Extraordinary Hall effect in magnetic granular alloys

We present the results of a theoretical investigation of the extraordinary Hall effect (EHE) in magnetic granular alloys which exhibit giant magnetoresistance. We consider the impurity scattering of spin-polarized electrons within the magnetic granules, the non-magnetic matrix and at the interfaces between the granules and the matrix in the Zhang-Levy model taking into account the skew scattering due to the spin-orbit interaction. The calculation of the EHE coefficient R(s) was carried out using the Boltzmann equation. We show that R(s) for granular systems may be larger than that for an homogeneous ferromagnet. Moreover, these coefficients may have opposite sign. The theory predicts that the EHE resistivity is proportional to the concentration of the granules when the electron mean-free path in the matrix is much larger than within the granules. We do not find any correlation between R(s) and rho(2), where rho is the resistivity of the granular alloy. However, for some values of the parameters, the EHE resistivity is proportional to rho(3.9). This is in agreement with the experimental data for Co20Ag80.