Bulk photospin effect: Calculation of electric spin susceptibility to second order in an electric field

We compute the electric spin susceptibility of Bloch electrons with spin-orbit coupling to second order. find that it is possible generate a nonequilibrium polarization in bulk nonmagnetic inversion-symmetric materials using linearly polarized fields, but process depends on interband coherence and produces heating. It may be avoid heating circular certain scenarios. The standard Edelstein effect orientation effects are recovered appropriate limits within formalism. Finally, metals has contributions proportional multipole moments Fermi sea dominate low frequency response.