Dynamics of Spin Relaxation in Finite-Size 2D Systems: an Exact Solution

TL;DR

This paper provides an exact solution for electron spin relaxation in finite 2D systems with Rashba interaction, revealing size-dependent relaxation times and exponential decay at long times, supported by simulations.

Contribution

It introduces an exact analytical solution for spin relaxation in finite 2D systems, highlighting the size dependence of relaxation times and decay behavior.

Findings

Longest spin relaxation time increases as system size decreases

Spin relaxation involves three stages with multiple relaxation times

Spin polarization decays exponentially at long times with size-dependent rate

Abstract

We find an exact solution for the problem of electron spin relaxation in a 2D circle with Rashba spin-orbit interaction. Our analysis shows that the spin relaxation in finite-size regions involves three stages and is described by multiple spin relaxation times. It is important that the longest spin relaxation time increases with decrease in system radius but always remains finite. Therefore, at long times, the spin polarization in small 2D systems decays exponentially with a size-dependent rate. This prediction is supported by results of Monte Carlo simulations.