Room temperature spin diffusion in (110) GaAs/AlGaAs quantum wells
 Changcheng Hu^{1, 2},
 Huiqi Ye^{2},
 Gang Wang^{2},
 Haitao Tian^{},
 Wenxin Wang^{2},
 Wenquan Wang^{1, 2},
 Baoli Liu^{2}Email author and
 Xavier Marie^{3}Email author
DOI: 10.1186/1556276X6149
© Hu et al; licensee Springer. 2011
Received: 14 September 2010
Accepted: 16 February 2011
Published: 16 February 2011
Abstract
Transient spin grating experiments are used to investigate the electron spin diffusion in intrinsic (110) GaAs/AlGaAs multiple quantum well at room temperature. The measured spin diffusion length of optically excited electrons is about 4 μm at low spin density. Increasing the carrier density yields both a decrease of the spin relaxation time and the spin diffusion coefficient D _{s}.
Introduction
The interest in the spin properties of carriers in semiconductors has increased dramatically in the past 10 years due to potential application in the field of spintronics [1, 2]. The design of practical spintronic devices usually requires efficient spin injection in the semiconductor, long carrier spin lifetimes, and long spin transport/diffusion lengths [3–7].
One of the key parameters describing the properties of carrier spin transport in semiconductors is the spin diffusion coefficient D _{s}, which is often assumed to be the same as charge diffusion coefficient D _{c}[8]. A direct optical measurement of the electron spin diffusion coefficient can be performed by creating electron spin grating in timeresolved fourwave mixing experiments [9]. This powerful transient spin grating (TSG) technique was used recently to study the spin transport properties and determine the spin diffusion coefficient D _{s}[9–11]. In particular it was demonstrated theoretically and experimentally that the spin diffusion coefficient D _{s} in ndoped (100)grown GaAs quantum wells can be smaller than the charge diffusion coefficient D _{c} due to Coulomb interaction among the electrons (the socalled Spin Coulomb Drag effect) [10, 12]. In these (100)grown GaAs quantum wells, the electron spin lifetime is of the order of 100 ps at room temperature (RT) due to very efficient D'yakonovPerel (DP) spin relaxation mechanism [13]. In the classical twocomponent driftdiffusion model [14], the spin diffusion length L _{s} is determined by the spin lifetime ${\tau}_{\text{s}}^{*}$ and the spin diffusion coefficient D _{s} through ${L}_{\text{s}}=\sqrt{{D}_{\text{s}}{\tau}_{\text{s}}^{*}}$. As a consequence, the spin diffusion length L _{s} at RT is smaller than 1 μm, limited by the short spin lifetime [10]. In (110)grown GaAs/AlGaAs QW, the DP spin relaxation mechanism is not efficient for electron spins parallel to the growth direction because the spin orientation of electrons is parallel to the direction of effective magnetic field induced by spinorbit coupling [15]. Spin relaxation times longer than 1 ns at RT in (110) GaAs QW have indeed been measured [16]. Long electron spin diffusion lengths can thus be expected at high temperature in these structures. In this report, the electron spin diffusion is measured by the TSG technique with heterodyne detection in (110) GaAs/AlGaAs QWs at RT. We find that the spin diffusion length L _{s} is about 4 μm at low carrier density. We also demonstrate that the spin diffusion coefficient D _{s} decreases when the carrier density increases.
Experimental procedure
where A is a constant, Γ_{s} is the decay rate of the spin grating, and Δt is the delay time between pump and probe beams.
Results and discussion
Figure 1b presents the signal of TSGs as a function of the time delay for two typical pump powers, 2 and 18 mW, respectively. The wave vector q of the spin grating is equal to $q=\frac{2\pi}{\mathrm{\Lambda}}=\text{2}.\text{51}\times {\text{10}}^{\text{4}}{\text{cm}}^{\text{1}}$. It is clear that both curves exhibit different monoexponential decays. Using equation (1), we find Γ_{s} = 0.063 and 0.044 ps^{1} for the pump powers 2 and 18 mW, respectively.
In order to obtain the spin diffusion length L _{s}, the spin lifetime ${\tau}_{\text{s}}^{*}$ is measured independently by timeresolved Kerr rotation [17]. The excitation powers are the same as the ones used in the measurement of TSG. Figure 2b presents the Kerr rotation dynamics for two excitation powers. The spin lifetimes ${\tau}_{\text{s}}^{*}$ are extracted by monoexponential fits, which yield ${\tau}_{\text{s}}^{*}$ ~1220 ps and ${\tau}_{\text{s}}^{*}$ ~880 ps with excitation powers of 2 and 18 mW, respectively. As expected for (110)grown QWs, the spin lifetimes for both excitation powers are much longer than the ones (${\tau}_{\text{s}}^{*}$ ~ 50100 ps) measured in (100)grown GaAs/AlGaAs QWs at RT [9]. By combining the D _{s} measurement obtained with the spin grating technique and the electron spin lifetime probed by the Kerr rotation experiment, we find that the spin diffusion length decreases from L _{s} ~ 3.5 μm down to 2.2 μm when the excitation power increases from 2 to 18 mW. To the best of our knowledge, these values are the longest electron spin diffusion lengths reported at room temperature in inorganic semiconductors.
In order to get further insights on this power dependence, we also measured the charge diffusion coefficient D _{c} with a concentration grating technique for different pump powers. We find that D _{c} remains constant with a typical value D _{c} ~ 12.5 cm^{2}/s (data not shown here). This value is in good agreement with previous studies performed in nonintentionally doped (100)grown GaAs QWs which demonstrate that the concentration grating experiments are governed by the hole diffusion [9].
where <v ^{2}> is the mean square velocity of electrons and τ_{p} is the momentum relaxation time. In a very simple approach, <v ^{2}> in a QW can be approximated by $<{v}^{\text{2}}>=\sqrt{2{k}_{\text{B}}T/{m}_{\text{e}}^{*}}$. The momentum relaxation τ_{p} is strongly dependent on the density of photogenerated electrons n _{e}, with a typical power law ${\tau}_{\text{p}}\propto {n}_{\text{e}}^{0.5}$[23]. In the low density regime below 2.5 × 10^{10} cm^{2}, which corresponds to a pump power of 10 mW, the experimental data are well fitted by this power law as shown by the blue line in Figure 3a. In the high density regime above 2.5 × 10^{10} cm^{2}, the spin diffusion coefficient is almost constant and the density dependence can no more be interpreted by the simple power law. In this density range, the above discussion is clearly oversimplified and we hope that these experimental results will stimulate theoretical investigations to elucidate the origin of the carrier density dependence of the spin diffusion coefficient.
Conclusions
We have measured optically the spin diffusion coefficient D _{s} in nonintentionally doped GaAs/AlGaAs (110) QWs at room temperature for different excitation powers. Under low excitation, the electron spin diffusion length L _{s} is around 4 μm; to the best of our knowledge, this is the largest reported value at T = 300 K in IIIV semiconductors. We also show that the spin diffusion coefficient of optically excited electrons decreases when the excitation density increases. These results could be useful to understand the spin transport properties in semiconductor structures, and possibly control/manipulate the spin transport by varying the excitation condition.
Open Access
This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
Abbreviations
 DP:

D'yakonovPerel
 TSG:

transient spin grating.
Declarations
Acknowledgements
We thank MingWei WU for useful discussions. We acknowledge the financial support of this study from National Science Foundation of China, Grant number: 10534030, 10774183, 10911130356, 10874212; also supported by Ministry of Finance and Chinese Academy of Sciences, National Basic Research Program of China (2006CB921300, 2009CB930500), the ANR project SpinMan.
Authors’ Affiliations
References
 Žutić I, Fabian J, Das Sama S: Spintronics: fundamentals and applications. Rev Mod Phys 2004, 76: 323.View Article
 Datta S, Das B: Electronic analog of the electrooptic modulator. Appl Phys Lett 1990, 56: 665. 10.1063/1.102730View Article
 Kikkawa JM, Smorchkova IP, Samarth N, Awschalom DD: Roomtemperature spin memory in twodimensional electron gases. Science 1997, 277: 1284. 10.1126/science.277.5330.1284View Article
 Vörös Z, Balili R, Snoke DW, Pfeiffer L, West K: Longdistance diffusion of excitons in double quantum well structures. Phys Rev Lett 2005, 94: 226401.View Article
 Hägele D, Oestreich M, Rühle WW, Nestle N, Eberl K: Spin transport in GaAs. Appl Phys Lett 1998, 73: 1580.View Article
 Liu BL, Senes M, Couderc S, Bobo JF, Marie X, Amanda T, Fontaine C, Arnoult A: Optical and electrical spin injection in spinLEDs. Physica E 2003, 17: 358. Zhu HJ, Ramsteiner M, Kostial H, Wassermeier M, Schönherr HP, Ploog KH: Roomtemperature spin injection from Fe into GaAs. Phys Rev Lett 2001, 87:016601 Zhu HJ, Ramsteiner M, Kostial H, Wassermeier M, Schönherr HP, Ploog KH: Roomtemperature spin injection from Fe into GaAs. Phys Rev Lett 2001, 87:016601 10.1016/S13869477(02)008093View Article
 Couto ODD Jr, Iikawa F, Rudolph J, Hey R, Santos PV: Anisotropic spin transport in (110) GaAs quantum wells. Phys Rev Lett 2007, 98: 036603. 10.1103/PhysRevLett.98.036603View Article
 Eldridge PS, Leyland WJH, Lagoudakis PG, Karimov OZ, Henini M, Taylor D, Phillips RT, Harley RT: Alloptical measurement of Rashba coefficient in quantum wells. Phys Rev B 2008, 77: 125344. 10.1103/PhysRevB.77.125344View Article
 Cameron AR, Riblet P, Miller A: Spin gratings and the measurement of electron drift mobility in multiple quantum well semiconductors. Phys Rev Lett 1996, 76: 4793. 10.1103/PhysRevLett.76.4793View Article
 Weber CP, Gedik N, Moore JE, Orenstein J, Stephens J, Awschalom DD: Observation of spin Coulomb drag in a twodimensional electron gas. Nature 2005, 437: 1330. 10.1038/nature04206View Article
 Carter SG, Chen Z, Cundiff ST: Optical measurement and control of spin diffusion in ndoped GaAs quantum wells. Phys Rev Lett 2006, 97: 136602. 10.1103/PhysRevLett.97.136602View Article
 D'Amico I, Vignale G: Theory of spin Coulomb drag in spinpolarized transport. Phys Rev B 2000, 62: 4853.View Article
 D'yakonov MI, Perel VI: Spin relaxation of conduction electrons in noncentrosymmetric semiconductors. Sov Phys Solid State 1972, 13: 3023.
 Zhang P, Wu MW: Spin diffusion in Si/SiGe quantum wells: Spin relaxation in the absence of D'yakonovPerel' relaxation mechanism. Phys Rev B 2009, 79: 075303. 10.1103/PhysRevB.79.075303View Article
 D'Yakonov MI, Kachorovskii VYu: Spin relaxation of twodimensional electrons in noncentrosymmetric semiconductors. Sov Phys Semicond 1986, 20: 110.
 Lombez L, Lagarde D, Renucci P, Amand T, Marie X, Liu BL, Wang WX, Xue QK, Chen DM: Optical spin orientation in (110) GaAs quantum wells at room temperature. Phys Status Solidic 2007, 4: 475. Ohno Y, Terauchi R, Adachi T, Matsukura F, Ohno H: Spin relaxation in GaAs(110) quantum wells. Phys Rev Lett 1999, 83:4196; Döhrmann S, Hägele D, Rudolph J, Bichler M, Schuh D, Oestreich M: Anomalous spin dephasing in (110) GaAs quantum wells: Anisotropy and intersubband effects. Phys Rev Lett 2004, 93:147405 Ohno Y, Terauchi R, Adachi T, Matsukura F, Ohno H: Spin relaxation in GaAs(110) quantum wells. Phys Rev Lett 1999, 83:4196; Döhrmann S, Hägele D, Rudolph J, Bichler M, Schuh D, Oestreich M: Anomalous spin dephasing in (110) GaAs quantum wells: Anisotropy and intersubband effects. Phys Rev Lett 2004, 93:147405 10.1002/pssc.200673296View Article
 Liu BL, Zhao HM, Wang J, Liu LS, Wang WX, Chen DM: Electron density dependence of inplane spin relaxation anisotropy in GaAs/AlGaAs twodimensional electron gas. Appl Phys Lett 2007, 90: 112111. 10.1063/1.2713353View Article
 Hu CC, Wang G, Ye HQ, Liu BL: Development of the transient spin grating system and its application in the study of spin transport. Acta Phys Sin 2010, 59: 597.
 Maznev AA, Nelson KA, Rogers JA: Optical heterodyne detection of laserinduced gratings. Opt Lett 1998, 23: 1319. Gedik N, Orenstein J: Absolute phase measurement in heterodyne detection of transient gratings. Opt Lett 2004, 29:2109 Gedik N, Orenstein J: Absolute phase measurement in heterodyne detection of transient gratings. Opt Lett 2004, 29:2109 10.1364/OL.23.001319View Article
 Eldridge PS, Leyland WJH, Mar JD, Lagoudakis PG, Winkler R, Karimov OZ, Henini M, Taylor D, Phillips RT, Harley RT: Absence of the Rashba effect in undoped asymmetric quantum wells. Phys Rev B 2010, 82: 045317. 10.1103/PhysRevB.82.045317View Article
 Quast JH, Astakhov GV, Ossau W, Molenkamp LW, Heinrich J, Höfling S, Forchel A: Lateral spin diffusion probed by twocolor HanleMOKE technique. Acta Physica Polonica A 2008, 114: 1311.
 Weng MQ, Wu MW, Cui HL: Spin relaxation in ntype GaAs quantum wells with transient spin grating. J Appl Phys 2008, 103: 063714. 10.1063/1.2899962View Article
 Bigot JY, Portella MT, Schoenlein RW, Cunningham JE, Shank CV: Twodimensional carriercarrier screening in a quantumwell. Phys Rev Lett 1991, 67: 636. 10.1103/PhysRevLett.67.636View Article
Copyright
This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.