# Spin relaxation in corrugated graphene

## TL;DR

This paper investigates how out-of-plane vibrations and static ripples in graphene influence electron spin relaxation, providing calculations for relaxation times under various conditions and highlighting the impact of substrate interactions and corrugation geometry.

## Contribution

It offers a comprehensive calculation of spin relaxation times in graphene considering all symmetry-allowed spin-phonon couplings and the effects of static ripples and tension.

## Key findings

- Flexural phonons set an upper bound of hundreds of nanoseconds for spin lifetimes at room temperature.
- Tensions and substrate pinning significantly alter spin relaxation behavior.
- Corrugation geometry can determine spin relaxation times up to tens of microseconds.

## Abstract

In graphene, out-of-plane (flexural) vibrations and static ripples imposed by the substrate relax the electron spin, intrinsically protected by mirror symmetry. We calculate the relaxation times in different scenarios, accounting for all the possible spin-phonon couplings allowed by the hexagonal symmetry of the lattice. Scattering by flexural phonons imposes the ultimate bound to the spin lifetimes, in the ballpark of hundreds of nano-seconds at room temperature. This estimate and the behavior as a function of the carrier concentration are substantially altered by the presence of tensions or the pinning with the substrate. Static ripples also influence the spin transport in the diffusive regime, dominated by motional narrowing. We find that the D'yakonov-Perel' mechanism saturates when the mean free path is comparable to the correlation length of the heights profile. In this regime, the spin-relaxation times are exclusively determined by the geometry of the corrugations. Simple models for typical corrugations lead to lifetimes of the order of tens of micro-seconds.