Dyakonov–Perel's spin relaxation under electron–electron collisions in QWs

M. M. Glazov and E. L. Ivchenko

Ioffe Physico-Technical Institute, St Petersburg, Russia

The Dyakonov–Perel' mechanism of spin relaxation is connected with the spin splitting of the electron dispersion curve in crystals lacking a center of symmetry. The splitting acts as an effective magnetic field with the Larmor frequency ${\bf\Omega}_{\bf k}$ dependent on the value and direction of the electron wavevector k. As a result, the related spin relaxation time $\tau_s$ is given by

$\tau_s^{-1} \propto \langle {\bf\Omega}^2_{\bf k} \rangle \tau ,$

where the angle brackets mean averaging over the electron energy distribution and $\tau$ is a microscopic time of electron relaxation. In a two-dimensional noncentrosymmetric system, e.g. quantum well or heterojunction, the frequency ${\bf\Omega}_{\bf k}$ is a linear function of k. In this case the time $\tau$ is usually identified with the momentum relaxation time that determines the electron mobility. We claim that the inverse time $\tau^{-1}$ is not only a sum of inverse times due to various momentum relaxation processes but contains also a contribution from electron–electron collisions which make no effect on the electron mobility. Really, electron–electron collisions change the direction of k and ${\bf\Omega}_{\bf k}$ and, therefore, they control the Dyakonov–Perel' spin relaxation in the same way as any scattering processes do.

In order to find the time $\tau$ due to the electron–electron collisions we have solved the two-dimensional kinetic equation for the electron spin density matrix $\rho_{ss'}({\bf k})$ neglecting and taking into account the exchange interaction. The results have been compared to the momentum scattering time due to elastic scattering of electrons by ionized impurities.

We will also present the results of calculation of the dependence of $\tau$ on the quantum well width and show how the theory can be extended to allow for degenerate distribution of the spin-polarized two-dimensional electron gas.

URL: http://link.edu.ioffe.ru/narw/2002/op2d/ivchenko
© Educational Centre at Ioffe Institute
(Search|About) Images: 11; Size: 4390; TeX size: 2328; Update: 04 Jun 2002; Converted: 26 May 2005 05:13:20; elapsed time: 0.066 sec.