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

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.