Magnetic Properties of the Skyrmion Gas in Two Dimensions

TL;DR

This paper investigates the magnetic behavior of a two-dimensional skyrmion gas in a classical ferromagnet, revealing temperature-dependent magnetization changes and comparing results with quantum Hall experiments.

Contribution

It provides a mean-field analysis of skyrmion gas magnetization in 2D ferromagnets at low temperatures and weak fields, connecting classical and quantum behaviors.

Findings

Magnetization decreases linearly with temperature at high skyrmion densities

Magnetization follows a Curie law at higher temperatures

Results align with recent Knight-shift experiments on quantum Hall states

Abstract

The classical ferromagnet is analyzed in two dimensions via a mean-field treatment of the CP$^1$ model valid in the limit of low temperature and of weak magnetic field. At high skyrmion densities, we find that the magnetization begins to decrease linearly with temperature, but it then crosses over to a Curie-law at higher temperature. The comparison of these results with recent Knight-shift experiments on the quantum Hall state is fair.