Importance of anisotropic Coulomb interactions in the electronic and magnetic properties of Mn$_3$O$_4$

TL;DR

This study highlights the crucial role of anisotropic Coulomb interactions in accurately predicting the electronic and magnetic properties of Mn₃O₄ using DFT+U, especially emphasizing the impact of interactions in Mn³⁺ ions.

Contribution

It demonstrates that anisotropic interactions in Mn³⁺ are essential for correctly modeling magnetic properties and superexchange in Mn₃O₄, a novel insight for first-principles calculations.

Findings

Anisotropic interactions in Mn³⁺ significantly affect magnetic moments and superexchange.

Weak ferromagnetism is only predicted with sizable anisotropic interactions in Mn³⁺.

Spin channels involving Mn³⁺ d_{x^2-y^2} orbitals are controlled by anisotropic interactions.

Abstract

We report the importance of anisotropic Coulomb interactions in DFT+U calculations of the electronic and magnetic properties of Mn$_3$O$_4$. The effects of anisotropic interactions in Mn$^{2+}$ and Mn$^{3+}$ are separately examined by defining two different sets of Hubbard parameters: $U^{2+}$ and $J^{2+}$ for Mn$^{2+}$ and $U^{3+}$ and $J^{3+}$ for Mn$^{3+}$. The anisotropic interactions in Mn$^{3+}$ have a significant impact on the physical properties of Mn$_3$O$_4$ including local magnetic moments, canted angle, spontaneous magnetic moment, and superexchange coupling, but those in Mn$^{2+}$ do not make any noticeable difference. Weak ferromagnetic interchain superexchange, observed in experiments, is predicted only if a sizable anisotropic interaction is considered in Mn$^{3+}$. By analyzing the eigenoccupations of the on-site Mn density matrix, we found that the spin channel involving Mn$^{3+}$ $d_{x^2-y^2}$ orbitals, which governs the 90$^\circ$ correlation superexchange, is directly controlled by the anisotropic interactions. These findings demostrate that the exchange correction $J$ for the intraorbital Coulomb potential is of critical importance for first-principles description of reduced Mn oxides containing Mn$^{3+}$ or Mn$^{4+}$.