Dynamical and current-induced Dzyaloshinskii-Moriya interaction: Role for damping, gyromagnetism, and current-induced torques in noncollinear magnets

TL;DR

This paper develops a theoretical framework for current-induced and dynamical Dzyaloshinskii-Moriya interactions in noncollinear magnets, revealing their effects on damping, gyromagnetism, and current-induced torques, and applying it to Rashba ferromagnets.

Contribution

The paper introduces a comprehensive theory of CIDMI and DDMI, linking them to magnetization dynamics, charge pumping, and torques, with applications to textured Rashba ferromagnets.

Findings

CIDMI and DDMI depend on local magnetization direction.

Spatial gradients of CIDMI and DDMI influence damping and torques.

Application to Rashba ferromagnets demonstrates the formalism's relevance.

Abstract

Both applied electric currents and magnetization dynamics modify the Dzyaloshinskii-Moriya interaction (DMI), which we call current-induced DMI (CIDMI) and dynamical DMI (DDMI), respectively. We report a theory of CIDMI and DDMI. The inverse of CIDMI consists in charge pumping by a time-dependent gradient of magnetization $\partial^2 M(r,t)/\partial r\partial t$, while the inverse of DDMI describes the torque generated by $\partial^2 M(r,t)/\partial r\partial t$. In noncollinear magnets CIDMI and DDMI depend on the local magnetization direction. The resulting spatial gradients correspond to torques that need to be included into the theories of Gilbert damping, gyromagnetism, and current-induced torques (CITs) in order to satisfy the Onsager reciprocity relations. CIDMI is related to the modification of orbital magnetism induced by magnetization dynamics, which we call dynamical orbital magnetism (DOM), and spatial gradients of DOM contribute to charge pumping. We present applications of this formalism to the CITs and to the torque-torque correlation in textured Rashba ferromagnets.