We present an analytical quantum statistical theory of giant magnetoresistance in magnetic multilayers (current flowing in the plane of the layers) which takes into account both spin-dependent scattering of conduction electrons (s, d or hybridized sd electrons) and spin-dependent potential barriers between successive layers. The model also includes quantization of the momentum of conduction electrons in the direction perpendicular to the plane of the layers (kz). The influence of the following parameters is discussed: ratio of spin-up to spin-down mean free paths, height of potential barriers between adjacent materials and thicknesses of the various layers. It is shown that the main contribution to the giant magnetoresistance is spin-dependent scattering rather than spin-dependent potential barriers. In fact, if the mean free paths of spin-up and spin-down electrons in the magnetic material are significantly different, the presence of potential barriers (spin-dependent or not) can only decrease the magnetoresistance amplitude. Furthermore, the quantization of component momentum kz leads to well-defined oscillations of magnetoresistance with respect to thicknesses of the various layers. It should be possible to observe these quantum oscillations experimentally.

We present an analytical quantum-statistical theory of the angular variation of the giant magnetoresistance (GMR) in magnetic multilayers (current flowing in the plane of the layers) which takes into account both spin-dependent scattering of conduction electrons and spin-dependent potential barriers between successive layers. We show that the widely accepted linear variation of the GMR with the cosine of the angle between the magnetizations in the successive ferromagnetic layers is valid when the GMR originates from a spin-dependent scattering mechanism without potential barriers between layers. In the presence of potential barriers, the angular variation of the GMR can be much more complex.

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