Suppression of nuclear spin diffusion at a GaAs/AlGaAs interface measured with a single quantum dot nano-probe A. E. Nikolaenko1, E. A. Chekhovich1, M. N. Makhonin1, I. W. Drouzas1, A. B. Vankov1, J. Skiba-Szymanska1, M. S. Skolnick1, P. Senellart2, A. Lemaˆıtre2, A. I. Tartakovskii1 1 Department of Physics and Astronomy, University of Sheffield, S3 7RH,UK 2 Laboratoire de Photonique et de Nanostructures, Route de Nozay, 91460 Marcoussis, France (Dated: January 15, 2009) 9 0 Nuclear spin polarization dynamics are measured in optically pumped individual GaAs/AlGaAs 0 interface quantum dots by detecting the time-dependence of the Overhauser shift in photolumi- 2 nescence (PL) spectra. Long nuclear polarization decay times of ≈ 1 minute have been found indicating inefficient nuclear spin diffusion from the GaAs dot into the surrounding AlGaAs n a matrix in externally applied magnetic field. A spin diffusion coefficient two orders lower than that J previously found in bulk GaAs is deduced. 5 1 Nuclear spin effects in semiconductors have attracted in the regime of high magnetic fields. By employing a ] h close attention for several decades. Recently these phe- 3D diffusion model, we obtain very good fits to the de- p nomena came into focus in the field of single elec- cay kinetics using a surprisingly low diffusion coefficient t- tronspinmanipulationinsemiconductornano-structures of ≈2·10−15cm2/s, two orders of magnitude lower than n [1, 2, 3, 4, 5]. The hyperfine interaction between the was found for bulk GaAs by Paget [26]. We also re- a u electron and nuclear spins in such semiconductor struc- port nuclear polarization rise times in the range of 0.5-5 q tures [6, 7] can serve as a powerful tool for control- s dependent on optical pumping power, polarization of [ ling spin properties of the localized electron. In par- excitation and the magnitude of the external magnetic ticular, polarization of nuclear spins occurring in GaAs- field. 1 v based heterostructures under circularly polarizedexcita- The sample investigated contains a nominally 13- 1 tion causes local Overhauser fields up to several Tesla monolayer GaAs quantum well (QW) embedded in 8 [8, 9, 10, 11, 12, 13, 14, 15, 16, 17], leading to marked Al Ga As barriers (see growth detail in Ref.[27]). 2 0.33 0.67 splittings of the electron spin states, and as a result, to Interface QDs are formed naturally by 1 monolayer QW 2 . a significant modification of the electron spin coherence width fluctuations. With the lateral dimensions on the 1 andlife-time[1,2,3,4,5,5,18,19,20,21]. Insuchcondi- order of 10-100 nm these potential fluctuations result in 0 tionsthenuclearspindynamicsonthedotsetsthetime- up to 15 meV change in the exciton energy sufficient for 9 0 scales for operations on the electron spin in a controlled zerodimensionalexcitonlocalizationatlowtemperatures : magnetic environment. The nuclear spin dynamics are [8, 9, 10, 27]. A 40/10/90 nm SiO /Ti/Al shadow mask v 2 influenced mainly by the hyperfine interactionwith elec- was deposited on the sample surface, with 800 nm di- i X tron spins and also the dipole-dipole coupling between ameter apertures opened for optical access to individ- r nuclei. In particular,the latter process leads to so-called ual dots. The nuclear spin dynamics were measured at a nuclear spin diffusion [22, 26]. a temperature T=4.2 K with magnetic field of several Inthis workwe introducea new approachto measure- Tesla applied in the Faraday geometry [28]. PL was de- mentsofthenuclearspindiffusioninGaAs/AlGaAshet- tectedwithadoublespectrometerandaCCD.Alaserat erostructures, the type of structures widely employed in 670 nm was employed to generate electrons and holes in electron[1,2,5]andnuclearspin[23,24]coherentcontrol the QW states ≈130meV above the QDs emission lines: experimentsandquantumHalleffectmeasurements[25]. absorption in the AlGaAs barriers at this wavelength is TheOverhausershift(OHS)ofasingleelectronspinstate negligible. inindividualQDs,actsasanaccuratelocalprobe,which Fig.1a shows unpolarized PL spectra measured for an provides a direct and quantitative measure of the degree individual GaAs/AlGaAs dot in an external magnetic of polarization of 104-105 nuclear spins [4, 8, 9, 10]. In field B =2 T for excitation with σ+ and σ− circularly z thisworkweusesuchanano-probepositionedinamono- polarized light (red and blue lines, respectively). These layerfluctuationquantumdottomonitorthenuclearspin peaks correspond to recombination of a neutral exciton diffusionattheinterfaceofaGaAsquantumwell(QWs) localized in the dot. The observed doublet is due to and an AlGaAs barrier. This provides important infor- theexcitonZeemansplittingmodifiedbytheOverhauser mation on the nuclear spin dynamics on the nano-scale, shift of the electron spin states. The collective effect removing the effects of sample inhomogeneities typical of the hyperfine interaction of the nuclear spins in the for macroscopic structures. QD with the photo-generated electron can be treated as Wefindveryslownuclearpolarizationdecaywithchar- an additional magnetic field B [6, 7], that builds up N acteristic times of ≈1 min in an individual interface QD dynamicallyunder circularlypolarizedopticalexcitation 2 Photon energy (eV) 5 µW, 0.4 s 1.7098 1.7100 1.7102 1 µW, 1.3 s (a) B=2 T 30 0.35 µW, 3.4 s y t si exc σ- n exc σ+ e nt V) exc σ+ I e 20 L µ P ( S 40 H (b) O 10 ) exc σ+ V20 Time CCD e µ shutter ( 0 S Erase (π) Pump (σ) H 0 -20 O exc σ- 0.01 0.1 1 10 100 -40 Time (s) 0.01 0.1 1 Optical Power (µW) FIG. 2: (color online). Nuclear polarization built-updynam- ics in a GaAs/AlGaAs interface QD measured in experiment FIG. 1: (color online). (a) Thin (thick) line shows a low- schematicallyshowedinthediagram. Thecurvesareobtained temperature PL spectrum of a single GaAs/AlGaAs dot ex- for the excitation power of 5 µW (circles), 1 µW (triangles) citedwithσ+(σ−)pumpinexternalmagneticfieldof2T.(b) and 0.35 µW (squares) of σ+ pump. The times shown are PowerdependencesoftheexcitonZeemansplittingforexcita- the results of a single exponent fitting (solid curves) of the tionwithσ+(circles)andσ−(squares)polarizations. Arrows experimental data. show the direction in which thepower was scanned. [14, 15, 17, 21]. [7]. B willacttogetherwiththeexternalmagneticfield N B resultinginaspectraldoublet(asseeninFig.1a)with Note, that saturation of the OHS at an absolute z a splitting ∆E(σ±)=µ [|g |B −|g |(B ∓B )] depen- value of 38 µeV is observed at high power for both B h z e z N dent on the polarization of excitation. Here g is the polarizations. The maximum OHS of ≈38µeV corre- e(h) electron (hole) g-factor and µ is the Bohr magneton. sponds to a nuclear polarization degree of ≈ 29%, as B In the restof this workwe use ∆E to probe nuclearspin deducedfromthemaximumOHSinafullypolarizeddot polarization on the dot. of δn100%=IGaAGa + IAsAAs=132 µeV. Here AGa=42 Fig.1b shows the dependences of the OHS on excita- µeV and AAs=46 µeV are the hyperfine constants and tion power for σ+ and σ− polarized excitation. Qual- IGa=IAs=3/2 are the spins of Ga and As nuclei [26]. itatively different dependences are observed in the two Inthis workthe nuclearspinlife-time ismeasuredem- cases: a strong threshold-like B switching and large ployinganall-opticalpump-probe method, where the ef- N hysteresis loop is observed for σ+ excitation, whereas fect of the strong pump is tested after a time-delay with a smooth curve with very weak hysteresis is measured aweakprobe. Inordertoidentifytheappropriatelength in the σ− case. The marked difference originates from andopticalpoweroftheprobesothatitdoesnotperturb feedbackoftheopticallyinducedOverhauserfieldonthe the system, the nuclear polarization rise time is firstly dot on the electron-to-nuclei spin transfer efficiency oc- measured. This is reportedin Fig.2 for a single optically curring due to the dependence of the electron Zeeman pumpedGaAs/AlGaAsdotinanexternalmagneticfield splitting (the major energy cost of the electron-nuclear B of2T.Theopticalpulsesequenceforthis measure- ext spin flip-flop) on both B and B [7, 11, 13, 14, 15]. ment is schematically shown in the inset of Fig.2. The z N The additional electron spin state splitting produced by pulses from two lasers are prepared by fast mechanical B either enhances the spin transfer when the electron shutters with a rise time <2 ms. The first laser pulse N Zeeman splitting E (σ±)=µ g (B ∓B ) is reduced (denoted as ’erase’) is 10 s long and has linear polariza- eZ B e z N (for σ+) or lead to inefficient spin pumping when E is tion. Thispulseisrequiredfordestructionofanynuclear eZ increased(forσ−). Thestrongfeedbackinthecaseofσ+ polarization in the dot and surrounding QW remaining excitation leads to the clear bistable behavior in Fig.1b from the previous measurement cycle. Nuclear polariza- 3 tion is then pumped by the second circularly polarized cluded since the sample is nominally undoped and no ’pump’ pulse of variable length. A mechanical shutter evidence for charging in either the QW or dots is found placed in the PL detection path allows PL signal acqui- in PL. The quadrupolar relaxation via phonon-assisted sition in a narrow time window at the end of the pump processesisratherweakfortemperaturesbelow30K[30] pulse. Thetimeresolutionofthedynamicsmeasurement leadingto characteristicdecaytimes ofthe orderof1000 is determined by the time this shutter is open. For the s in GaAs. On the other hand, the nuclear polarization shortest delay times the resolution was as low as 5 ms. intheextremelysmallvolumeofthedotisverysensitive In order to improve signal to noise ratio in the PL spec- tothe spin”leakage”intothe surroundingbulk. Inwhat tra measured for each delay, sequences of the erase and follows we will focus on this decay mechanism. pump laser pulses and the PL acquisition were repeated Decay of the nuclear polarization S due to diffusion N severaltimesforeachspectrummeasured. Thedegreeof can be described with a standard 3D diffusion equation nuclear polarization for each delay was determined from dS (r,t)/dt=D ∆S (r,t), (1) the modification of the exciton Zeeman splitting due to N QD N the OHS. whereD isthenuclearspindiffusioncoefficient. Inour QD We find a strong dependence of the nuclear spin rise modelingweapproximatethedotshapewitha5nmhigh time on the pumping power. Fig.2 shows evolution of disk with a 20 nm diameter andassume thatthe nuclear the OHS with time under the σ+ polarized pumping spin is pumped optically inside the dot volume, whereas measured with different optical excitation powers. The the material around the dot is not polarized directly by measured dynamics curves in Fig.2 can be well approx- optical excitation. This description is an approximation imated with exponential fits with rise times of 0.4, 1.3, of the actual nuclear spin pumping process. In a more and3.4sforexcitationpowerof5,1and0.35µW,respec- complexmodel,spatiallynon-uniformopticalpumpingof tively[29]. Thesefindingscanbeexplainedbythepower- thenuclearspininthewholetwo-dimensionalsheetofthe dependent supply rate of the spin polarized electrons to QWshouldbetakenintoaccount. Fromourcalculations the dot: faster nuclear spin pumping occurs when the we find, however, that the low aspect ratio of the model spinsupplyrateisincreasedatahigherexcitationpower dot effectively leads to a one-dimensional spin diffusion [15? ]. process, rather insensitive to the nuclear polarization in In order to investigate the nuclear polarization decay adjacent parts of the well. In what follows we assume thepulsesequencewasmodifiedintoa’pump-probe’con- that the nuclei outside the dot are polarized only via figurationschematicallyshownin the inset of Fig.3. Nu- spin diffusion from the dot. clear polarization is pumped by a 10 s long circularly Initially, at the beginning of the pumping pulse, the polarized pump pulse. Then a short linearly polarized dotandsurroundingmaterialarenotpolarized. We first pulse is applied at a variable delay after the end of the calculate the distribution of the nuclear spin due to the pumppulsetoprobetheexcitonZeemansplitting. Based diffusion from the dot in the first 10 seconds during the on the measured nuclear polarization built-up dynamics optical pulse. For this we assume an instantaneous in- shown in Fig.2 we set the length of the probe pulse to crease of the polarization inside the dot, which is kept 100 ms to minimize its effect on the nuclear polarization constant for the duration of the pumping pulse. Using in the dot. In the time period between the two pulses this distribution as the initial condition (the high polar- the sampleiskeptinthedark. The CCDshutterisopen ization in the dot and the decreasing polarization away duringtheprobepulseonly. Inordertoimprovesignalto from the dot in the bulk), we then simulate the time- noise ratio several pump-probe measurement cycles are evolution of the nuclear spin polarization on the dot in performed with no dark time between the cycles as the the dark by allowing the polarization inside the dot to dot is polarized to saturation by the long pump pulse decay with time. independently on the initial polarization. The only fitting parameter that we vary in our model Fig.3showsthenuclearspindecaydynamicsmeasured is the diffusion coefficient D . Solid curves in Fig.3 QD at Bext=2T. The exciton Zeeman splitting is plotted as show the results obtained for three different diffusion a function of the ’dark’ delay time between the pump coefficients. The thin black line shows the decay with andprobepulses. As seenfromthe figuredecayforboth D = 10−13cm2/s found by Paget in Ref.[26] for bulk QD polarizations of the pump occurs with a characteristic GaAs. Ourcalculationspredictthatforthis valueofdif- time of ≈1 min. fusioncoefficient the spinpolarizationon the dot falls to The most likely mechanisms for the nuclear spin de- 30%levelafter5second,about12timesfasterthanfound polarization ”detected” by the QD nano-probe is nu- in our experiment on GaAs/AlGaAs dots. The thick clear spin diffusion into the unpolarized barrier. Two blacklineprovidinganexcellentfittoourdatashowsre- other mechanisms that could contribute are depolariza- sults for a verylow magnitude ofD =2·10−15cm2/s. QD tion due to interaction with an electron gas in the QW This is about 20 times smaller than that we recently and phonon-assisted spin-lattice relaxation. The relax- found for InGaAs/GaAs dots [17] and 50 times smaller ation via interaction with residual electrons can be ex- than in bulk GaAs [26]. To exclude a scenario where the 4 under non-resonant circularly polarized optical excita- 2x10-15cm2/s tion. The rise time is found to be sensitive to the ex- 10-12cm2/s citation power and external magnetic field and varies in 10-13cm2/s the range of ≈ 0.4 ÷ 5 seconds. A very slow rate of the nuclear polarization decay has been measured with 20 a characteristic depolarization time exceeding 1 min in + magnetic field of several Tesla. This indicates suppres- σ V) sionofthe nuclearspin diffusionfromthe GaAs dotinto e theAlGaAsbarrier. Wefindanalmost2ordersofmagni- µ tudesmallerdiffusioncoefficientcomparedtobulkGaAs ( Time S 0 CCD andInGaAsdotsreportedrecently. Thisobservationcan H shutter beexplainedbytheincreaseddistanceattheinterfaceof O thedotandinthebarrierbetweenthelikenuclearspecies Pump (σ) Probe (π) - contributing to the flip-flop-like diffusion process in the σ external magnetic field. The increased separation leads to a notable weakening of the dipole-dipole interaction -20 and, consequently, to a slower nuclear spin decay in a B=2T GaAs/AlGaAs dot. This work has been supported by EPSRC grants 0.1 1 10 100 1000 EP/C54563X/1 and EP/C545648/1, Programme Grant Time (s) GR/S76076,ProgrammeGrantEP/G601642/1,the EP- SRC IRC for Quantum Information Processing, and by the Royal Society. FIG. 3: (color online). Nuclear polarization decay curves measured for GaAs/AlGaAs interface QDs for two polariza- tionsof thepumppulsein externalmagnetic fieldof 2T(cir- cles). Lines show polarization decay curves calculated using E(tqh.i1nwbiltahckD)QanDd=102−·1210c−m152/csm(g2/rasy()t.hik black), 10−13 cm2/s [1] J. R.Petta et al.,Science 309, 2180 (2005). [2] F. H.L. Koppenset al., Science 309, 1346, (2005). [3] M. Atatre,J. Dreiser, A. Badolato, A. Hgele, K. Karrai, A. Imamoglu, Science312, 551 (2006). volume around the dot is polarized by a very fast dif- [4] M. V. Gurudev Dutt, J. Cheng, Bo Li, X. Xu, X. Li, P. fusion during the 10 s pumping time, which then would R. Berman, D. G. Steel, A. S. Bracker, D. 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