# Electron Induced Massive Dynamics of Magnetic Domain Walls

## TL;DR

This paper develops a theoretical framework to describe how conduction electrons influence the dynamics of magnetic domain walls in ferromagnetic nanowires, revealing electron-induced mass and novel control mechanisms.

## Contribution

It introduces a Keldysh collective coordinate approach to derive equations of motion for domain walls, uncovering electron-induced mass and correlated noise effects.

## Key findings

- Electron-induced mass affects domain wall inertia.
- Hysteresis observed in domain wall dynamics.
- Resonant response to alternating current predicted.

## Abstract

We study the dynamics of domain walls (DWs) in a metallic, ferromagnetic nanowire. We develop a Keldysh collective coordinate technique to describe the effect of conduction electrons on rigid magnetic structures. The effective Lagrangian and Langevin equations of motion for a DW are derived. The DW dynamics is described by two collective degrees of freedom: position and tilt-angle. The coupled Langevin equations therefore involve two correlated noise sources, leading to a generalized fluctuation-dissipation theorem (FDT). The DW response kernel due to electrons contains two parts: one related to dissipation via FDT, and another `inertial' part. We prove that the latter term leads to a mass for both degrees of freedom, even though the intrinsic bare mass is zero. The electron-induced mass is present even in a clean system without pinning or specifically engineered potentials. The resulting equations of motion contain rich dynamical solutions and point toward a new way to control domain wall motion in metals via the electronic system properties. We discuss two observable consequences of the mass, hysteresis in the DW dynamics and resonant response to ac current.