Some aspects of the theory of magnets with competing double exchange and superexchange interactions

In colossal magnetoresistance materials, ferromagnetic double exchange presumably coexists with a direct nearest-neighbor antiferromagnetic interaction. We construct a single-site mean-field theory that explicitly takes into account the different nature of carrier-mediated ferromagnetism vs Heisenberg-like superexchange. We find, in contrast to previous results in the literature, that the competition between these two exchange interactions leads to ferromagnetic or antiferromagnetic order with incomplete saturation of the magnetization (or sublattice magnetization), rather than spin canting. The associated experimental implications are discussed.