Spin-Transfer Torque on Curved Surfaces: A Generalized Thiele Formalism

TL;DR

This paper generalizes the Thiele formalism to include curvature effects on spin-transfer torque, revealing a coupling between current and curvature that influences skyrmion dynamics on curved surfaces.

Contribution

It introduces an expanded Thiele equation with new curvature-related terms, providing a theoretical framework for understanding magnetic textures on curved nanostructures.

Findings

Coupling between current and curvature acts as a gyrovector and dissipative tensor.

Curvature induces an additional Hall effect in skyrmion dynamics.

Generalizes the Walker limit condition for curved magnetic structures.

Abstract

Curvature is a highly relevant parameter when considering nanostructures, favoring the stability and affecting the dynamics of magnetic textures. In this work, we address the spin-transfer torque phenomenon by deriving an expanded Thiele equation with the Zhang-Li term for curved surfaces. Our results show a coupling between current and curvature, which is perceived as a gyrovector and an additional dissipative tensor associated with this coupling. Using this model, we determine the dynamics of a skyrmion in a nanotube with Gaussian and variable mean curvature. The new terms included in the Thiele equation are responsible for an additional Hall effect in the skyrmion dynamics and for the generalization of the Walker limit condition.