# Spin-orbit coupling and spin relaxation in phosphorene: Intrinsic versus extrinsic effects

## TL;DR

This study uses first-principles calculations to analyze intrinsic and extrinsic spin-orbit effects in phosphorene, revealing anisotropic spin relaxation mechanisms and their dependence on electric fields and substrates.

## Contribution

It provides a detailed comparison of intrinsic and extrinsic spin relaxation mechanisms in phosphorene, highlighting the role of electric fields and substrate effects.

## Key findings

- Intrinsic spin mixing probability is about 10^{-4} with large anisotropy.
- Intrinsic spin relaxation times range from hundreds of picoseconds to nanoseconds.
- Extrinsic spin relaxation via D'yakonov--Perel' mechanism can dominate under strong electric fields.

## Abstract

First-principles calculations of the essential spin-orbit and spin relaxation properties of phosphorene are performed. Intrinsic spin-orbit coupling induces spin mixing with the probability of $b^2 \approx 10^{-4}$, exhibiting a large anisotropy, following the anisotropic crystalline structure of phosphorene. For realistic values of the momentum relaxation times, the intrinsic (Elliott--Yafet) spin relaxation times are hundreds of picoseconds to nanoseconds. Applying a transverse electric field (simulating gating and substrates) generates extrinsic $C_{2v}$ symmetric spin-orbit fields in phosphorene, which activate the D'yakonov--Perel' mechanism for spin relaxation. It is shown that this extrinsic spin relaxation also has a strong anisotropy, and can dominate over the Elliott-Yafet one for strong enough electric fields. Phosphorene on substrates can thus exhibit an interesting interplay of both spin relaxation mechanisms, whose individual roles could be deciphered using our results.