The superexchange intertacion in transition-metal oxides, proposed initially by Anderson in 1950, is treated using contemporary tight-binding theory and existing parameters. We find also a direct exchange for nearest-neighbor metal ions, larger by a factor of order five than the superexchange. This direct exchange arises from Vddm coupling, rather than overlap of atomic charge densities, a small overlap exchange contribution which we also estimate. For FeO and CoO there is also an important negative contribution, related to Stoner ferromagnetism, from the partially filled minority-spin band which broadens when ionic spins are aligned. The corresponding J1 and J2 parameters are calculated for MnO, FeO, CoO, and NiO. They give good accounts of the Neel and the Curie-Weiss temperatures, show appropriate trends, and give a reasonable account of their volume dependences. For MnO the predicted value for the magnetic susceptibility at the Neel temperature and the crystal distortion arising from the antiferromagnetic transition were reasonably well given. Application to CuO2 planes in the cuprates gives J=1220oK, compared to an experimental 1500oK, and for LiCrO2 gives J1=4 50oK compared to an experimental 230oK.
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