Self-consistent model of a solid for the description of lattice and magnetic properties

TL;DR

This paper develops a self-consistent theoretical model coupling lattice and magnetic properties in a solid with magnetoelastic interaction, demonstrating how magnetic and elastic subsystems influence each other near phase transitions.

Contribution

It introduces a novel self-consistent formalism that combines magnetic and elastic parameters based on Gibbs free energy minimization, with numerical validation for a ferromagnetic cubic lattice.

Findings

Magnetic subsystem significantly affects elastic properties near phase transitions.

Lattice properties influence magnetic critical temperature and magnetization under pressure.

The model predicts notable changes in thermal expansion and compressibility close to magnetic transitions.

Abstract

In the paper a self-consistent theoretical description of the lattice and magnetic properties of a model system with magnetoelastic interaction is presented. The dependence of magnetic exchange integrals on the distance between interacting spins is assumed, which couples the magnetic and the lattice subsystem. The framework is based on summation of the Gibbs free energies for the lattice subsystem and magnetic subsystem. On the basis of minimization principle for the Gibbs energy, a set of equations of state for the system is derived. These equations of state combine the parameters describing the elastic properties (relative volume deformation) and the magnetic properties (magnetization changes). The formalism is extensively illustrated with the numerical calculations performed for a system of ferromagnetically coupled spins $S$=1/2 localized at the sites of simple cubic lattice. In particular, the significant influence of the magnetic subsystem on the elastic properties is demonstrated. It manifests itself in significant modification of such quantities as the relative volume deformation, thermal expansion coefficient or isothermal compressibility, in particular, in the vicinity of the magnetic phase transition. On the other hand, the influence of lattice subsystem on the magnetic one is also evident. It takes, for example, the form of dependence of the critical (Curie) temperature and magnetization itself on the external pressure, which is thoroughly investigated.