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 Néel 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 Néel 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.

We report the direct observation of surface magnetization domains of the magnetoelectric ${\mathrm{Cr}}_2{\mathrm{O}}_3$ using photoemission electron microscopy with magnetic circular dichroism contrast and magnetic force microscopy. The domain pattern is strongly affected by the applied electric field conditions. Zero-field cooling results in an equal representation of the two domain types, while electric-field cooling selects one dominant domain type. These observations confirm the existence of surface magnetization, required by symmetry in magnetoelectric antiferromagnets.