  A novel, 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 CPP
(current perpendicular to planes) geometry in the limit of large coherence
length. The magnetic materials considered are Co and Ni, with various
non-magnetic 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 non-magnetic metal (i) form an almost perfect match with one of spin
sub-bands of the magnetic metal (as in Cu/Co spin valves); (ii) have almost
pure sp character at the Fermi level (e.g. Ag); (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
non-magnetic metal and one of spin sub-bands of the magnetic metal, and (iii)
strong interband scattering in one of spin sub-bands of a magnetic metal. The
present results show that GMR oscillates with variation of the thickness of
either non-magnetic or magnetic layers, as observed experimentally.
