Anomalous Hall effect in granular alloys

A theoretical study is performed of the anomalous Hall effect in granular alloys with giant magnetoresistance. The calculation is carried out within the Kubo formalism and the Green’s function method. The mechanism of asymmetric scattering of the spin-polarized current carriers is considered with allowance for a size effect associated with scattering not only by one grain, but also with more complicated processes of transport among two and three grains. It is shown that scattering of conduction electrons by the interfaces of the grains and the matrix has a substantial effect on the magnitude of the anomalous Hall effect and determines its sign. In general, correlation between the quantities ρH and ρ2 is absent, where ρH is the Hall resistivity and ρ is the total resistivity of the granular alloy. However, numerical calculation shows that for certain values of the model parameters ρH∼ρ3.8 and for these same parameter values the amplitude of the giant magnetoresistance reaches 40%, which is found to be in quantitative agreement with the experimental data for Co20Ag80 alloys [P. Xiong, G. Xiao, J. Q. Wang et al., Phys. Rev. Lett. 69, 3220 (1992)]. It is also shown that increasing the resistivity of the matrix leads to a significant growth in the anomalous Hall effect, and more substantial growth for alloys with small grain size, which is in good agreement with experiment [A. B. Pakhomov, X. Yan, and Y. Xu, J. Appl. Phys. 79, 6140 (1996); [X. N. Jing, N. Wang, and A. B. Pakhomov, Phys. Rev. B 53, 14032 (1996)].