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

Abstract

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 field-induced magnetization to the saturation magnetization. The scaling factor is C Ϸ 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.'Colossal' magnetoresistance (CMR) in some manganese oxides (such as the perovskite La 1−x Sr x MnO 3 and the pyrochlore Tl 2 Mn 2 O 7 ) has been found to accompany a transition from a metallic ferromagnetic low-temperature phase to a paramagnetic high-temperature phase 4 . The implication is that magnetic scattering of itinerant carriers from enhanced fluctuations near T c has an important role. This prompts one to ask what are the principal differences from the behaviour in more familiar metallic ferromagnets such as Ni and Fe, other perovskite ferromagnets (for example, La 1−x Ca x CoO 3 ), or doped magnetic semiconductors (for example, Ge 1−x Mn x Te and Eu 1−x Gd x Te). The size of the magnetoresistance differs by at least an order of magnitude among these compounds, and each material might seem to demand a separate analysis, because the magnetic mechanisms can be very different. In the perovskite manganites and cobaltites as well as traditional ferromagnets such as Fe and Ni, the magnetic exchange itself arises from hopping of the conduction electrons (either the local 'double exchange' or the longer-range RKKY coupling), whereas in the Mn pyrochlores and magnetic semiconductors such as EuSe and CdCr 2 Se 4 the magnetic coupling is mediated at least partly by bound electrons (superexchange). We argue that, provided that the transport remains metallic, the detailed model for the magnetism matters much less than a simple trend with carrier density.Scattering from magnetic ...

Evaluation of evidence for magnetic polarons inEuB6

“…The dominant modes near a ferromagnetic transition are those with small q. They only produce substantial backscattering if 2k F is itself small [18,30]. This is the case of EuB 6 as its carrier density is very small.…”

Colossal Magnetocapacitance and Colossal Magnetoresistance inHgCr2S4

“…The enhancement of these correlations in an external magnetic field induces the detected magnetoresistance. In contrast to the CMR manganites [1], double exchange can be excluded in the present case, Cr 3+ having a half-filled t 2g level, and the observed CMR probably results from the reduction of spin-disorder scattering in the induced FM state, an effect that may be considerably enhanced for low charge carrier densities [16].…”

Scaling Theory of Magnetoresistance and Carrier Localization inGa1−xMnxAs

“…The resistivity also shows another upturn at much lower temperatures. There have been a number of attempts to explain the resistivity peak so far [3], which invoked, e.g., scattering by critical fluctuations [4], the formation of magnetic polarons [5,6], 'dynamical' mean field calculations [7], or the interplay with universal conductance fluctuations [8]. Although these theoretical approaches have been quite successful in addressing a particular range or qualitative aspect of the data, however, a theoretical framework that could quantitatively explain all characteristic features observed in Ga 1−x Mn x As has not been available so far.…”