Domain-wall free energy in Heisenberg ferromagnets

TL;DR

This paper derives analytical expressions for the free energy of domain walls in Heisenberg ferromagnets, linking thermal fluctuations to spatial scales like correlation length and magnetic domain size, and discusses chiral order stability.

Contribution

It provides new analytic formulas for domain wall free energy and explores their implications for thermal stability and spatial scale behavior in ferromagnetic systems.

Findings

Analytic expressions for domain wall free energy are derived.

Temperature dependence of correlation length and domain size is established.

Chiral order stability within domain walls is analyzed.

Abstract

We consider Gaussian fluctuations about domain walls embedded in one- or two-dimensional spin lattices. Analytic expressions for the free energy of one domain wall are obtained. From these, the temperature dependence of experimentally relevant spatial scales -- i.e., the correlation length for spin chains and the size of magnetic domains for thin films magnetized out of plane -- are deduced. Stability of chiral order inside domain walls against thermal fluctuations is also discussed.