Lifting mean-field degeneracies in anisotropic classical spin systems

TL;DR

This paper introduces a method using Hubbard-Stratonovich transformation to compute free energy in anisotropic classical spin systems, revealing how fluctuations break mean-field degeneracies and pin magnetization directions.

Contribution

It presents a novel approach to calculate free energy via functional integrals and demonstrates how fluctuations select specific magnetization directions in anisotropic spin systems.

Findings

Fluctuations lift mean-field degeneracies in anisotropic spin systems.

Magnetization becomes pinned along preferred lattice directions due to fluctuations.

Method applicable to systems with strong spin-orbit coupling and multiorbital interactions.

Abstract

In this work, we propose a method for calculating the free energy of anisotropic classical spin systems. We use a Hubbard-Stratonovich transformation to express the partition function of a generic bilinear super-exchange Hamiltonian in terms of a functional integral over classical time-independent fields. As an example, we consider an anisotropic spin-exchange Hamiltonian on the cubic lattice as is found for compounds with strongly correlated electrons in multiorbital bands and subject to strong spin-orbit interaction. We calculate the contribution of Gaussian spin fluctuations to the free energy. While the mean-field solution of ordered states for such systems usually has full rotational symmetry, we show here that the fluctuations lead to a pinning of the spontaneous magnetization along some preferred direction of the lattice.