  A theory of spin transport and spin detection in Zeeman-split superconducting
films at low temperatures is developed. It is shown that an injection of
spin-unpolarized quasiparticles into a Zeeman-split superconductor gives rise
to a spin imbalance. The relaxation length of such a spin signal is determined
by the energy relaxation length and can be extremely large as compared to the
relaxation length of spin-polarized quasiparticles. There can exist two types
of signals: due to nonthermalized quasiparticle distribution and due to
thermalized overheated electron distribution. They have different decay lengths
and can be distinguished by their different dependencies on the applied
voltage. The decay length of the nonthermalized signal is determined by the
electron-electron scattering rate, renormalized due to superconductivity. The
decay length of the thermalized signal is determined by the length on which
energy leaves the electronic subsystem and can be very large under special
conditions. Applications of the theory to recent experimental data on spin
relaxation in Zeeman-split and exchange-split superconductors are discussed. In
particular, it can explain the extremely high spin relaxation lengths,
experimentally observed in Zeeman-split superconductors, and their growth with
the magnetic field and with the applied voltage.
