Quantum effects in the giant magnetoresistance (GMR) of magnetic multilayers

We present a quantum-statistical theory using the Kubo formalism to describe both CIP (current in plane) and CPP (current perpendicular to the plane) giant magnetoresistance (GMR) of thin magnetic sandwiches. It is shown that GMR for both geometries oscillates with the thicknesses of the sandwichʹs layers due to the confinement of electrons in quantum wells. The deviation of the GMR dependence on the angle γ between the magnetizations of successive layers from linear cos γ dependence is predicted. It is shown that for CIP geometry this deviation is large only for a large value of the parameter(kF↑ − kF↓)/(kF↑ + kF↓), where kF↑(↓) is Fermi momentum of spin-up (down) electron, but for CPP GMR for noncollinear configuration of the magnetizations a new mechanism (interference between spin-up and spin-down electron waves) is predicted, and the deviation from linear cos γ dependence in this case is large even for small values of the parameter (kF↑ − kF↓)/(kF↑ + kF↓), but not for very large values of the parameter (kF↑ − kF↓)/(1/l↑ + 1/l↓), where l↑(↓) is the mean free path for spin-up(down) electron