Topological order generated by random field in a 2D exchange model

TL;DR

This paper investigates how a weak static random field influences a large 2D exchange model, revealing the emergence of a skyrmion-antiskyrmion glass state characterized by topological order and specific correlation behaviors.

Contribution

It demonstrates that static randomness induces topological order in a 2D ferromagnetic system, leading to a skyrmion-antiskyrmion glass state with measurable correlation properties.

Findings

Ferromagnetic correlations persist on the Imry-Ma scale inversely proportional to the random-field strength.

The correlated area's energy is close to the skyrmion ground-state energy.

Topological charge exhibits oscillations with a period related to the ferromagnetic correlation length.

Abstract

We study a 2D exchange model with a weak static random field on lattices containing over one hundred million spins. Ferromagnetic correlations persist on the Imry-Ma scale inversely proportional to the random-field strength and decay exponentially at greater distances. We find that the average energy of the correlated area is close to the ground-state energy of a skyrmion, while the topological charge of the area is close to $\pm 1$. Correlation function of the topological charge density exhibits oscillations with a period determined by the ferromagnetic correlation length, while its Fourier transform exhibits a maximum. These findings suggest that static randomness transforms a 2D ferromagnetic state into a skyrmion-antiskyrmion glass.