  Nonlinear photomagnetization is a process by which an oscillating electric
field can induce a static magnetization. We show that all 32 crystallographic
point groups admit spin polarization to second order using circularly polarized
electric fields (as in the usual spin orientation) but only 29 points groups
admit spin polarization to second order using linearly polarized electric
fields. The excluded point groups are the highly symmetric $m$-3$m$, -$43m$ and
432. To illustrate our results, we compute the second order electric spin
susceptibility of Te, Se, SnS$_2$, GaAs, InSb and Si using density functional
theory which corresponds to nonmagnetic materials with and without inversion
symmetry. We show that our nonlinear photomagnetization can reach magnetic
moments of 0.39 $\mu_B/\text{atom}$ comparable to those of naturally occurring
ferromagnets.
