  The phenomenon of crossed Andreev reflection (CAR) is known to play a key
role in non-local electron transport across three-terminal
normal-superconducting-normal (NSN) devices. Here we review our general theory
of non-local charge transport in three-terminal disordered
ferromagnet-superconductor-ferromagnet (FSF) structures. We demonstrate that
CAR is highly sensitive to electron spins and yields a rich variety of
properties of non-local conductance which we describe non-perturbatively at
arbitrary voltages, temperature, degree of disorder, spin-dependent interface
transmissions and their polarizations. We demonstrate that magnetic effects
have different implications: While strong exchange field suppresses
disorder-induced electron interference in ferromagnetic electrodes,
spin-sensitive electron scattering at SF interfaces can drive the total
non-local conductance negative at sufficiently low energies. At higher energies
magnetic effects become less important and the non-local resistance behaves
similarly to the non-magnetic case. Our results can be applied to
multi-terminal hybrid structures with normal, ferromagnetic and half-metallic
electrodes and can be directly tested in future experiments.
