Resistivity of Lightly Doped Ferromagnetic Semiconductors

In metallic magnets with a low carrier density, scattering from magnetic fluctuations above and near the transition temperature T sub c provides a large contribution to the electrical resistance. Because the fluctuations can be suppressed by a magnetic field, a large negative magnetoresistance ensues. In a simple model, we find the low field magnetoresistance scales with the ratio of field induced magnetization m(H) to the saturation magnetization M sub (sat)). DELTA rho/rho = (rho(T,0) - rho (T,H)/rho (T,0) ~ C(m/m sub (sat) sup 2. At very low carrier densities, magnetic polarons should form in a range of temperatures above T sub c. The CMR perovskite manganites cannot be explained without strong coupling of the magnetic order to lattice distortions (of the Jahn-Teller type) above T sub c.