# Equations of Motion and Frequency Dependence of Magnon-Induced Domain Wall Motion

## TL;DR

This paper derives equations describing how spin waves induce domain wall motion in ferromagnets, revealing frequency-dependent effects and clarifying the role of magnonic spin-transfer torque without causing Walker breakdown.

## Contribution

It introduces a new one-dimensional model that captures the frequency dependence of spin wave excitation and domain wall motion, clarifying previous numerical observations.

## Key findings

- Magnonic spin-transfer torque does not induce Walker breakdown.
- Spin wave amplitude depends on excitation frequency and spatial profile.
- A simple model reproduces observed frequency dependence in domain wall motion.

## Abstract

Spin waves can induce domain wall motion in ferromagnets. We derive the equations of motion for a transverse domain wall driven by spin waves. Our calculations show that the magnonic spin-transfer torque does not cause rotation-induced Walker breakdown. The amplitude of spin waves that are excited by a localized microwave field depends on the spatial profile of the field and the excitation frequency. By taking this frequency dependence into account, we show that a simple one-dimensional model may reproduce much of the puzzling frequency dependence observed in early numerical studies.