Order parameters in the Verwey phase transition

TL;DR

This paper analyzes the Verwey phase transition in magnetite using Landau theory, identifying primary order parameters and explaining elastic constant softening.

Contribution

It introduces a Landau theory-based model with specific order parameters to describe the Verwey transition and predicts elastic constant behavior.

Findings

Identification of primary order parameters X_3 and Δ_5

Prediction of shear elastic constant C_44 softening

Low-temperature monoclinic P2/c phase emergence

Abstract

The Verwey phase transition in magnetite is analyzed on the basis of the Landau theory. The free energy functional is expanded in a series of components belonging to the primary and secondary order parameters. A low-temperature phase with the monoclinic P2/c symmetry is a result of condensation of two order parameters X_3 and \Delta_5 . The temperature dependence of the shear elastic constant C_44 is derived and the mechanism of its softening is discussed.