Magnetism of transition metal (TM) oxides is usually described in terms of the Heisenberg model, with orientation-independent interactions between the spins. However, the applicability of such a model is not fully justified for TM oxides because spin polarization of oxygen is usually ignored. In the conventional model based on the Anderson principle, oxygen effects are considered as a property of the TM ion and only TM interactions are relevant. Here, we perform a systematic comparison between two approaches for spin polarization on oxygen in typical TM oxides. To this end, we calculate the exchange interactions in NiO, MnO, and hematite (Fe2O3) for different magnetic configurations using the magnetic force theorem. We consider the full spin Hamiltonian including oxygen sites, and also derive an effective model where the spin polarization on oxygen renormalizes the exchange interactions between TM sites. Surprisingly, the exchange interactions in NiO depend on the magnetic state if spin polarization on oxygen is neglected, resulting in non-Heisenberg behavior. In contrast, the inclusion of spin polarization in NiO makes the Heisenberg model more applicable. Just the opposite, MnO behaves as a Heisenberg magnet when oxygen spin polarization is neglected, but shows strong non-Heisenberg effects when spin polarization on oxygen is included. In hematite, both models result in non-Heisenberg behavior. General applicability of the magnetic force theorem as well as the Heisenberg model to TM oxides is discussed.
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