  We theoretically and computationally demonstrate that static magnetization
can be generated under light illumination via nonlinear Edelstein effect
(NLEE). NLEE is applicable to semiconductors under both linearly and circularly
polarized light, and there are no constraints from either spatial inversion or
time-reversal symmetry. Remarkably, magnetization can be induced under linearly
polarized light in nonmagnetic materials. With ab initio calculations, we
reveal several prominent features of NLEE. We find that the orbital
contributions can be significantly greater than the spin contributions. And
magnetization with various orderings, including anti-ferromagnetic,
ferromagnetic, etc., are all realizable with NLEE, which may facilitate many
applications, such as unveiling hidden physical effects, creating a spatially
varying magnetization, or manipulating the magnetization of anti-ferromagnetic
materials. The relationship between NLEE and other magneto-optic effects,
including the inverse Faraday effect and inverse Cotton-Mouton effect, is also
discussed.
