Spin relaxation

Aside spin injection, long and as far as possible variable spin relaxation times are key factors for the evaluation of spintronic devices. Typical timescales for electron spin relaxation in semiconductors vary from a few picoseconds to minutes [34-36]. Most electron spin relaxation mechanisms are based on spin-orbit-coupling. The Dyakonov-Perel (DP) mechanism often dominates at room temperature and it is based on the inversion asymmetry induced spin splitting of the conduction band [37, 38]. The DP mechanism can be described by electrons precessing around a statistically changing, k-depending magnetic field B(k). The spin relaxation time of the DP mechanism is inversely proportional to the impulse scattering of electrons due to the 'motional narrowing' during fast scattering. The DP mechanism usually is stronger in direct bandgap semiconductors with small band gap compared to direct bandgap semiconductors with large band gap because of the typically stronger spin-orbit coupling at small band gaps. Additionally, the strength of the DP mechanism depends on the crystal direction. In (110) quantum wells, the DP-mechanism for electron spins is suppressed in growth direction. The k-depending magnetic field has only one component in growth direction and electron spins can not precess around a magnetic field which is parallel to the spin [39]. In those heterostructures, the longest spin relaxation times are possibly limited by the intersubband spin relaxation mechanism (ISR) [40]. The quantum well thickness dependence of the spin relaxation time especially at room temperature is still unknown. Other spin relaxation mechanisms are the Elliot-Yafet mechanism (EY), the Bir-Aronov-Pikus mechanism (BAP) and the hyperfine interaction with the nuclear spin [41]. The EY mechanism is based on the intermixture of spin states of conduction band electrons due to k*p coupling, the mixing of valence and conduction band and spin-orbit splitting of the valence band. This mechanism is relatively weak compared to the other mechanisms. The BAP mechanism describes the electron spin relaxation based on the electron-hole interaction. Here, the fast fluctuating magnetic moment of the holes leads to a statistically fluctuating precession of the electron spins. This mechanism is relevant especially for spin-optoelectronic devices. The hyperfine interaction of nuclear spin is an efficient spin relaxation mechanism at localized electrons.

The theory for spin relaxation of spin polarized electrons in semiconductors is summarized in references [41, 42, 43]. In most publications, the different mechanisms for spin relaxation are investigated individually. The most frequently appearing DP mechanism has already been investigated in detail. A good agreement with measured spin relaxation times has been achieved in (100) oriented systems. Recently, Wu et al. presented first numerical calculations to the DP spin relaxation on the basis of many-body Bloch equations [45]. E. Ya. Sherman has shown a spin relaxation which is familiar to the DP mechanism appears in symmetric quantum wells via intrinsic fluctuations of the spin-orbit coupling due to statistically distributed donor atoms [46]. The EY mechanism is often neglected compared with other relaxation mechanisms and has not yet been systematically investigated.

From the technological point of view, it is important to have long relaxation times during the transport of electron spins over great distances. First measurements have shown no significant spin relaxation in the transport of electrons in GaAs over distances of 4 µm in large electric fields of 6 kV/cm [47]. Complimentary measurements in weak electric fields demonstrate spin transport over 100 µm [48]. Both measurements were performed at low temperatures with only weak DP mechanism. Those experiments are therefore not transferable to room temperature.