Splitting of the zone-center phonon in MnO and NiO

We develop a model based on the superexchange interaction and the Heisenberg Hamiltonian to understand the zone-center transverse optical (TO) phonon splittings in the late transition-metal oxides with type-II antiferromagnetic ordering. Even for a cubic rocksalt lattice, the anisotropic magnetic coupling due to the non-cubic distribution of the spin density can produce a splitting of the TO phonon energies. To calculate these splittings for MnO and NiO, we apply a recently implemented LSDA+U method based on a pseudopotential plane-wave formalism and obtain results for both MnO and NiO which are consistent with our model predictions. The calculated splitting for MnO is in excellent agreement with a recent experiment, while the result for NiO appears to be inconsistent with current experimental results and entails further investigation.