Extraordinary Hall effect in a hybrid ferromagnetic/super conductor (F/S) bilayer

¹ Department of Physics, M. V. Lomonosov Moscow State University 119899 Moscow, Russia
² CEA/Grenoble, Département de Recherche Fondamentale sur la Matière Condensée SP2M/SPINTEC - 38054 Grenoble, France
³ Laboratoire de Magnétisme Louis Néel, CNRS - BP166, 38042 Grenoble, France

Received: 3 June 2002
Accepted: 11 December 2002

Abstract

The extraordinary Hall effect (EHE) in bilayers of the form ferromagnetic/super-conductor (F/S) or ferromagnetic/normal metal (F/N) was investigated theoretically. The conductivity tensor is calculated in the Kubo formalism with Green functions found as the solutions of the Gorkov equations. We considered diffuse transport in the ferromagnetic layer, taking into account s-d scattering as the main mechanism of electron resistivity. In this model, the Gorkov equations for s-electrons in the ferromagnetic layer remain linear and are solved easily. It is shown that the Hall fields for both F/S and F/N contacts are step functions of the coordinate perpendicular to the planes of the layers and have zero value in the S(N) layer. The Andreev reflection increases the value of the Hall constant R_s for the F/S case. The value of the Hall constant is , where and are conductivities of electrons with up and down spins, and is the Hall constant in the bulk ferromagnetic metal. In fact, coincides with the EHE constant of the bilayer of two ferromagnetic metals with equal thickness and opposite directions of their magnetizations. So, we can conclude that an ideal interface between a ferromagnetic metal and a superconductor may be considered like a mirror with inversion in spin space.