Toroidal nonreciprocity of optical second harmonic generation

We demonstrate mechanisms of reciprocity breaking in nonlinear optics driven by the toroidal dipole moment which characterizes nontrivial spatial distributions of spins in solids. Using high-resolution femtosecond spectroscopy at electronic resonances in the magnetoelectric antiferromagnet CuB2O4, we show that nonreciprocity reaches 100% for opposite magnetic fields due to the interference of nonlinear coherent sources of second harmonic generation originating from the toroidal dipole moment, applied magnetic field, and noncentrosymmetric crystal structure. The experimental results are corroborated by theoretical analysis based on the crystal and magnetic symmetry of CuB2O4. Our findings open degrees of freedom in nonlinear optics and pave the way for future nonreciprocal spin-optronic devices operating on the femtosecond timescale.