Second harmonic generation (SHG) is an effect observed in materials where the 

inversion symmetry (P) is broken, resulting in the doubling of the frequency of light signals under illumination. This phenomenon finds wide applications in manufacturing lasers, designing various optical devices, and exploring the symmetries and physical properties of materials.

The breaking of P symmetry is typically attributed to lattice structure, leading to SHG invariant under time-reversal (T) operation, referred to as crystal SHG. Interestingly, P symmetry can also be broken solely by the magnetic order of the material, giving rise to SHG with reversed sign under the corresponding T operation, referred to as MSHG. crystal SHG and MSHG together can exhibit interference effects under T operation (i.e., flipping of magnetic moments), leading to changes in the SHG signal and generating a rich variety of optical phenomena based on the system's symmetry, known as the nonlinear magneto-optical (NLMO) effect. However, early experiments focused on NLMO effect in bulk materials, where MSHG was always much smaller than crystal SHG, resulting in weak interference effects and severely limiting their applications.

A recent breakthrough emerged when significant MSHG was observed in two-dimensional magnetic materials, such as bilayer antiferromagnetic CrI3, surpassing even some two-dimensional materials with substantial crystal SHG like MoS2.

Inspired by this, we investigated two-dimensional magnetic materials simultaneously exhibiting crystal SHG and MSHG through first-principles calculations and symmetry analysis, unveiling a class of enormous and tunable NLMO effects. We discovered that unlike previous experimental studies on bulk materials, certain two-dimensional magnetic materials, such as trilayer CrI3 and monolayer Cr2I3Br3, can exhibit crystal SHG and MSHG with comparable amplitudes at specific incident light frequencies. This enables maximized interference effects upon flipping of magnetic moments, resulting in the rotation of the polarization plane of linearly polarized SHG light by 90°, switching on/off the intensity of circularly polarized SHG light, and selectively transmitting  circularly polarized light with specific helicity—achieving 100% SHG circular dichroism. These effects can serve as magnetic-field-controlled linear-to-circular polarization converters, circular polarization switches, and filters in monolayer materials, and can also be used to distinguish subtle magnetic configurations in multilayer materials.

Additionally, we derived the SHG amplitude and phase conditions necessary to achieve these effects and proposed methods to control the absolute and relative magnitudes of crystal SHG and MSHG through the highly tunable nature of two-dimensional materials, such as by adjusting interlayer spacing, spin-orbit coupling strengths, and stacking configurations. Finally, we validated the effectiveness and transferability of these control methods through CrBr3 and multilayer VSe2, demonstrating the tunability of these significant NLMO effects.

This study enriches our understanding of NLMO effects, enhances their applications, and provides new methods to control the magnitudes of different types of SHG, opening up new possibilities for the applications of two-dimensional magnetic materials.

The link to this article: https://www.nature.com/articles/s41524-024-01266-x