Evaluation of Neel temperatures from fully self-consistent broken-symmetry GW and high-temperature expansion: application to cubic transition-metal oxides

Using fully self-consistent thermal broken-symmetry GW we construct effective magnetic Heisenberg Hamiltonians for a series of transition metal oxides (NiO, CoO, FeO, MnO), capturing a rigorous but condensed description of the magnetic states. Then applying high-temperature expansion, we find the decomposition coefficients for spin susceptibility and specific heat. The radius of convergence of the found series determine the Neel temperature. The NiO, CoO, and FeO contain a small ferromagnetic interaction between the nearest neighbors (NN) and the dominant antiferromagnetic interaction between the next-nearest neighbors (NNN). For them the derived Neel temperatures are in a good agreement with experiment. The case of MnO is different because both NN and NNN couplings are antiferromagnetic and comparable in magnitude, for which the error in the estimated Neel temperature is larger, which is a signature of additional effects not captured by electronic structure calculations.