# Transition-metal monoxides: Itinerant versus localized picture of superexchange

## Abstract

We demonstrate that energy-band theory based on the local-spin-density- functional treatment of exchange and correlation accounts well for the insulating behavior of MnO, MnS, and NiO. This is true, however, only if the magnetization is allowed to vary in the [111] direction, as is observed experimentally. As a further test of the itinerant picture of these materials, the "exchange integrals" entering a Heisenberg model are calculated, using muffin-tin CPA theory to describe the interaction between two magnetized atoms embedded in a medium of disordered spins. These parameter-free calculations of the coupling strength are the first nonempirical estimates to be in qualitative agreement with measurements. The numerical overestimate of the coupling strength by approximately a factor of three is consistent with the fact that both of the fundamental approximations underlying the estimate act to overestimate the coupling strength; these are: (1) the neglect of magnetic order in the CPA calculations and (2) the neglect of screening effects caused by the response of the electrons to the spin-wave-like perturbations described by a Heisenberg Hamiltonian. The band-theoretic description of superexchange differs qualitatively from the traditional localized-electron picture. Two of the most interesting of these differences concern the observed sharp increase in the coupling strength at the end of the transition series, and the ferromagnetic coupling of nearest Ni neighbors in NiO. The band picture, provides a natural explanation for both observations, whereas the localized picture does not.