Angular dependence of giant magnetoresistance in a superlattice

Most discussions of giant magnetoresistance (GMR) have focused on collinear cases where the magnetizations in adjacent layers are either parallel or antiparallel. To explore the relative importance of the superlattice potential and of the impurity scattering on the angular dependence of GMR, we calculate the electrical resistivity for noncollinear magnetizations. The electronic structure of the superlattice is modeled by a Kronig-Penney potential. When the magnetizations of the adjacent layers are neither parallel nor antiparallel, spinor forms of Bloch states and dispersion relations are derived. Then the conductivity as a function of the angle between magnetization directions of adjacent layers is calculated in the homogeneous limit where the mean free path is much larger than the layer thickness. We find the angular dependence of the resistivity and hence of the GMR for current in the plane of layers and perpendicular to the plane of the layers depends on the spin-dependent superlattice potential, and the details of the scattering potential.