First-principles study of magnetism in spinel ${\mathrm{MnO}}_2$

First-principles electronic structure methods have been used to calculate the ground state, transition temperature, and thermodynamic properties of magnetic excitations in spinel ${\mathrm{MnO}}_2.$ The magnetic interactions are mapped onto a Heisenberg model whose exchange interactions are fitted to results of first-principles calculations of different spin configurations. The thermodynamics are calculated using Monte Carlo methods. The Heisenberg model gives an extremely accurate representation of the true first-principles magnetic energies. We find a critical temperature and Weiss constant significantly larger than experimental results and believe the error to come from the local spin density approximation. We predict a new magnetic ground state different from that proposed previously, but consistent with experimental data.