Theory of itinerant-electron ferromagnetism

A theory of Kondo lattices or a 1/d expansion theory, with d being the spatial dimensionality, is applied for studying itinerant-electron ferromagnetism. Two relevant multiband models are examined: a band-edge model where the chemical potential is at one of band edges, the top or the bottom of the bands, and a flat-band model where one of bands is almost flat or dispersionless and the chemical potential is at the flat band. In both the models, a ferromagnetic exchange interaction arises from the virtual exchange of pair excitations of quasiparticles. It has two properties: Its strength is in proportion to the effective Fermi energy of quasiparticles and its temperature dependence is responsible for the Curie-Weiss law. When the Hund coupling J is strong enough, the superexchange interaction, which arises from the virtual exchange of pair excitations of electrons across the Mott-Hubbard gap, is ferromagnetic. In particular, it is definitely ferromagnetic for any nonzero J>0 in the large limit of band multiplicity. Ferromagnetic instability occurs when the sum of the two exchange interactions is ferromagnetic and it overcomes the quenching of magnetic moments by the Kondo effect or local quantum spin fluctuations and the suppression of magnetic instability by the mode-mode coupling among intersite spin fluctuations.