Angular dependence of giant magnetoresistance in magnetic multilayers

Dependence of the current-in-plane giant magnetoresistance (GMR) in magnetic multilayers on the angle phi between the magnetizations of successive magnetic films is analyzed theoretically in the quasiclassical and quantum limits. Spin dependent electron scattering on impurities as well as on interfacial roughness is taken into account. In the quasiclassical limit GMR is shown to vary approximately linearly with sin(2)(phi/2). In the quantum limit the linear behavior occurs only for symmetrical structures with a crystal electronic potential independent of the electron spin orientation. Deviations from the linear behavior occur when either the crystal potential is spin dependent or the structure is asymmetrical.