Walker solution for Dzyaloshinskii domain wall in ultrathin ferromagnetic films

TL;DR

This paper derives exact analytical solutions for domain wall motion in ultrathin ferromagnetic films influenced by Dzyaloshinskii-Moriya interaction, revealing conditions for high-velocity domain walls driven by currents and magnetic fields.

Contribution

It provides the first exact Walker-type solutions for domain walls in the presence of Dzyaloshinskii-Moriya interaction in ultrathin films, including effects of anisotropies and external stimuli.

Findings

Exact Walker-type solutions for domain wall motion derived.

In-plane anisotropy can enable velocities over 500 m/s.

Domain wall velocity depends on material parameters and external fields.

Abstract

We analyze the electric current and magnetic field driven domain wall motion in perpendicularly magnetized ultrathin ferromagnetic films in the presence of interfacial Dzyaloshinskii-Moriya interaction and both out-of-plane and in-plane uniaxial anisotropies. We obtain exact analytical Walker-type solutions in the form of one-dimensional domain walls moving with constant velocity due to both spin-transfer torques and out-of-plane magnetic field. These solutions are embedded into a larger family of propagating solutions found numerically. Within the considered model, we find the dependencies of the domain wall velocity on the material parameters and demonstrate that adding in-plane anisotropy may produce domain walls moving with velocities in excess of 500 m/s in realistic materials under moderate fields and currents.