Journal of Luminescence
(I 997) 307-308
Exciton spin dynamics in GaAs quantum wells S. Adachi”, *, T. Miyashita”, S. Takeyama”, Y. Takagi”, A. Tackeuchib aDepartment of Material Science, Himeji Institute of Technology, 1479-1 Kanaji, Harima Science Garden City, Hyogo 678-12, Japan b Fujitsu Laboratories Ltd., Atsuyi, Japan
Abstract We have investigated the temperature dependence of the exciton spin relaxation between 10 and 300 K in undoped GaAs quantum wells by using the nonlinear transmission pump-probe and the four-wave-mixing techniques. The electron spin relaxation rate above 40 K is found to be proportional to the product of the temperature and the momentum relaxation time, which indicates that the D’yakonov-Perel’ interaction governs the spin-flip dynamics. The temperature independence below 30 K is considered to be due to the band-mixing effect that determines effective to the exciton spin relaxation in these temperatures. Keywords:
GaAs; Quantum wells; Exciton spin relaxation;
We present a detailed experimental study on the exciton spin relaxation mechanisms in GaAs quantum wells (QWs) by using the nonlinear transmission pump-probe and two-pulse self-diffracted four-wavemixing (FWM) techniques. The sample investigated is an undoped GaAs/AlGaAs QW structure that consists of 120 periods of alternating 45 A thick GaAs layers and 4OA thick Alo.siGas.49As layers. There are two concepts for the spin relaxation of excitons; excitonspin and separate-particle spin (the electron part and hole part of excitonic wave function). Recently, Maialle et al. [l] developed the comprehensive model for resonantly excited heavy-hole excitons in QWs, where the exciton-spin concept was introduced. In the theory, exciton spin, electron spin, and hole spin are considered and thus the model is so flexible so as to fit to the asymmetrical features of the observed signals. They claim that the spin relaxation should be analyzed
* Corresponding author. Fax: 81-7915-8-0137; @sci.himeji-tech.ac,jp.
0022-23131971$17.00 0 1997 Elsevier Science B.V. All rights reserved PIZSOO22-2313(96)00139-I
the hole spin relaxation,
and the spin exchange
by the exciton spin concept and the observed relaxation at 300 K  is not the electron spin relaxation. However, we compared the calculated results with both concepts and showed that the experimental results at 300 K could not be explained by their theory. In addition, we found that the excition-spin concept cannot be applied if the observed relaxation time is shorter than the time l/At, (dh: spin exchange energy, -200 ueV for our sample) required for the spin exchange interaction to be defined . We analyzed our experimental results in terms of separate particle spin relaxation rates on the basis of the above criterion. Fig. l(a) shows the temperature dependence of the hole and electron spin relaxation rates. The temperature dependence of both carrier-spin relaxations seems to be divided into two different regions. The rate for electrons r;l is almost constant below 30 K, it increases gradually with increasing temperature, and indicates T”.(j-dependence in the range 40-300 K. The rate for hole spins rh--I is similarly temperatureindependent below 30 K, shows an abrupt increase at
S. Aduchi et ul. 1Journal qf Luminescence 72 74 i 1997) 307-308
T (K) (b) 2
4! 2-10 K
IO27 4: 21
0.1 f,,,, 0
Ahh_lh b-W Fig. I. (a) Temperature dependence of the spin relaxation rates in the range 10 < T < 300 K. Open circles, solid circles, and open triangles are the relaxation rates for hole spin, electron spin, and exciton momentum, respectively. (b) The hole spin relaxation time at low temperatures (4-10 K) versus hh-lh splitting energy.
around 40K, and further increases approximately to To.6 above 70 K. The hole-spin relaxation times including other two GaAs/AlAs-QW-samples with 100 and 150 A wells at 10 K are indicated by solid circles in Fig. l(b). The observed values agree well with the relationship rh cc (&,h_th)X (x N 3.2 at k = 0) , where AEhh_th is a heavy hole-light hole (hh-lh) splitting energy. The hh-lh valence-band mixing is inversely proportional to A&,h-lh. Therefore, the hole spin relaxation is found to be determined essentially by the strength of the hh-lh mixing at low temperatures. Temperature independence of r; ’ below 30 K is considered to be due to the weak temperature dependence of the band-mixing effect at low temperatures. The spin relaxation time at low temperatures ( 5 40 ps) is slower than that at 300 K (- 12 ps) and the spin relaxation becomes to be dominated by the
spin exchange interaction. In this region, the electron spin-flip in an exciton is promoted by the hole spin-flip and r, ’ also indicates the temperature independence below 30 K. At higher temperatures, the hole spin relaxation is largely affected by the hh-lh mixing effects since the hole distribution extends to higher energy regions due to thermal effects. From Fig. l(a) the exchange interaction is effective below 30 K and the single particle spin-flip process must be dominant above 40 K for electrons because of the abrupt reduction of the hole spin memory compared with the reciprocal of the rate of simultaneous spin-flip. Therefore, the exchange interaction becomes ineffective above 40 K regardless of very fast hole spin relaxation. D’yakonov and Kachorovskii  have shown that the spin relaxation time of nondegenerate carriers in the conduction band for QWs due to D’yakonov-Perel’ (DP) interaction is given by r;’ = where x is a numerical co2ctEfksTz,(T)/Egh2, efficient representing the strength of spin splitting, El is the first electron confined state in the QW, E, is the band-gap energy and rm is the carrier momentum relaxation time. The temperature-dependence of the FWM signal decay rate is also shown by triangles in Fig. l(a). The spin relaxation obtained by the resonant pump-probe method can correspond to the momentum relaxation in FWM measurements because of no-energy relaxation process. The dashed line represents the best fits to a power law, which results in a T”.5-dependence above 40 K. The result 7;’ o< Tt,(T) = To.5 is close to the observed T”.6temperature dependence. The above discussion leads to the conclusion that the observed electron spin relaxation above 40 K can be described by the DP interaction.
References [I] M.Z. Maialle, E.A. de Andrada e Silva and L.J. Sham, Phys. Rev. B 47 (1993) 15776.  A. Tackeuchi, S. Muto, T. Inata and T. Fujii, Appl. Phys. Lett. 56 (1990) 2213.  S. Adachi and Y. Takagi, Phys. Rev. Lett., submitted.  I. Brener, W.H. Knox, K.W. Goossen and J.E. Cunningham, Phys. Rev. Lett. 70 (1993) 319.  B. Baylac. X. Marie, T. Amand, M. Brousseau, J. Barrau and Y. Shekun, Surf. Sci. 326 ( 1995) 16 I.  M.1. D’yakonov and V.Yu. Kachorovskii, Sov. Phys. Semicond. 20 (1986) 1IO.