Mechanism of the Verwey transition in magnetite

TL;DR

This paper elucidates the microscopic mechanism behind the Verwey transition in magnetite by combining ab initio electronic and phonon calculations with group theory, highlighting the role of specific order parameters and Coulomb interactions.

Contribution

It identifies the primary order parameters and clarifies how Coulomb interactions drive the phase transition in Fe$_3$O$_4$.

Findings

Two primary order parameters with $X_3$ and $ riangle_5$ symmetries induce the transition.

Coulomb interaction $U$ amplifies phonon-electron coupling, opening a gap at the Fermi level.

Transition from cubic to monoclinic structure explained by combined electronic and phononic effects.

Abstract

By combining {\it ab initio} results for the electronic structure and phonon spectrum with the group theory, we establish the origin of the Verwey transition in Fe$_3$O$_4$. Two primary order parameters with $X_3$ and $\Delta_5$ symmetries are identified. They induce the phase transformation from the high-temperature cubic to the low-temperature monoclinic structure. The on-site Coulomb interaction $U$ between 3d electrons at Fe ions plays a crucial role in this transition -- it amplifies the coupling of phonons to conduction electrons and thus opens a gap at the Fermi energy. {\it Published in Phys. Rev. Lett. {\bf 97}, 156402 (2006).}