Effectively nonlinear magneto-optical detection under strong laser fields

We report a strong-field detection method for magnetic materials, based on the characterization of crystal time-reversal symmetry through the elliptical dichroism of harmonics. The consistency of the low-order harmonics driven by laser fields with opposite helicities originates from the time-reversal symmetry of crystals, and thus the appearance of harmonic elliptical dichroism can serve as evidence for the breaking of crystal time-reversal symmetry. We have used the semiconductor Bloch equation to calculate the harmonic spectra of the bilayer ferromagnetic material Cr2Ge2Te6, with and without spin-orbit coupling. In magnetic materials, strong spin-orbit coupling causes the loss of time-reversal symmetry in the phase of polarization currents between different spin states, inducing elliptical dichroism in the harmonics. Here we extend the magneto-optical Faraday or Kerr effect to the nonlinear domain using strong laser fields, improving the sensitivity and applicability of magneto-optical detection methods.