Charge order in Magnetite. An LDA+$U$ study

TL;DR

This study uses LDA and LDA+U methods to analyze charge order in monoclinic Fe₃O₄, revealing that LDA+U accurately captures charge disproportionation consistent with experimental observations.

Contribution

It demonstrates that LDA+U effectively models charge order in Fe₃O₄, providing a method to calculate the effective U parameter within augmented plane wave frameworks.

Findings

LDA shows minimal charge disproportionation.

LDA+U reveals charge disproportionation along the c-axis.

Effective U can be computed within augmented plane wave methods.

Abstract

The electronic structure of the monoclinic structure of Fe$_3$O$_4$ is studied using both the local density approximation (LDA) and the LDA+$U$. The LDA gives only a small charge disproportionation, thus excluding that the structural distortion should be sufficient to give a charge order. The LDA+$U$ results in a charge disproportion along the c-axis in good agreement with the experiment. We also show how the effective $U$ can be calculated within the augmented plane wave methods.