Antiferromagnetism in Narrow-Band Solids

The single-band Hubbard Hamiltonian is examined in the limit of bandwidth much less than intraatomic Coulomb interaction of electrons. We make use of the canonical transformation and "spectral decomposition" of the electron creation operators proposed by Harris and Lange to write down a Green's function which describes electrons in the lower of the split bands of Hubbard's solution. The equation of motion is solved using the moment-conserving decoupling approximation of Tahir-Kheli and Jarrett. We find within our approximation that it is impossible to have an antiferromagnetic state for other than one electron per site. To remedy this defect of the single-band model, we investigate a simplified two-band model in the limit of intra-atomic Coulomb and exchange interaction much greater than the bandwidth, and find that antiferromagnetism is possible for the two nearly half-filled bands. We also discuss effects of the antiferromagnetic ordering on the conductivity in our simplified model and discuss applicability of the theory to real transition metals and transition-metal oxides.