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Observation of a ferro-rotational order coupled with second-order nonlinear optical fields


Ferroic orders can be classified by the symmetry of their order parameters, and ferroelectric, ferromagnetic and ferro-toroidal orders have already been observed. The ferro-rotational order1,2,3, whose order parameter is an axial vector invariant under both time-reversal and spatial-inversion operations, is the final ferroic to be identified and has a vector order parameter. This order is closely related to a number of phenomena such as polar vortices4, giant magnetoelectric coupling5 and spin-helicity-driven ferroelectricity6, but it has received little attention so far. Here, using high-sensitivity rotational-anisotropy second-harmonic generation, we have exploited the electric quadrupole contribution to the second-harmonic generation to directly couple to this centrosymmetric ferro-rotational order in an archetype of type-II multiferroics, RbFe(MoO4)2. We found that two domain states with opposite ferro-rotational vectors emerge with distinct populations at the critical temperature Tc ≈ 195 K and gradually evolve to reach an even ratio at lower temperatures. Moreover, we have identified the ferro-rotational order phase transition as weakly first order and have revealed its coupling field as a unique combination of the induced electric quadrupole second-harmonic generation and the incident fundamental electric fields.

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Fig. 1: Categorizing ferroic orders with vector order parameters.
Fig. 2: Identifying the bulk EQ contribution to room-temperature SHG.
Fig. 3: Tracking the temperature dependence of the ferro-rotational order.
Fig. 4: Resolving the temperature dependence of fitting parameters.

Data availability

The data represented in Figs. 2b,c, 3 and 4 are available with the online version of this paper. All other data that supports the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


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We acknowledge technical assistance from K. Mattioli. L.Z. acknowledges support from NSF CAREER grant no. DMR-174774. E.D. acknowledges support by the NSF Graduate Research Fellowship Program under grant no. DGE-1256260. S.C. acknowledges that the work at Rutgers is funded by the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF4413 to the Rutgers Center for Emergent Materials. K.S. acknowledges support from NSF grant no. NSF-EFMA-1741618 and the Alfred P. Sloan Foundation.

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Authors and Affiliations



W.J., S.-W.C. and L.Z. conceived and initiated the project. A.A. and S.-W.C. synthesized the bulk RbFe(MoO4)2 crystals. W.J., E.D. and S.L. performed RA SHG measurements. W.J. and E.D. carried out the Landau theory analysis under the guidance of K.S. and L.Z. W.J., E.D. and L.Z. analysed the data and wrote the manuscript. All authors participated in the discussion of the results.

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Correspondence to Liuyan Zhao.

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Peer review information Nature Physics thanks Manfred Fiebig, Shiwei Wu and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary Figs. 1–8, Supplementary Tables 1–3 and Supplementary references 1 and 2.

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Jin, W., Drueke, E., Li, S. et al. Observation of a ferro-rotational order coupled with second-order nonlinear optical fields. Nat. Phys. 16, 42–46 (2020).

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