# Spin-relaxation time in materials with broken inversion symmetry and large spin-orbit coupling

## TL;DR

This paper investigates spin-relaxation times in materials with strong spin-orbit coupling and broken inversion symmetry, using combined Monte Carlo and diagrammatic methods to reveal new regimes and analogies with NMR phenomena.

## Contribution

It introduces a combined computational approach that accurately models spin relaxation, identifying novel regimes and providing a comprehensive phase space analysis.

## Key findings

- Quantitative agreement between Monte Carlo and diagrammatic methods.
- Identification of non-exponential spin relaxation regimes.
- Discovery of regimes where spin relaxation equals momentum relaxation.

## Abstract

We study the spin-relaxation time in materials where a large spin-orbit coupling (SOC) is present which breaks the spatial inversion symmetry. Such a spin-orbit coupling is realized in zincblende structures and heterostructures with a transversal electric field and the spin relaxation is usually described by the so-called D'yakonov-Perel' (DP) mechanism. We combine a Monte Carlo method and diagrammatic calculation based approaches in our study; the former tracks the time evolution of electron spins in a quasiparticle dynamics simulation in the presence of the built-in spin-orbit magnetic fields and the latter builds on the spin-diffusion propagator by Burkov and Balents [Burkov and Balents Phys. Rev. B. 69, 245312 (2004).]. Remarkably, we find a parameter free quantitative agreement between the two approaches and it also returns the conventional result of the DP mechanism in the appropriate limit. We discuss the full phase space of spin relaxation as a function of SOC strength, its distribution, and the magnitude of the momentum relaxation rate. This allows us to identify two novel spin-relaxation regimes; where spin relaxation is strongly non-exponential and the spin relaxation equals the momentum relaxation. A compelling analogy between the spin-relaxation theory and the NMR motional narrowing is highlighted.