We performed path integral simulations of spin evolution controlled by the Rashba spin-orbit interaction in the semiclassical regime for chaotic and regular quantum dots. The spin polarization dynamics have been found to be strikingly different from the D'yakonov-Perel' (DP) spin relaxation in bulk systems. Also an important distinction have been found between long time spin evolutions in classically chaotic and regular systems. In the former case the spin polarization relaxes to zero within relaxation time much larger than the DP relaxation, while in the latter case it evolves to a time independent residual value. The quantum mechanical analysis of the spin evolution based on the exact solution of the Schrödinger equation with Rashba SOI has confirmed the results of the classical simulations for the circular dot, which is expected to be valid in general regular systems. In contrast, the spin relaxation down to zero in chaotic dots contradicts to what have to be expected from quantum mechanics. This signals on importance at long time of the mesoscopic echo effect missed in the semiclassical simulations. I INTRODUCTIONSpin relaxation in semiconductors is an important physical phenomenon being actively studied recently in connection with various spintronics applications [1]. In doped bulk samples and quantum wells (QW) of III-V semiconductors at low temperatures spin relaxation is mostly due to the DP mechanism [2]. This mechanism does not involve any inelastic processes, so that the exponential decay of the spin polarization is determined entirely by the spin-orbit interaction (SOI) and elastic scattering of electrons on the impurities. However, in case of confined systems such as quantum dots (QD) with atomic-like eigenstates, the SOI has been incorporated into the structure of the wave functions of the discrete energy levels. Without inelastic interactions, an initial wave packet with a given spin polarization will evolve in time as a coherent superposition of these discrete eigenstates. Therefore, the corresponding expectation value of the spin polarization will oscillate in time without any decay. To obtain a polarization decay in the QD's, extra effects have to be introduced into the system, e.g., the inelastic interactions between electrons and phonons mediated by the spin-orbit [3,4] and nuclear hyperfine effects [3,5,6]. Accordingly, a spin relaxation in QD's induced by these effects is a real dephasing process.Unlike such an inelastic relaxation in QD's, the DP spin relaxation in unbounded systems seems to be a quite different phenomenon, because the scattering on impurities is elastic and there is no dephasing of the electron wave functions in the systems. However, the spin polarization does decay in time exponentially, as if it would be a true dephasing process. To explain this phenomenon, let us consider an electron moving diffusively through an unbounded system with random elastic scatters. This electron is described by a wave packet represented by a superposition of continuum eigenstates. During a ...

No abstract

The semiclassical path integral (SPI) method has been applied for studying spin relaxation in a narrow 2D strip with the Rashba spin-orbit interaction. Our numerical calculations show a good agreement with the experimental data, although some features of experimental results are not clear yet. We also calculated the relaxation of a uniform spin-density distribution in the ballistic regime of very narrow wires. With the decreasing wire width, the spin polarization exhibits a transition from the exponential decay to the oscillatory Bessel-like relaxation. The SPI method has been also employed to calculate the relaxation of the particularly long-lived helix mode. A good agreement has been found with calculations based on the diffusion theory.