Extraordinary Hall effect in magnetic multilayers

A. Crépieux, J. Wunderlich, P. Bruno

The study of transport properties in magnetic thin film, sandwich and multilayer systems is a research topic with growing interest. Most of the works are devoted to the giant magnetoresistance effect (GMR) which is characterized by a change in the resistivity according to the change of the applied magnetic field. The mechanisms which contribute to the GMR are various : spin dependent scattering, roughness at the interfaces, size effect ... Therefore, it seems  difficult to find a simple interpretation of GMR measurements. Extensive theoretical studies concerning all magnetic and electronic properties of such systems are necessary.

Among these properties, we have chosen to study the extraordinary Hall effect (EHE). In spite of the interesting and unusual experimental results [1], only few theoretical works deal with this effect in such systems. Besides, these works are limited to the skew-scattering contribution in thin films [2] and sandwiches [3] or to the side-jump contribution in multilayers [4].

Our present work is oriented to the following directions :

• Derivation of the skew-scattering and the side-jump contributions to the EHE

  Two different mechanisms contribute to the EHE: the skew-scattering mechanism and the side-jump mechanism. Both are the result of the spin-orbit coupling. Formally, the derivation of these two contributions is related to the model chosen to describe the system. Starting from the Pauli Hamiltonian, the skew-scattering and the side-jump contributions appear respectively when the Green functions and the velocities are corrected by the spin-orbit coupling. If we start from the Dirac Hamiltonian, these two contributions and also higher order contributions (with the spin-orbit constant) are directly taken into account. We have shown the coherence and the continuity (by taking the weak relativistic limit) between these two approaches.

  Numerical calculation of the extraordinary Hall resisitivity in magnetic multilayers

  We are developing numerical calculation to determine the electrical resistivity and the extraordinary Hall resistivity taking both the skew-scattering and the side-jump into account. We apply the coherent potential approximation to treat disorder at the interfaces and we use the Kubo formalism to calculate the conductivity tensor.

[1] T. Sato, Y. Kobayashi, Y. Aoki, Y. Saito, K. Inomata, JMMM 156 (1996) 247
[2] A. Crépieux, C. Lacroix, N. Ryzhanova and A. Vedyayev, Phys. Lett. A 229 (1997) 401
[3] N. Ryzhanova, A. Vedyayev, A. Crépieux and C. Lacroix, Phys. Rev. B 57 (1998) 2943
[4] S. Zhang, Phys, Rev. B 51 (1995) 3632