Spin-deformation coupling in two-dimensional polar materials

TL;DR

This paper investigates how geometrical deformations in two-dimensional polar materials influence spin dynamics, revealing that spin is uncoupled from extrinsic geometry and identifying a new scalar potential related to Rashba spin-orbit coupling.

Contribution

It demonstrates gauge invariance in spin-deformation coupling, incorporates Rashba SOC as a non-Abelian gauge field on curved surfaces, and uncovers a new scalar geometrical potential.

Findings

Spin is uncoupled from extrinsic surface geometry due to gauge invariance.

Rashba SOC can be modeled as an SU(2) gauge field on curved surfaces.

A new scalar geometrical potential dependent on SOC strength is identified.

Abstract

The control of the spin degree of freedom is at the heart of spintronics, which can potentially be achieved by spin-orbit coupling or band topological effects. In this paper, we explore another potential controlled mechanism under debate: the spin-deformation coupling (SDC) - the coupling between intrinsic or extrinsic geometrical deformations and the spin degree of freedom. We focus on polar-deformed thin films or two-dimensional compounds, where the Rashba spin-orbit coupling (SOC) is considered as an $SU(2)$ non-Abelian gauge field. We demonstrate that the dynamics between surface and normal electronic degrees of freedom can be properly decoupled using the thin-layer approach by performing a suitable gauge transformation, as introduced in the context of many-body correlated systems. Our work leads to three significant results: (i) gauge invariance implies that the spin is uncoupled from the surface's extrinsic geometry, challenging the common consensus; (ii) the Rashba SOC on a curved surface can be included as an $SU(2)$ non-Abelian gauge field in curvilinear coordinates; and (iii) we identify a previously unnoticed scalar geometrical potential dependent on the Rashba SOC strength. This scalar potential, independent of spin, represents the residual effect remaining after decoupling the normal component of the non-Abelian gauge field. The outcomes of our work open novel pathways for exploring the manipulation of spin degrees of freedom through the use of the SDC.