Anomalous Hall Effect in Double Exchange Magnets

We investigate the possible origin of anomalous Hall effect in the CMR (colossal magnetoresistance) materials - the doped rare earth manganites - observed recently by Matl et al. It is demonstrated that the spin-orbit interaction in the double exchange model couples magnetization to the Berry phase associated with three dimensional spin textures and induces a non-zero average topological flux which in turn generates an anomalous contribution to transverse resistivity. The same effect, but involving the orbital Berry phase, occurs in the model with orbital degeneracy and Coulomb repulsion.