Curvature effects in statics and dynamics of low dimensional magnets

TL;DR

This paper develops a theoretical framework to analyze how curvature influences the static and dynamic magnetic properties of low-dimensional ferromagnetic structures, revealing curvature-induced effective interactions.

Contribution

It introduces a method to incorporate curvature effects into magnetic energy models, deriving new effective interactions and solutions for curved ferromagnetic systems.

Findings

Curvature induces effective magnetic anisotropy.

Curvature generates Dzyaloshinskii-like interactions.

Ground states depend on curvature, excluding tangential solutions.

Abstract

We develop an approach to treat magnetic energy of a ferromagnet for arbitrary curved wires and shells on the assumption that the anisotropy contribution much exceeds the dipolar and other weak interactions. We show that the curvature induces two effective magnetic interactions: effective magnetic anisotropy and effective Dzyaloshinskii-like interaction. We derive an equation of magnetisation dynamics and propose a general static solution for the limit case of strong anisotropy. To illustrate our approach we consider the magnetisation structure in a ring wire and a cone surface: ground states in both systems essentially depend on the curvature excluding strictly tangential solutions even in the case of strong anisotropy. We derive also the spectrum of spin waves in such systems.