Spin dynamics in the regime of hopping conductivity
I. S. Lyubinskiy, A. P. Dmitriev, V. Yu. Kachorovskii
A. F. Ioffe Physico-Technical Institute RAS, 194021 St. Petersburg, Russia
PACS: 71.70.Ej, 73.63.-b, 75.40.Gb, 85.75.-d
Abstract
We consider spin dynamics in the impurity band of a
semiconductor with spin-split spectrum. Due to the splitting,
phonon-assisted hops from one impurity to another are accompanied by
rotation of the electron spin, which leads to spin relaxation. The system is
strongly inhomogeneous because of exponential variation of hopping times.
However, at very small couplings an electron diffuses over a distance
exceeding the characteristic scale of the inhomogeneity during the time of
spin relaxation, so one can introduce an averaged spin relaxation rate. At
larger values of coupling the system is effectively divided into two
subsystems: the one where relaxation is very fast and another one where
relaxation is rather slow. In this case, spin decays due to escape of the
electrons from one subsystem to another. As a result, the spin dynamics is
non-exponential and hardly depends on spin-orbit coupling.