Solitary Waves of Planar Ferromagnets and the Breakdown of the Spin-Polarized Quantum Hall Effect

TL;DR

This paper identifies solitary wave solutions in planar ferromagnets and links their formation to the breakdown of the spin-polarized quantum Hall effect, revealing a transition from spin-wave droplets to Skyrmion pairs.

Contribution

It introduces a new class of solitary wave solutions in ferromagnets and connects their instability to quantum Hall effect breakdown mechanisms.

Findings

Solitary waves in ferromagnets are characterized by energy dispersion and structure.

A transition from droplet-like to Skyrmion-like structures occurs with increasing momentum.

The instability of these waves explains the electric field-induced breakdown of the quantum Hall effect.

Abstract

A branch of uniformly-propagating solitary waves of planar ferromagnets is identified. The energy dispersion and structures of the solitary waves are determined for an isotropic ferromagnet as functions of a conserved momentum. With increasing momentum, their structure undergoes a transition from a form ressembling a droplet of spin-waves to a Skyrmion/anti-Skyrmion pair. An instability to the formation of these solitary waves is shown to provide a mechanism for the electric field-induced breakdown of the spin-polarized quantum Hall effect.