Ab initioHartree-Fock investigation of the structural, electronic, and magnetic properties ofMn3O4

Abstract

Noncubic ${\mathrm{Mn}}_3{\mathrm{O}}_4$ spinel (Hausmannite) has been investigated by using the periodic Hartree-Fock CRYSTAL95 program. The structure has been fully optimized, and the computed geometry compares well with the experimental data. The analysis of the wave function in terms of Mulliken charges shows that the net charge of the tetrahedral cation $\left({\mathrm{Mn}}_A\right)$ is very close to the formal one $(+1.86\mathrm{}$ electrons to be compared to $+2);$ for the octahedral site $\left({\mathrm{Mn}}_B\right)$ the net charge is far from the ideal ionic model $(+2.3\mathrm{}$ electrons instead of $+3),$ and the ${\mathrm{Mn}}_B-\mathrm{O}$ bonds show some covalent character. The same analysis performed on the spin density gives magnetic moments very close to the ones corresponding to the ideal $d^4$ and $d^5$ configurations $(4.90\mathrm{}$ and $3.97$ electrons for ${\mathrm{Mn}}_A$ and ${\mathrm{Mn}}_B,$ respectively). The total energy of seven different spin configurations has been evaluated and the corresponding wave function analyzed. Superexchange coupling constants are evaluated by mapping the ab initio energy data to the Ising hamiltonian. It turns out that the intertetrahedral and tetrahedral-octahedral magnetic interactions are small and antiferromagnetic, in agreement with experimental evidence. The ${\mathrm{Mn}}_B-{\mathrm{Mn}}_B$ along the octahedra chains is ten times larger, whereas the interchain interaction is small and ferromagnetic.