Transport and Magnetoresistance in Low Carrier Density Ferromagnets

In metallic magnets, scattering from magnetic fluctuations above and near T sub c may provide a substantial contribution to the electrical p(T). However, this effect is usually small because the dominant fluctuations are near q~0, which does not produce substantial backscattering across the Fermi surface unless 2k sub F is itself small; such a situation can be realized in metallically-doped ferromagnetic semiconductors. A simple adaptation of the theory of deGennes and Friedel shows the low field magnetoresistance scales with the ratio of field induced magnetization m(H) to the saturation magnetization m sub (sat): DELTA p/p~C(m/m sub (sat)) sup 2, where C~x sup (-2/3) with x the number of charge carriers per magnetic unit cell. Comparison to data on very different ferromagnetic metals and doped semiconductors is in broad quantitative agreement with this trend, with the prime exception of perovskite manganese oxides, already understood to involve the extra physics of dynamic lattice distortions. At very low doping, the physics should involve ferromagnetic polarons, and polaron formation and transport are discussed.