Noncollinear spin configurations can induce nonreciprocal nonlinear optical responses, but their microscopic mechanism remains unclear. Here, we start with an effective tight-binding model to investigate how the spin configuration affects the geometric Pancharatnam-Berry (PB) tensor which is at the center of the nonlinear optical response. We find that the nonreciprocity of the PB tensor reaches a maximum for the perpendicular spin configuration. Our first-principles calculations in ${\mathrm{Cr}}_2{\mathrm{I}}_3{\mathrm{Br}}_3$ confirm this finding and further reveal that the nonlinear optical response, here the second-harmonic generation (SHG) susceptibility, is maximized for the perpendicular spin configuration, where the two spin configurations are not connected by time-reversal symmetry. The underlying physics stems from the constructive interference between the magnetization- and crystal-induced second-harmonic signals, which are reproduced by our dynamic high-harmonic generation (HHG). Our results identify the PB tensor as a band-geometric descriptor of nonreciprocal harmonic generation in noncollinear spin configurations, and establish nonreciprocal SHG and HHG as sensitive optical probes of such magnetic states.

Close

PrevNext

View figure in article

• Nonlinear optics
• Second order nonlinear optical processes
• Noncollinear magnets
• Density functional theory
• Tight-binding model