  In the CMR materials, ferromagnetic double exchange (DE) presumably coexists
with a direct nearest-neighbour 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 ferro- or antiferromagnetic
order with incomplete saturation of the magnetization (or sublattice
magnetization), rather than spin canting. The associated experimental
implications are discussed.
