Nonlinear photomagnetization in insulators

Nonlinear photomagnetization is a process by which an oscillating electric field induces a static magnetization. We show that all 32 crystallographic point groups admit such spin polarization using circularly polarized electric fields to second order (as in the usual spin orientation or inverse Faraday effect) but only 29 points groups admit spin polarization using linearly polarized electric fields to second order. The excluded point groups are the highly symmetric $m$-3$m$, -$43m$ and 432. Using density functional theory we compute the spectrum of the second-order electric spin susceptibility of prototypical semiconductors Te, Se, SnS$_2$, GaAs, InSb and Si which corresponds to nonmagnetic materials with and without inversion symmetry. We show that nonlinear photomagnetization can be comparable to those of naturally occurring ferromagnets.