  The interplay of polarization and magnetism in materials with light can
create rich nonlinear magneto-optical (NLMO) effects, and the recent discovery
of two-dimensional (2D) van der Waals magnets provides remarkable control over
NLMO effects due to their superb tunability. Here, based on first-principles
calculations, we reported giant NLMO effects in CrI3-based 2D magnets,
including a dramatic change of second-harmonics generation (SHG) polarization
direction (90 degrees) and intensity (on/off switch) under magnetization
reversal, and a 100% SHG circular dichroism effect. We further revealed that
these effects could not only be used to design ultra-thin multifunctional
optical devices, but also to detect subtle magnetic orderings. Remarkably, we
analytically derived conditions to achieve giant NLMO effects and propose
general strategies to realize them in 2D magnets. Our work not only uncovers a
series of intriguing NLMO phenomena, but also paves the way for both
fundamental research and device applications of ultra-thin NLMO materials.
