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Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics


Lars Onsager and Richard Feynman envisaged that the three-dimensional (3D) superfluid-to-normal λ transition in 4He occurs through the proliferation of vortices. This process should hold for every phase transition in the same universality class. The role of topological defects in symmetry-breaking phase transitions has become a prime topic in cosmology and high-temperature superconductivity, even though direct imaging of these defects is challenging. Here we show that the U(1) continuous symmetry that emerges at the ferroelectric critical point of multiferroic hexagonal manganites leads to a similar proliferation of vortices. Moreover, the disorder field (vortices) is coupled to an emergent U(1) gauge field, which becomes massive by means of the Higgs mechanism when vortices condense (span the whole system) on heating above the ferroelectric transition temperature. Direct imaging of the vortex network in hexagonal manganites offers unique experimental access to this dual description of the ferroelectric transition, while enabling tests of the Kibble–Zurek mechanism.

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Figure 1: Dual description of a phase transition with Z2 × Z3 symmetry.
Figure 2: 3D picture of vortex cores: depth profiling of vortex domain patterns.
Figure 3: Vortex–antivortex pair correlation function.
Figure 4: Domain patterns for different initial annealing temperatures Ti (above, near and below Tc).
Figure 5: Dependence of vortex density nv on cooling rate.
Figure 6: Winding numbers for KZM defects.


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We thank S. C. Chae, A. del campo and V. Zapf for stimulating discussion. This project was in part supported by the DOE under the LDRD program at the Los Alamos National Laboratory. The work at Rutgers University was supported by the DOE under Grant No. DE-FG02-07ER46382. Y.K. acknowledges the financial support by the RIKEN iTHES Project. The work was also supported by China Scholarship Council.

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Authors and Affiliations



S-W.C. designed and supervised the experiment. W.H.Z. and C.D.B. discussed the simulations and experiments, and wrote the section on the Kibble–Zurek mechanism. X.W. carried out annealing experiments, AFM and PFM work. F.F. performed PFM work. D.F., B.C. and Y.L. analysed vortex–antivortex optical images and V.K. calculated the experimental correlation functions. S-Z.L., Y.K. and G-W.C. simulated the theoretical results. S-Z.L., X.W., S-W.C., W.H.Z., C.D.B. and V.K. co-wrote the paper. All authors discussed the results.

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Correspondence to Sang-Wook Cheong.

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Lin, SZ., Wang, X., Kamiya, Y. et al. Topological defects as relics of emergent continuous symmetry and Higgs condensation of disorder in ferroelectrics. Nature Phys 10, 970–977 (2014).

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