe sample surface were < ◦ and ≈ ◦ for the pumpand probe beams, respectively (see Appendix A). How-ever, the polarization of nuclei happens only if there is anon-zero component of the optically injected spins in thedirection of the magnetic field, lying in the sample planein our experimental configuration (see Eq. B2). So, theangle between B (the sample plane) and P e (the direc-tion of the pump beam) has to be different from 90 ◦ - i.e.,the angle of incidence of the pump beam has to be non-zero for an efficient polarization of the nuclei. To achievethis, we exchanged the role which the optical beams playin our setup (see Fig. 5). Consequently, the angle of in-cidence of the pump beam in this configuration was ≈ ◦ and the range of accessible time delays was shifted to∆ t = 9 −
13 ns.Since the spin transfer from electrons to nuclei via thehyperfine channel is a rather slow process whose char-acteristic time T n is of the order of minutes or tens ofminutes, the process of nuclei polarization can bemeasured directly in the laboratory time. As an ex-ample, in Fig. 6(a) shows a sequence of time-resolvedMO signals measured for σ − pump helicity at depictedtimes after a long term sample exposure to light withthe helicity σ + . Clearly, we observe a gradual changeof the precession frequency Ω = g s µ B B tot / ¯ h due to theincrease of the total magnetic field B tot = B + B n ex-perienced by spin-polarized electrons. In Fig. 6(b) weshow the values of B tot inferred from the fits of mea-sured dynamics as a function of the laboratory time forboth helicities of pump pulses. We observe that the nu-clear polarization saturation occurs after t ≈
60 minutes.This time is roughly one order of magnitude longer thanthe values reported in literature for n -doped GaAs (with n ≈ − × cm − ). Considering that charg-ing times longer than tens of minutes are reported inundoped GaAs, these data suggest a low density of thespin-polarized electron sub-system in agreement with theconcentration of the order of ∼ cm − which was de-termined experimentally for this sample in Ref. 16.Following Eq. B1, the precise value of B n of the satu-rated nuclear polarization, which is depicted as a verticalarrow in Fig. 6(b), can be determined by fitting the de-duced values of B tot for both helicities by B tot ( t ) = B ± tot ± C ± e − t/T ± n . (B3)Here, B ± tot are the saturation total magnetic fields for theexcitation with σ ± , C ± are the corresponding amplitudesof the charging process, and T ± n are the characteristictimes. We note that B n is parallel or antiparallel to B with respect to the excitation by σ + and σ − . Consider-ing the error bars, the fits give B n = ( B +tot − B − tot ) / . ± . T n = (13 ±
1) minutes. Fi-nally, the degree of electron spin-polarization P e ≈ n = 3 .
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