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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.

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Fig. 1: Room-temperature linear and SHG RA of Co3Sn2S2.
Fig. 2: Temperature dependence of linear and SHG responses of Co3Sn2S2.
Fig. 3: Broken mirror symmetries in the magnetic phases.
Fig. 4: Critical behaviours of the two magnetic phase transitions.

Data availability

All data that support the findings of this work are shown in the main text and Supplementary Information. Source data are provided with this paper.


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We acknowledge valuable discussions with I. Mazin and L. Li. L.Z. acknowledges support by AFOSR YIP grant no. FA9550-21-1-0065, NSF CAREER grant no. DMR-174774 and Alfred P. Sloan Foundation. K.S. acknowledges support from the Office of Navy Research grant no. N00014-21-1-2770 and the Gordon and Betty Moore Foundation grant no. N031710. D.M. acknowledges support from AFSOR MURI grant FA9550-20-1-0322.

Author information

Authors and Affiliations



Y.A. and L.Z. conceived the project. Y.A. planned and performed the experiment under the advice of L.Z. Y.A. and X.G. performed the point-group symmetry simulation under the guidance of L.Z. R.X., K.Q. and D.M. grew and characterized the samples. Y.A., K.S. and L.Z. analysed the data. Y.A. and L.Z. wrote and revised the manuscript with comments from all authors.

Corresponding author

Correspondence to Liuyan Zhao.

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The authors declare no competing interests.

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Peer review information

Nature Photonics thanks Manfred Fiebig and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figs. 1–11 and Sections 1–6.

Source data

Source Data Fig. 1

Room-temperature RA SHG and RA linear reflectivity of Co3Sn2S2 for Fig. 1c.

Source Data Fig. 2

Temperature-dependent SHG and linear reflectivity intensity of Co3Sn2S2 for Fig. 2.

Source Data Fig. 3

Low-temperature RA SHG, low-temperature MCD map and location-dependent RA SHG data for Fig. 3.

Source Data Fig. 4

Temperature-dependent RA SHG and the fitted temperature dependence of the SHG intensity and RA orientation for Fig. 4a–c.

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Ahn, Y., Guo, X., Xue, R. et al. Electric quadrupole second-harmonic generation revealing dual magnetic orders in a magnetic Weyl semimetal. Nat. Photon. (2023).

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