Физика и техника полупроводников, 2002, том 36, вып. Spin relaxation in asymmetrical heterostructures Figure 4. Spin relaxation rates, 1/z (solid line), 1/ (dashed line), and 1/+ (dotted line), in a triangular GaAs QW at different electric field; a — degenerate electron gas, b —Boltzmann gas.
The value of is determined by the difference of both between them is very small. This leads to a minimum in the the wavefunction and band parameters at the interfaces . dependence of 1/+ on E. The cancellation condition (18) This may lead to a more complicated dependence of on E is fulfilled at E 1.9 · 106 V/cm. The electric field of this than (6). However if E is not too high, we have a the linear strength can be created in heterostructures containing a gate, law and, therefore, we use Eq. (6) in our calculations. allowing experimental observation of the non-monotonic In Fig. 4 the spin relaxation rates are plotted for the trian- spin relaxation rate dependence shown in Fig. 5.
gular GaAs QW at different electric fields. It can be seen that total spin relaxation anisotropy occurs for both degenerate 5. Conclusion and Boltzmann gases in wide ranges of concentrations and temperatures. The times + and coincide only at It has been shown [19–21] that inclusion of both the BIA a specific concentration or temperature. For degenerate and SIA terms (4) and (5) into HSO leads to conduction band electrons, according to Eq. (16), the corresponding curves spin-splitting anisotropy in k-space in AIIIBV semiconductor intersect at N 3.4 · 1012 cm-2 for E = 105 V/cm and heterojunctions. However, the spin relaxation analysis at N 7 · 1012 cm-2 for E = 3·105 V/cm in agreement with performed in  ignored this effect.
Fig. 4, a. For a Boltzmann gas, the intersection of + and The authors of  showed that the BIA and SIA occurs according to (17), at T 150 K for E = 104 V/cm terms interfere in weak localization but are additive in spin and at T 240 K for E = 2 · 104 V/cm. This is also relaxation. In this paper, we demonstrate that the terms confirmed by Fig. 4, b.
in HSO linear in the wavevector cancel out in spin relaxation The behavior of the reciprocal spin relaxation times in as well.
electric field is illustrated in Fig. 5 for both degenerate and Boltzmann electron gas. The dependences of k2 In a recent experiment , the spin relaxation anisotropy z and on electric field are similar to those in the inset of was observed for uncommonly used (110) GaAs QWs. In Fig. 1: their values are close in magnitude, so the difference this experiment, the spin relaxation in the growth direction Физика и техника полупроводников, 2002, том 36, вып. 102 N.S. Averkiev, L.E. Golub, M. Willander relaxation times, one has to take into account of the fact that, in asymmetrical heterostructures, the Land g-factor has not only diagonal in-plane components (gxx) but also offdiagonal ones (gxy) . The degree of photoluminescence polarization in a magnetic field B z is described by the following expression P(0) P(B) =, (21) 1 + µB(gxx ± gxy)B/ z where the upper and lower signs correspond to the experi mental geometry B  and B , respectively (µB is the Bohr magneton).
We show that the linear in the wavevector terms in the spin-orbit Hamiltonian interfere, which leads to a huge anisotropy of the spin relaxation times. At a high concentration or temterature, this effect starts to disappear owing to domination of the cubic in k terms in HSO which are present only in HBIA. However the higher-order terms in HSIA are not forbidden by symmetry either. These terms can also interfere with these in HBIA, and cause adiitional non-monotonic peculiarities in the dependences of the spin relaxation times on the structure parameters.
In conclusion, we have calculated the spin relaxation times for a AIIIBV heterojunction and triangular QW. The observance of spin relaxation anisotropy in all three directions is predicted in a wide range of structure parameters and temperatures.
We thank J. Vincent for critical reading of the manuscript.
This work supported by the Russian Foundation for Basic Research (projects 00-02-17011, 00-02-16894, and 01-0217528) and the Russian State Programme ”Physics of Solid State Nanostructures”.
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Физика и техника полупроводников, 2002, том 36, вып. Spin relaxation in asymmetrical heterostructures  W. Knap, C. Skierbiszewski, A. Zduniak, E. Litvin-Staszevska, D. Bertho, F. Kobbi, J.L. Robert, G.E. Pikus, F.G. Pikus, S.V. Iordanskii, V. Moser, K. Zekenes, Yu.B. Lyanda-Geller.
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