General Green’s-function formalism for transport calculations withspdHamiltonians and giant magnetoresistance in Co- and Ni-based magnetic multilayers

A general Green’s-function technique for elastic spin-dependent transport calculations is presented, which (i) scales linearly with system size and (ii) allows straightforward application to general tight-binding Hamiltonians $(spd$ in the present work). The method is applied to studies of conductance and giant magnetoresistance (GMR) of magnetic multilayers in current perpendicular to planes geometry in the limit of large coherence length. The magnetic materials considered are Co and Ni, with various nonmagnetic materials from the $3d,$ $4d,$ and $5d$ transition metal series. Realistic tight-binding models for them have been constructed with the use of density functional calculations. We have identified three qualitatively different cases which depend on whether or not the bands (densities of states) of a nonmagnetic metal (i) form an almost perfect match with one of spin subbands of the magnetic metal (as in Cu/Co spin valves), (ii) have almost pure $\mathrm{sp}$ character at the Fermi level (e.g., Ag), and (iii) have almost pure d character at the Fermi energy (e.g., Pd, Pt). The key parameters which give rise to a large GMR ratio turn out to be (i) a strong spin polarization of the magnetic metal, (ii) a large energy offset between the conduction band of the nonmagnetic metal and one of spin subbands of the magnetic metal, and (iii) strong interband scattering in one of spin subbands of a magnetic metal. The present results show that GMR oscillates with variation of the thickness of either nonmagnetic or magnetic layers, as observed experimentally.