Nonlinear Magneto-Optical Probing of Time-Reversal Symmetry Breaking
Solid-state harmonic generation provides a nonlinear probe of symmetries encoded in electronic wave functions. In the subgap and weak-injection regime, time reversal pairs the harmonic responses driven by fields of opposite ellipticity, strongly suppressing elliptical dichroism in time-reversal-symmetric crystals. We show that, in a magnetic crystal, spin-orbit coupling transfers time-reversal-symmetry breaking from the spin sector to the orbital wave functions and lifts this pairing through the geometric phases of the electric-dipole current. Semiconductor-Bloch-equation calculations for centrosymmetric bilayer Cr2Ge2Te6 predict pronounced third-harmonic elliptical dichroism that reverses with the magnetization. Under linearly polarized driving, SOC-induced geometric-phase accumulation generates a nonlinear transverse current and strongly enhances the harmonic rotation and ellipticity. These results identify the geometric phase as a key microscopic contribution to the nonlinear magneto-optical response. This work establishes helicity-resolved harmonic emission and nonlinear polarimetry as complementary probes of spin-orbit-coupled magnetic order.