Magnetism of chromia from first-principles calculations

The electronic structure and magnetism of chromia (corundum-type ${\text{Cr}}_{2}{\text{O}}_{3}$) are studied using full-potential first-principles calculations. The electronic correlations are included within the $\text{LSDA}+U$ method. The energies of different magnetic configurations are very well fitted by the Heisenberg Hamiltonian with strong exchange interaction with two nearest neighbors and additional weak interaction up to the fifth neighbor shell. These energies are insensitive to the position of the oxygen states, indicating that magnetism in ${\text{Cr}}_{2}{\text{O}}_{3}$ is dominated by direct exchange. The N\'eel temperature is calculated using the pair-cluster approximation for localized quantum spins of magnitude 3/2. Very good agreement with experiment is found for all properties including the equilibrium volume, spectral density, local magnetic moment, band gap, and the N\'eel temperature for the values of $U$ and $J$ that are close to those obtained within the constrained occupation method. The band gap is of the Mott-Hubbard type.