Role of anisotropic Coulomb interactions in the superexchange coupling of mixed-valent Mn3O4

Abstract

We report the importance of anisotropic Coulomb interactions in $\mathrm{DFT}+U$ calculations of the electronic and magnetic properties of ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$. The effects of anisotropic interactions in ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Mn}}^{3+}$ are examined separately by defining two different sets of Hubbard parameters: ${U}^{2+}$ and ${J}^{2+}$ for ${\mathrm{Mn}}^{2+}$ and ${U}^{3+}$ and ${J}^{3+}$ for ${\mathrm{Mn}}^{3+}$. The anisotropic interaction in ${\mathrm{Mn}}^{3+}$ has significant effects on the physical properties of ${\mathrm{Mn}}_{3}{\mathrm{O}}_{4}$ including local magnetic moments, canted angle, spontaneous magnetic moment, and superexchange coupling, but that in ${\mathrm{Mn}}^{2+}$ has no noticeable effect. Weak ferromagnetic interchain superexchange observed experimentally is predicted only if a sizable anisotropic interaction is considered in ${\mathrm{Mn}}^{3+}$. By analyzing the eigenoccupations of the on-site Mn density matrix, we find that the spin channel involving ${\mathrm{Mn}}^{3+}\phantom{\rule{4pt}{0ex}}{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ orbitals, which governs the ${90}^{\ensuremath{\circ}}$ correlation superexchange, is directly controlled by the anisotropic interactions. These findings indicate that the exchange correction $J$ for the intraorbital Coulomb potential is critical for the first-principles description of Mn oxides containing ${\mathrm{Mn}}^{3+}$ or ${\mathrm{Mn}}^{4+}$.