Unified Spin Order Theory via Gauge Landau-Lifshitz Equation

TL;DR

This paper introduces a unified gauge Landau-Lifshitz equation framework that describes various spin orders, including skyrmion crystals, and demonstrates its advantages over traditional models through simulations of magnetic field and temperature effects.

Contribution

It develops a gauge Landau-Lifshitz equation unifying multiple spin orders and extends the understanding of skyrmion phases beyond conventional models.

Findings

Unified description of spin orders including skyrmions

Double periodic solutions encompass various spin configurations

Wider skyrmion-crystal phase range compared to Dzyaloshinsky-Moriya model

Abstract

The continuum limit of the tilted SU(2) spin model is shown to give rise to the gauge Landau-Lifshitz equation which provides a unified description for various spin orders. For a definite gauge, we find a double periodic solution, where the conical spiral, in-plane spiral, helical, and ferromagnetic spin orders become special cases, respectively. For another gauge, we obtain the skyrmion-crystal solution. By simulating the influence of magnetic field and temperature for our covariant model, we find a spontaneous formation of skyrmion-fragment lattice and obtain a wider range of skyrmion-crystal phase in comparison to the conventional Dzyaloshinsky-Moriya model.