Dependence of magnetoresistivity on charge-carrier density in metallic ferromagnets and doped magnetic semiconductors

Magnetoresistance-the field-dependent change in the electrical resistance of a ferromagnetic material-finds applications in technologies such as magnetic recording. Near and above the Curie point, T-c, corresponding to the onset of magnetic order, scattering of charge carriers by magnetic fluctuations can substantially increase the electrical resistance(1,2). These fluctuations can be suppressed(3) by a magnetic field, leading to a negative magnetoresistance. Magnetic scattering might also have a role in the 'colossal' magnetoresistance observed in some perovskite manganese oxides(4-6), but is it not yet clear how to reconcile this behaviour with that of the conventional ferromagnetic materials. Here we show that, in generic models of magnetic scattering, the bulk low-field magnetoresistance (near and above T-c) is determined by a single parameter: the charge-carrier density. In agreement with experiment(3,7,8), the low-field magnetoresistance scales with the square of the ratio of the held-induced magnetization to the saturation magnetization. The scaling factor is C approximate to x(-2/3), where x is the number of charge carriers per magnetic unit cell. Data from very different ferromagnetic metals and doped semiconductors are in broad quantitative agreement with this relationship, with the notable exception of the perovskite manganese oxides (in which dynamic lattice distortions complicate and enhance(4,9-12) the effects of pure magnetic scattering). Our results might facilitate searches for new materials with large bulk magnetoresistive properties.