The spin relaxation time of localized charge carriers is a few orders of magnitude larger than that of free electrons and holes. Therefore, mutual conversion of spin polarization, charge current, and spin current turns out to be underlined in the hopping conductivity regime. We reveal different regimes of the coupled spin and charge dynamics depending on the relation between the spin relaxation time and the characteristic hopping time. We derive kinetic equations to describe electrical spin orientation, dc spin Hall effect, and spin-galvanic effect in the transverse magnetic field. The generalized macroscopic conductivities describing these effects are calculated using percolation theory supported by numerical simulation. The conductivities change the sign at least once as functions of magnetic field for all values of the spin relaxation time.

• Received 14 May 2018
• Revised 23 August 2018

DOI:https://doi.org/10.1103/PhysRevB.98.155304