Phenomenological Theory for Giant Magnetoresistance Oscillation in Magnetic Multiplayer

A phenomenological theoretical model for magnetic multilayer based on Boltzmann equation and Fuchs-Sondheimer theory is studied. An oscillatory transmission coefficient (Ts) is introduced into the boundary conditions to simulate the alternate ferromagnetic and anti-ferromagnetic coupling between the magnetic layers. The transmission coefficient has an oscillatory factor relating to the thickness of space layer. Other effects such as interface roughness on Ts are also taken into account. The numerical results for [Fe/Cr]n multilayer agree with the experimental data very well, both in the period and range of osciallation, which is leaded by the dependence of giant magnetoresistance(GMR) on layer thickness of space layer.