Non-reciprocal spin-wave excitations in Rashba-Hubbard ferromagnets

TL;DR

This paper investigates how spin-wave excitations in Rashba-Hubbard ferromagnets exhibit nonreciprocal behavior depending on the magnetization orientation, revealing asymmetric dispersion and velocity characteristics influenced by spin-orbit coupling.

Contribution

It demonstrates the directional nonreciprocity of spin waves in Rashba-Hubbard ferromagnets and how it depends on the magnetization direction, with detailed analysis of low-energy dispersion behavior.

Findings

Nonreciprocal spin-wave dispersion for in-plane magnetization.

Symmetric spin-wave behavior for out-of-plane magnetization.

Linear dispersion dominates at low energy for in-plane magnetization.

Abstract

We explore the nonreciprocity of spin-wave excitations in the Rashba-Hubbard ferromagnet on a square lattice. Our study reveals that the propagation of spin-wave excitations exhibit non-reciprocal behavior, i.e., spin waves traveling in opposite directions display asymmetry in energy dispersion $\omega({\bf q}) \ne \omega(-{\bf q)}$, which also results in an asymmetric behavior of group velocity, spin stiffness, etc. We find that this asymmetric behavior arises only when the magnetic moments are aligned inside the atomic plane, while the excitations remain symmetric for out-of-plane magnetization. The first dominating term in the low-energy dispersion is linear. However, if the magnetic moments are out-of-plane, then the first dominant term is quadratic instead. The low-energy non-quadratic behavior is examined in the intermediate-to-strong coupling regime for various strengths of Rashba spin-orbit coupling.