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Using fully self-consistent thermal broken-symmetry GW we construct effectivemagnetic Heisenberg Hamiltonians for a series of transition metal oxides (NiO,CoO, FeO, MnO), capturing a rigorous but condensed description of the magneticstates. Then applying high-temperature expansion, we find the decompositioncoefficients for spin susceptibility and specific heat. The radius ofconvergence 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-nearestneighbors (NNN). For them the derived Neel temperatures are in a good agreementwith experiment. The case of MnO is different because both NN and NNN couplingsare antiferromagnetic and comparable in magnitude, for which the error in theestimated Neel temperature is larger, which is a signature of additionaleffects not captured by electronic structure calculations.

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