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
The effect of weak localization on spin relaxation in a two-dimensional system with a spin-split spectrum is considered. It is shown that the spin relaxation slows down due to the interference of electron waves moving along closed paths in opposite directions. As a result, the averaged electron spin decays at large times as 1/t. It is found that the spin dynamics can be described by a Boltzmann-type equation, in which the weak localization effects are taken into account as nonlocal-in-time corrections to the collision integral. The corrections are expressed via a spindependent return probability. The physical nature of the phenomenon is discussed and it is shown that the "nonbackscattering" contribution to the weak localization plays an essential role. It is also demonstrated that the magnetic field, both transversal and longitudinal, suppresses the power tail in the spin polarization.
We discuss classical dynamics of electron spin in two-dimensional semiconductors with a spin-split spectrum. We focus on a special case, when spin-orbit induced random magnetic field is directed along a fixed axis. This case is realized in III-V-based quantum wells grown in [110] direction and also in [100]-grown quantum wells with equal strength of Dresselhaus and Bychkov-Rashba spin-orbit couplings. We show that in such wells the long-time spin dynamics is determined by non-Markovian memory effects. Due to these effects the non-exponential tail 1/t 2 appears in the spin polarization.PACS numbers: 71.70Ej, 72.25.Dc, Continuous reduction of the device sizes in last decades has initiated active research of transport, optical and spin-dependent properties of low-dimensional nanostructures. In recent years, it was clearly understood that not only quantum but also purely classical phenomena might lead to rich physics in such structures. In particular, a number of non-trivial transport phenomena, such as magnetic-field-induced classical localization [1,2], highfield negative [1,2,3,4,5] and positive [6] magnetoresistance, low-field anomalous magnetoresistance [7,8], zerofrequency conductivity anomaly [9], and non-Lorentzian shape of cyclotron resonance [10] might be realized in two-dimensional (2D) disordered systems. All these phenomena arise due to classical non-Markovian memory effects which are neglected in the Drude-Boltzmann approach. The strength of these effects is governed by a classical parameter d/l (d is the characteristic scale of the disorder and l is the transport scattering length). Since the role of quantum effects is characterized by a parameter λ/l (λ is the electron wavelength), the classical effects might dominate in systems with long-range disorder, where d ≫ λ.Usually, classical memory effects slow down relaxation processes leading to non-exponential decay of correlation functions. In particular, the velocity autocorrelation function in a 2D disordered system has a power tail [11,12] in contrast to exponential decay exp(−t/τ ) predicted by the Boltzmann equation. Here τ = l/v F is the transport scattering time, v F is the Fermi velocity and C is the coefficient which depends on the type of disorder: C = 2d/3πl for the Lorentz gas model, where electrons scatter on hard disks of radius d randomly distributed in a 2D plane with concentration n (nd 2 ≪ 1) [11], andfor the scattering on the smooth random potential with a characteristic scale d. Physically, this long-lived tail is due to "non-Markovian memory" specific for diffusive returns to the same scattering center [12] (see also recent discussion in Refs. [9,13]).In spite of the large number of publications devoted to the study of non-Markovian transport phenomena, the role of memory effects in spin dynamics is not well understood. In this paper we discuss the slow down of the spin relaxation in 2D systems due to the non-Markovian memory. This effect is of particular interest for new rapidly growing branch of semiconductor physics, spintronics...
Spin relaxation in the impurity band of a 2D semiconductor with spin-split spectrum in the external magnetic field is considered. Several mechanisms of spin relaxation are shown to be relevant. The first one is attributed to phonon-assisted transitions between Zeeman sublevels of the ground state of an isolated impurity, while other mechanisms can be described in terms of spin precession in a random magnetic field during the electron motion over the impurity band. In the later case there are two contributions to the spin relaxation: the one given by optimal impurity configurations with the hop-waiting time inversely proportional to the external magnetic field and another one related to the electron motion on a large scale. The average spin relaxation rate is calculated.PACS numbers: 71.55. Jv, 71.70.Ej, 72.25.Rb, Spin dynamics in semiconductors has attracted much attention in the last decades [1,2]. In particular, a number of experimental [3,4,5,6,7] and theoretical [8,9,10,11] works are devoted to the investigation of spin relaxation in the impurity band of a semiconductor. An increasing interest to this problem is motivated by experimental observation of up-to-300ns spin lifetimes in n-doped bulk GaAs and GaAs/AlGaAs heterostructures [3,4,5,6], which makes them good candidates for the use in possible spintronics applications. Yet, a consistent theory of spin relaxation in the impurity band is still to be developed. Depending on the donor concentration, spin relaxation in the impurity band might be driven either by hyperfine interaction or spin-orbit coupling. Since the nuclear spin relaxation time is typically very long, hyperfine interaction can be treated as a random-in-space static magnetic field with the associated spin precession frequency ω N ∼ A/ √ N , where A is the hyperfine coupling constant and N is the number of nuclei within the volume occupied by the wave function [12] (the directions of the random magnetic field for electrons located on different impurities are not correlated). In the case of spin-orbit coupling, the associated spin precession frequency ω p is a power function of the electron momentum p [13,14,15] (in the 2D case, ω p is linear in p). As a result, spin-orbit coupling leads to spin rotation in the process of phonon-assisted hops from one impurity to another by the angle φ ≈ ω p0 ∆r/v 0 , where ∆r is the distance between impurities and p 0 = mv 0 is the underthe-barrier momentum. There are several mechanisms of spin relaxation in the impurity band. As in quantum dots, spin relaxation might be driven by phonon-assisted transitions between Zeeman sublevels of the ground state of separate impurities. Other mechanisms, that involve electron hops from one donor to another, are specific for the impurity band. In Ref. [7], the spin relaxation rate was estimated as:for the case of hyperfine interaction and spin-orbit coupling respectively and the characteristic hop waiting time τ hc was assumed to depend only on the average distance between impurities. These equations are based on the cla...
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