Electric quadrupole second-harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal

Broken symmetries and electronic topology are well manifested together in the second-order nonlinear optical responses from topologically non-trivial materials. Although second-order nonlinear optical effects from the electric dipole contribution have been extensively explored in polar Weyl semimetals with broken spatial-inversion symmetry, they are rarely studied in centrosymmetric magnetic Weyl semimetals with broken time-reversal symmetry due to the complete suppression of the electric dipole contribution. Here we report the experimental demonstration of optical second-harmonic generation (SHG) in a magnetic Weyl semimetal Co3Sn2S2 from the electric quadrupole contribution. By tracking the temperature dependence of the rotational anisotropy of SHG, we capture two magnetic phase transitions, with both SHG intensity increasing and its rotational anisotropy pattern rotating at TC,1 = 175 K and TC,2 = 120 K subsequently. The fitted critical exponents for the SHG intensity and rotational anisotropy orientation near TC,1 and TC,2 suggest that the magnetic phase at TC,1 is a three-dimensional Ising-type out-of-plane ferromagnetism, whereas the other at TC,2 is a three-dimensional XY-type all-in–all-out in-plane antiferromagnetism. Our results show the success of the detection and exploration of electric quadrupole SHG in a centrosymmetric magnetic Weyl semimetal and hence open the pathway towards future investigations into its association with band topology. Optical second-harmonic waves are generated from the electric quadrupole contribution in a centrosymmetric magnetic Weyl semimetal Co3Sn2S2. Two magnetic orders and phase transitions are explored in temperature-dependent rotational anisotropy measurements by second-harmonic generation.