Quantum singularities in the angular dependence of giant magnetoresistance in ultrathin ferromagnetic sandwiches

We present an analytical quantum statistical theory of the angular variation of the giant magnetoresistance (GMR) in thin ferromagnetic sandwiches (current flowing in the plane of the layers). Both spin-dependent scattering of conduction electrons and the existence of spin-dependent potential barriers between the successive layers are taken into account. We show that quantum singularities can arise in the variation of the electrical resistivity of the structure with the angle between the magnetizations in the ferromagnetic layers. These singularities result from the quantization of the momentum of electrons in the direction perpendicular to the plane of the layers.