5
Spin of Semiconductor Quantum Dots under Hydrostatic Pressure Yun Tang, Alexander F. Goncharov, Viktor V. Struzhkin, Russell J. Hemley, and Min Ouyang* ,† Department of Physics and Center for Nanophysics and Advanced Materials, University of Maryland, College Park, Maryland 20742 and Geophysical Laboratory, Carnegie Institution of Washington, D.C. 20015 ABSTRACT Spin coherence dynamics of semiconductor quantum dots under hydrostatic pressure has been investigated by combining the ultrafast optical orientation method with the diamond-anvil cell technique. Spin confined within quantum dots is observed to be robust up to several gigapascals, while electron and exciton Lande ´ g factors show novel bistable characteristics prior to the first-order structural transition. This observation is attributed to the existence of a theoretically predicted metastable intermediate state at the nanoscale, for which there has been no previous experimental support. The results also reveal pressure enhanced fundamental exchange interactions for large-sized quantum dots with sizable anisotropy. These findings shed insight into underlying mechanisms of long-debated nanoscale solid-state transformations in semiconductors and are also crucial for the development of future quantum information processing and manipulation based on spin qubits of quantum dots. KEYWORDS spin, quantum dots, hydrostatic pressure, Landé g factors, solid-state transformation S emiconductor quantum dots (QDs) are model systems to study various fundamental physics at the nano- scale, including solid-state phase transformation, 1-3 as well as represent attractive building blocks for scalable solid-state implementations of quantum information pro- cessing by using spins of electrons and excitons as qubits. 4 While recent progress has been achieved in understanding spins confined within QDs, 5-7 crucial issues such as stability of spin states as well as the manipulation of spin and spin-orbit coupling require more work, mainly due to the experimental challenges involved. The application of hydro- static pressure represents an important means by which to precisely tune and modify key material parameters, and thus offers a unique opportunity to explore various fundamental spin properties and interactions in QDs. Here we report the dependence of spin coherence dynamics in artificial lattice structures of semiconductor QDs measured by a new method that combines ultrafast optical orientation methods with diamond-anvil cell techniques. Spin confined within QDs is observed to be robust up to several gigapascals, while electron and exciton Lande ´ g factors show novel bistable characteristics prior to the first-order structural transition. This observation is attributed to the existence of a theoreti- cally predicted metastable intermediate state at the nano- scale, for which there has been no previous experimental support. The results further reveal pressure-enhanced fun- damental exchange interactions for large-sized quantum dots with sizable anisotropy. Therefore, our findings shed light on the underlying mechanisms of long-debated nano- scale solid-state transformations in semiconductors, 1-3 and the results are also important for understanding structure- spin correlations as well as engineering nanoscale structures to achieve desired spin property for the future development of spin-based quantum devices. CdSe QDs with diameters tunable from 2.5 to 7.0 nm were synthesized via a modified chemical method, 8 and possessed a narrow size distribution of 4% and high crystal- linity with the wurtzite structure under ambient conditions (Figure 1). These chemically synthesized QDs were originally capped/stabilized with a monolayer of surfactant, trioctylphos- phine oxide, and were redissolved in 4-ethylpyridine as a pressure medium up to 10 GPa. 2 Pressure was determined by the standard ruby fluorescence technique with a non- magnetic Be-Cu diamond-anvil cell. 9 A two-color time- resolved Faraday rotation (TRFR) technique was applied to measure spin coherence dynamics under pressure (Figure 1a) (see Supporting Information). 10 Briefly, a circularly polarized laser beam with tunable energy is used to excite spin polarization of CdSe QDs at a selected energy level. At a delay time t, a linearly polarized probe pulse with independent tunable photon energy measures the spin magnetization along the laser propagation direction by monitoring rotation of its linear polarization orientation (θ). When an in-plane magnetic field (H) is applied, the spins precess about the field direction, which leads to an oscilla- tory Faraday rotation at the sample-dependent Larmor frequency (v L ). This process can be described by Ae -t/T 2 * cos(2πν L t + φ), where A is the amplitude, T 2 * is the transverse spin lifetime, and φ is the phase. A custom-made UV-visible spectrometer with fs- whitelight is used for the linear optical absorption measurements. * To whom correspondence should be addressed, [email protected]. Received for review: 11/9/2009 Published on Web: 12/15/2009 pubs.acs.org/NanoLett © 2010 American Chemical Society 358 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

Spin of Semiconductor Quantum Dots under Hydrostatic Pressure

  • Upload
    min

  • View
    214

  • Download
    0

Embed Size (px)

Citation preview

Spin of Semiconductor Quantum Dots underHydrostatic PressureYun Tang,† Alexander F. Goncharov,‡ Viktor V. Struzhkin,‡ Russell J. Hemley,‡ andMin Ouyang*,†

†Department of Physics and Center for Nanophysics and Advanced Materials, University of Maryland, College Park,Maryland 20742 and ‡Geophysical Laboratory, Carnegie Institution of Washington, D.C. 20015

ABSTRACT Spin coherence dynamics of semiconductor quantum dots under hydrostatic pressure has been investigated by combiningthe ultrafast optical orientation method with the diamond-anvil cell technique. Spin confined within quantum dots is observed to berobust up to several gigapascals, while electron and exciton Lande g factors show novel bistable characteristics prior to the first-orderstructural transition. This observation is attributed to the existence of a theoretically predicted metastable intermediate state at thenanoscale, for which there has been no previous experimental support. The results also reveal pressure enhanced fundamentalexchange interactions for large-sized quantum dots with sizable anisotropy. These findings shed insight into underlying mechanismsof long-debated nanoscale solid-state transformations in semiconductors and are also crucial for the development of future quantuminformation processing and manipulation based on spin qubits of quantum dots.

KEYWORDS spin, quantum dots, hydrostatic pressure, Landé g factors, solid-state transformation

Semiconductor quantum dots (QDs) are model systemsto study various fundamental physics at the nano-scale, including solid-state phase transformation,1-3

as well as represent attractive building blocks for scalablesolid-state implementations of quantum information pro-cessing by using spins of electrons and excitons as qubits.4

While recent progress has been achieved in understandingspins confined within QDs,5-7 crucial issues such as stabilityof spin states as well as the manipulation of spin andspin-orbit coupling require more work, mainly due to theexperimental challenges involved. The application of hydro-static pressure represents an important means by which toprecisely tune and modify key material parameters, and thusoffers a unique opportunity to explore various fundamentalspin properties and interactions in QDs. Here we report thedependence of spin coherence dynamics in artificial latticestructures of semiconductor QDs measured by a new methodthat combines ultrafast optical orientation methods withdiamond-anvil cell techniques. Spin confined within QDs isobserved to be robust up to several gigapascals, whileelectron and exciton Lande g factors show novel bistablecharacteristics prior to the first-order structural transition.This observation is attributed to the existence of a theoreti-cally predicted metastable intermediate state at the nano-scale, for which there has been no previous experimentalsupport. The results further reveal pressure-enhanced fun-damental exchange interactions for large-sized quantumdots with sizable anisotropy. Therefore, our findings shedlight on the underlying mechanisms of long-debated nano-

scale solid-state transformations in semiconductors,1-3 andthe results are also important for understanding structure-spin correlations as well as engineering nanoscale structuresto achieve desired spin property for the future developmentof spin-based quantum devices.

CdSe QDs with diameters tunable from 2.5 to 7.0 nmwere synthesized via a modified chemical method,8 andpossessed a narrow size distribution of 4% and high crystal-linity with the wurtzite structure under ambient conditions(Figure 1). These chemically synthesized QDs were originallycapped/stabilized with a monolayer of surfactant, trioctylphos-phine oxide, and were redissolved in 4-ethylpyridine as apressure medium up to 10 GPa.2 Pressure was determinedby the standard ruby fluorescence technique with a non-magnetic Be-Cu diamond-anvil cell.9 A two-color time-resolved Faraday rotation (TRFR) technique was applied tomeasure spin coherence dynamics under pressure (Figure1a) (see Supporting Information).10 Briefly, a circularlypolarized laser beam with tunable energy is used to excitespin polarization of CdSe QDs at a selected energy level. Ata delay time ∆t, a linearly polarized probe pulse withindependent tunable photon energy measures the spinmagnetization along the laser propagation direction bymonitoring rotation of its linear polarization orientation (θ).When an in-plane magnetic field (H) is applied, the spinsprecess about the field direction, which leads to an oscilla-tory Faraday rotation at the sample-dependent Larmorfrequency (vL). This process can be described by Ae-∆t/T2*

cos(2πνL∆t + φ), where A is the amplitude, T2* is thetransverse spin lifetime, and φ is the phase. A custom-madeUV-visible spectrometer with fs- whitelight is used for thelinear optical absorption measurements.

* To whom correspondence should be addressed, [email protected] for review: 11/9/2009Published on Web: 12/15/2009

pubs.acs.org/NanoLett

© 2010 American Chemical Society 358 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

At low pressure linear absorption spectra of QD samplesclearly exhibited discrete electronic states, which were inaccord with previous calculations (Figure 1b).11,12 When thepressure was slowly increased to a critical value, absorptionof CdSe QDs suddenly became featureless with the absorp-tion changing continuously over a broad energy range. Thefeatureless optical absorption structure at high pressurearises from the first-order solid-solid phase transition fromwurtzite (with direct band gap) to rock-salt structure (withindirect band gap), a transformation first identified by X-raydiffraction (XRD) measurements.2 This critical pressurecould be used as a reference to characterize structural phasetransition as a function of QD size (Figure 1c). Qualitatively,this size dependence agreed well with previous experimentalhystersis measurements and thermodynamics consider-ations of the transformation,1,2 and provided a cross checkon the experiments reported here.

Importantly, our TRFR measurements clearly revealedspin coherence dynamics of electrons and excitons confinedwithin CdSe QDs under pressure (Figure 2a). Two Larmorprecession frequencies could be distinguished from fastFourier transform (FFT) as well as beating pattern presentedin raw TRFR data, which led to two different Lande g factorsbased on the relation

g )hνL

µBH

(detailed procedure for determining g factors from the TRFRdata is available in the Supporting Information), where µB is

FIGURE 1. All optical spin resonance measurements of semiconduc-tor QDs under pressure. (a) Experimental setup. (b) Linear opticalabsorption spectra of 3.4 nm CdSe QDs under selected hydrostaticpressure labeled by different number and color (1, 0.1 MPa; 2, 1.0GPa; 3, 1.9 GPa; 4, 2.8 GPa; 5, 3.1 GPa; 6, 3.5 GPa; 7, 4.7 GPa; 8, 5.5GPa; 9, 6.0 GPa). (Inset) Typical high-resolution transmission elec-tron microscope image of CdSe QDs with wurtzite structure. Scalebar: 5 nm. The QDs manifest spherical symmetry with the aspectratio of 1. (c) Size dependence of first-order structural transitionpressure obtained from (b).

FIGURE 2. Spin coherence dynamics of 3.4 nm CdSe QDs underhydrostatic pressure. (a) Typical TRFR data at 1.2 GPa. Circle:experimental data with H ) 0.21 T. Red solid curve: theoretical fitwith two Larmor precession frequencies. The inset shows FFT ofTRFR data revealing two distinct Larmor frequencies (1.98 and 2.23GHz). (b) Dependence of electron (lower) and exciton (upper) gfactors on applied hydrostatic pressure, showing a novel g factortransition before the first-order structural phase transition occurred.Dashed lines are guides to the eye for the evolution of experimentalg factors (red diamonds). Squares are theoretical calculations ofpressure dependence of electron g factor by assuming continuallattice deformation of ambient wurtzite phase. In the calculation,the pressure dependence of Eg and R were determined from linearoptical absorption measurement. Pressure dependence of Ep and ∆SO

were obtained from theory prediction.26,27 The best fit of ambientg factor was obtained with a ) 1.7 eV·nm2, which was close to theaccepted literature value.12

© 2010 American Chemical Society 359 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

Bohr magnet and h is Planck’s constant. Following theprevious report under ambient conditions6 as well as ourexperimental result of size dependence of both g factors (seeFigure S1 in the Supporting Information), we can assignunambiguously observed two g factors at low pressure to theelectron (lower) and the exciton (higher), respectively.

We further characterized in detail both the electron andexciton g factors as a function of pressure (Figure 2b).Surprisingly, a novel bistable characteristic of the g factorswas clearly observed: Both the electron and exciton g factorsremained stable over a specific pressure range above ambi-ent conditions and then increased with pressure and stabi-lized at different values up to the onset of the rock-salt phase.This observed g factor transition was further ascertained byassigning transition pressure to the midpoint of the twobistable g factors (Figure 2b and 3a). The monotonic increasein the g factor transition pressure with decreasing QD sizesuggests that the transition is an intrinsic pressure-driveneffect in the QDs.

As compared with the Figure 1c, the observed g factortransition happens at a much lower pressure; thus it couldnot explicitly arise from the first-order structural transition,which has been confirmed by XRD measurements. In orderto gain insight of pressure-induced evolution of g factors, thetransformation path needs to be examined carefully. Due

to the lack of effective experimental characterization, theunderlying mechanism of such a phase transition remainsan unresolved issue. Furthermore, the wurtzite/zinc blendestructure and rock-salt structure represent the most stableforms of most of the four- and six-coordinated binarycompounds, respectively; hence understanding the transi-tion mechanism of CdSe QDs is essential for manipulatingthe energetics of different semiconductor nanostructures toimprove materials synthesis and to achieve desired materialsfunctionalities and properties in a controlled manner. So far,two different mechanisms have been proposed (Figure 3b):the first is based on a continual deformation model, assum-ing high correlated atom motions during transformation;13-16

the second is a two-step process, in which a long-livedmetastable intermediate phase with a hypothetic five-coordinated structure exists before the first-order phasetransition occurs.17-21 Even though a metastable intermedi-ate state was suggested based on shock wave compressionexperiments with bulk semiconductors,22-24 direct experi-mental evidence of such metastable states at the nanoscalehas been lacking. Instead, earlier reports of high-pressureXRD measurements of CdSe QDs leaned to support acontinual deformation model because of no detectablechanges of XRD peaks before first-order transition.1-3 Ascompared with experimental techniques based on structuralcharacterization, our experiment provides a unique op-portunity to directly measure electronic and excitonic effec-tive g factors with a high degree of precision under pressure.This g factor probe plays a central role in gaining fundamen-tal understanding of electronic band structure as well asinterband optical processes. Thus our measurements offera valuable alternative insight (from the viewpoint of elec-tronic structure) for an underlying nanoscale solid-statetransformation path.

From perturbation theory the electron g factor of spheri-cal QDs can be generalized in terms of fundamental bandstructure parameters, including size-dependent band gap Eg,the Kane matrix element Ep, and the spin-orbit splitting∆SO

6,25-27

ge(R) ) g0 - 23

Ep∆SO

(Eg + a

R2+ ∆SO)(Eg + a

R2)where R is radius of the QDs and a is a fitting parameter inthe simplest parabolic approximation. If the continual de-formation model is correct, a smooth increase of ge factoris expected (Figure 2b), which is obviously in conflict withbistable g factor characteristics observed during the high-pressure transformation. Therefore, our observed bistableg factor characteristics strongly suggest the existence of along-lived metastable intermediate state during the trans-formation process, and the distinct g factors correspond todifferent electronic states induced by pressure. In particular,our measured g factor transient pressure range is qualita-tively consistent with the ∼2 GPa pressure range of the onsetof the theoretically predicted intermediate state.20

FIGURE 3. Lande g factor transition at intermediate pressure. (a)QD size dependence of g factor transition pressure. (b) Schematicsof two different underlying transformation mechanisms of first-order phase transition. A five-coordinated structure (P63 mmcspace group) is used to represent metastable intermediate struc-ture in path 2.

© 2010 American Chemical Society 360 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

While the g-factor transition was observed for all the QDswe investigated (as summarized in Figure 3a), there existedsubtle differences between small- and large-sized CdSe QDs:For all large-sized QDs (g5 nm in diameter) we consistentlyobserved three g factors at higher pressure (Figure 4a; alsosee Figure S2 in the Supporting Information), which sug-gested that this observation should be an intrinsic size-related effect. In order to reveal such fine effect, we furtherinvestigated correlation between energy level scheme andg factors by carrying out additional spectroscopic measure-ments. In general, optical study of the quantum size levelsis very challenging because of inhomogeneous broadeningand cannot be achieved simply by linear absorption mea-surements (Figure 1b). In contrast, TRFR has been demon-strated to be not only a unique and sensitive experimentalprobe for spin coherence dynamics but also a precisespectroscopic technique for directly identifying individualexciton transitions that reveal the fine electronic energy levelscheme (Figure 4b).28-30 For example, related TRFR spec-troscopic study of a colloidal CdS@CdSe quantum dot-quantum well system has revealed its fine energy levels,which showed consistency with kp perturbation calcula-tions.28 Similarly, we carried out measurement of depen-dence of TRFR oscillation amplitude on probe energy underdifferent pressures. In these experiments, a wavelengthtunable probe with ∼5 meV energy resolution was achievedby passing the light through a monochromator after trans-mission through the DAC. Under ambient conditions, TRFRspectra exhibited pronounced resonances close to the ab-

sorption edges that could not be seen in linear absorptionspectra and could be further assigned to fine energy leveltransition evaluated with kp calculations (Figure 4c).28 Whileall the resonance peaks that appeared under ambient condi-tions remained as the pressure was increased, two morenew resonance peaks could be immediately identified withsmall amplitude and became more pronounced at higherpressure, which agreed well with the increased number of gfactors within the same pressure range. In contrast, wecarried out the same measurements for small-sized QDs andsuch a control experiment showed no new resonance peaksduring the entire transformation path.

Therefore, we attributed our observed increased numberof g factors to the pressure-enhanced fundamental exchangeinteractions in large-sized QDs,31 based on following facts:(i) For chemically synthesized QDs it has been shown thatwhile smaller size QDs possessed very symmetrical sphericalshape, larger size QDs started manifesting anisotropy.8 Thiscan also be clearly seen by comparing high-resolution TEMimages in the Figures 1b and 4b and in Figure S2 inSupporting Information, which shows the increase of aspectratio of QDs with the size. Under hydrostatic pressure, theaspect ratio can be significantly enhanced due to differentcompression ratios along different crystal axis. (ii) Theevolution of initially 8-fold degenerate ground state in awurtzite spherical QD could be obtained from theoreticalanalysis of fine band-edge exciton structure when electron-hole exchange interactions, crystal field. and anisotropyeffects were considered (Figure 4b).6,32 As a result, crystal

FIGURE 4. Pressure-enhanced exchange interactions in 5.1 nm CdSe QDs. (a) Evolution of g factors with applied pressure. (b) (Left) Typicalhigh-resolution transmission electron microscope image of a 5.1 nm CdSe QDs. Scale bar: 5 nm. The QDs manifest structural anisotropy withthe aspect ratio of 1.04; (Right) Schematic of degeneracy lifting of the exciton fine band-edge structure (represented by HOMO-LUMO typeenergy levels) due to enhanced exchange interactions under pressure. Dashed lines are guides to the eye for the evolution of experimentalg factors. (c) Dependence of TRFR amplitude on probe photon energy under three different pressures. Data were taken at fixed time delay ∆t) 300 ps and normalized by the probe beam power. Green arrows highlight resonance peaks existing in all pressures, and red arrows highlightthe appearance of new resonance peaks at higher pressure. For comparison, linear optical absorption spectra for different pressures are alsopresent.

© 2010 American Chemical Society 361 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362

field splitting and electron-hole exchange interactions wouldbe significantly augmented in the more anisotropic QDs dueto stronger confinement,11 thus leading to energy leveldegeneracy lifting and the g factors splitting. (iii) The cor-relation between energy level splitting and the increasednumber of g factors of large sized quantum dots at highpressure was indeed clearly observed in the Figure 4c.

In summary, investigations of quantum confined spincoherence dynamics of semiconductor QDs under pressurereveal that the spin of semicnoductor QDs is very robust upto ∼2 GPa. This observation is important for understandingthe stability of spin qubits of QDs in the future quantuminformation processing devices. In contrast to former studiesof nanoscale solid-state transformation by XRD and linearoptical absorption, our new combinatory technique by usingTRFR and diamond-anvil cell high-pressure technique to-gether provides a unique insight into the transformationprocess from the viewpoint of electronic state propertychanges. A surprising pressure-driven g-factor transition wasobserved along the transformation path that could be at-tributed to the theoretically predicted metastable intermedi-ate state not been explicitly observed yet at the nanoscale.This finding marks an important step toward deep under-standing of the underlying mechanism of related longdebated nanoscale solid-state transformation. Furthermore,the current study reveals pressure-enhanced fundamentalfine exchange interactions that should provide deepenedunderstanding necessary for future manipulation of spinstates by interfacial/surface strain layer fabrication.33,34

Acknowledgment. We gratefully acknowledge fundingfrom an NSF CAREER award (DMR-0547194), ONR YIPaward (N000140710787), Beckman YIP grant (0609259093),NSF MRSEC seed fund, NSF/EAR (EAR-0711358), DOE/BES(DE-FG02-02ER45955) for supporting the high pressuremeasurements, NSF/DMR (DMR 0805056), CDAC (DE-FC52-08NA28554), and the Balzan Foundation.

Supporting Information Available. Experimental meth-ods and supporting figures (Figures S1 and S2). This materialis available free of charge via the Internet at http://pubs.acs.org.

REFERENCES AND NOTES(1) Tolbert, S. H.; Alivisatos, A. P. Science 1994, 265, 373–376.(2) Tolbert, S. H.; Alivisatos, A. P. J. Chem. Phys. 1994, 102, 4642–

4656.

(3) Wickham, J. N.; Herhold, A. B.; Alivisatos, A. P. Phys. Rev. Lett.2000, 84, 923–926.

(4) Burkard, G.; Loss, D. In Semiconductor Spintronics and QuantumComputation; Awschalom, D. D., Samarth, N., Loss, D., Eds.;Springer-Verlag: Berlin, Germany, 2002; pp 229-276.

(5) Wong, C. Y.; Kim, J.; Sreekumari Nair, P.; Nagy, M. C.; Scholes,G. D. J.Phys.Chem.C 2009, 113, 795–811.

(6) Gupta, J. A.; Awschalom, D. D.; Efros, Al. L.; Rodina, A. V. Phys.Rev. B. 2002, 66, 125307.

(7) Ouyang, M.; Awschalom, D. D. Science 2003, 301, 1074–1078.(8) Murray, C. B.; Norris, D. J.; Bawendi, M. G. J. Am. Chem. Soc. 1993,

115, 8706–8715.(9) Hemley, R. J.; Mao, H. K. In High-Pressure Phenomena, Proceedings

of the International School of Physics, “Enrico Fermi” CourseCXLVII, (eds Hemley, R. J., Chlarottl, G. L., Bernasconi, M., Ulivi,L., Eds.; IOS Press: Amsterdam, 2002; pp 3-40.

(10) Awschalom, D. D.; Samarth, N. In Semiconductor Spintronics andQuantum Computation; Awschalom, D. D., Samarth, N., Loss, D.,Eds.; Springer-Verlag: Berlin, Germany, 2002; pp 147-194.

(11) Efros, Al. L.; Rosen, M. Annu. Rev. Mater. Sci. 2000, 30, 475–521.(12) Efros, Al. L.; Rosen, M.; Kuno, M.; Nirmal, M.; Norris, D. J.;

Bawendi, M. Phys. Rev. B 1996, 54, 4843–4856.(13) Limpijumnong, S.; Jungthawan, S. Phys. Rev. B 2004, 70, No.

054104.(14) Sowa, H. Acta Crystallogr., Sect. A 2005, 61, 325–330.(15) Zahn, D.; Grin, Y.; Leoni, S. Phys. Rev. B 2005, 72, No. 064110.(16) Wilson, M.; Hutchinson, F.; Madden, P. A. Phys. Rev. B 2002, 65,

No. 094109.(17) Catti, M. Phys. Rev. B 2002, 65, 224115.(18) Grunwald, M.; Rabani, E.; Dellago, C. Phys. Rev. Lett. 2006, 96,

255701.(19) Limpijumnong, S.; Lambrecht, W. R. L. Phys. Rev. B 2001, 63,

104103.(20) Miao, M. S.; Lambrecht, W. R. L. Phys. Rev. Lett. 2005, 94,

225501.(21) Shimojo, F.; Kodiyalam, S.; Ebbsjo, I.; Kalla, R. K.; Nakano, A.;

Vashishta, P. Phys. Rev. B 2004, 70, 184111.(22) Knudson, M. D.; Gupta, Y. M. J. Appl. Phys. 2002, 91, 9561–9571.(23) Sharma, S. M.; Gupta, Y. M. Phys. Rev. B 1998, 58, 5964–5971.(24) Tang, Z. P.; Gupta, Y. M. J. Appl. Phys. 1997, 81, 7203–7212.(25) Kiselev, A. A.; Ivchenko, E. L.; Rossler, U. Phys. Rev. B 1998, 58,

16353–16359.(26) Kapustina, A. B.; Petrov, B. V.; Rodina, A. V.; Seisyan, R. P. Phys.

Solid State 2000, 42, 1242–1252.(27) Li, J. B.; Li, G.-H.; Xia, J.-B.; Zhang, J.-B.; Lin, Y.; Xiao, X.-R. J. Phys.:

Condens. Matter 2001, 13, 2033–2043.(28) Berezovsky, J.; Ouyang, M.; Meier, F.; Awschalom, D. D.; Batta-

glla, D.; Peng, X. Phys. Rev. B 2005, 71, 081309(R).(29) Schrier, J.; Whaley, K. B. Phys. Rev. B 2003, 67, 235301.(30) Meier, F.; Awschalom, D. D. Phys. Rev. B 2005, 71, 205315.(31) Nahalkova, P.; Sprinzl, D.; Maly, P.; Nemec, P.; Gladilin, V. N.;

Devreese, J. T. Phys. Rev. B 2007, 75, 113306.(32) Fu, H. X.; Wang, L. W.; Zunger, A. Phys. Rev. B 1999, 59, 5568–

5574.(33) Kato, Y.; Myers, R. C.; Gossard, A. C.; Awschalom, D. D. Nature

2004, 427, 50–53.(34) Smith, A. M.; Mohs, A. M.; Nie, S. Nat. Nanotechnol. 2009, 4, 56–

63.

© 2010 American Chemical Society 362 DOI: 10.1021/nl9037399 | Nano Lett. 2010, 10, 358-362