Bloch-Wall Phase Transition in the Spherical Model

TL;DR

This paper studies a spherical model of ferromagnets to analyze the temperature-driven transition from Bloch to linear domain walls, revealing how thermal fluctuations influence the transition temperature and wall behavior.

Contribution

It introduces an exactly solvable spherical model that captures the phase transition of domain walls in uniaxial ferromagnets, avoiding unphysical behaviors of previous models.

Findings

Thermal fluctuations lower the Bloch-wall transition temperature T_B.

Linear walls are favored at finite T_B due to fluctuations.

Purely uniaxial ferromagnets do not exhibit Bloch wall ordering.

Abstract

The temperature-induced second-order phase transition from Bloch to linear (Ising-like) domain walls in uniaxial ferromagnets is investigated for the model of D-component classical spin vectors in the limit D \to \infty. This exactly soluble model is equivalent to the standard spherical model in the homogeneous case, but deviates from it and is free from unphysical behavior in a general inhomogeneous situation. It is shown that the thermal fluctuations of the transverse magnetization in the wall (the Bloch-wall order parameter) result in the diminishing of the wall transition temperature T_B in comparison to its mean-field value, thus favouring the existence of linear walls. For finite values of T_B an additional anisotropy in the basis plane x,y is required; in purely uniaxial ferromagnets a domain wall behaves like a 2-dimensional system with a continuous spin symmetry and does not order into the Bloch one.