  Despite the fact that the problem of interference mechanism of
magnetoresistance in semiconductors with hopping conductivity was widely
discussed, most of existing studies were focused on the model of spinless
electrons. This model can be justified only when all electron spins are frozen.
However there is always an admixture of free spins in the semiconductor.
  This study presents the theory of interference contribution to
magnetoresistance that explicitly includes effects of both frozen and free
electron spins. We consider the cases of small and large number of scatterers
in the hopping event. For the case of large number of scatterers the approach
is used that takes into account the dispersion of the scatterer energies. We
compare our results with existing experimental data.
