  We propose a mechanism for negative isotropic magnetoresistance in the
hopping regime. It results from a memory effect encrypted into spin
correlations that are not taken into account by the conventional theory of
hopping conductivity. The spin correlations are generated by the nonequilibrium
electric currents and lead to the decrease of the conductivity. The application
of the magnetic field destroys the correlations thus enhancing the conductance.
This effect can occur even at magnetic fields as small as a few gauss.
