Nonlinear optical detection of dual ferromagnetism and antiferromagnetism in a magnetic Weyl semimetal Co₃Sn₂S₂

Identification of the magnetic ground state lies at the heart of realizing a magnetic Weyl semimetal and understanding its electronic band topology. In the archetypical magnetic Weyl semimetal Co₃Sn₂S₂, there remains multiple puzzles about its magnetic state, as well as its magnetic domains and domain walls. In this presentation, I will present a set of rotational anisotropy (RA) second harmonic generation (SHG) studies of this centrosymmetric magnetic Weyl semimetal Co₃Sn₂S₂. I will first show the leading order contribution to SHG in this compound is electric quadrupole. Then, by exploring temperature dependence of RA SHG patterns, I will show the presence of two magnetic phase transitions, one being a transition to the ferromagnetic state at T_C,1 = 175 K for the out-of-plane component of magnetic moments and the other to the antiferromagnetic state at T_C,2 = 120 K for the in-plane component. I will further illustrate that the intensity/orientation of the RA SHG scales with even/odd powers of order parameters, from which I can extract the critical exponents of both order parameters independently and consistently. Finally, I will comment on our RA SHG results in comparison with reflection magnetic circular dichroism results that are acquired on the same samples at the same experimental apparatus. Our investigations not only pin down the nature of the magnetism in Co₃Sn₂S₂, but also extends capabilities of nonlinear optics to explore topological material systems preserving spatial inversion symmetry.