Abstract
Electronic nematicity is a state of matter in which rotational symmetry is spontaneously broken and translational symmetry is preserved. In strongly correlated materials, nematicity often emerges from fluctuations of a multicomponent primary order, such as spin or charge density waves, and is termed vestigial nematicity. One widely studied example is Ising nematicity, which arises as a vestigial order of collinear antiferromagnetism in the tetragonal iron pnictide superconductors. Because nematic directors in crystals are restricted by the underlying crystal symmetry, recently identified quantum materials with three-fold rotational symmetry offer a new platform to investigate nematic order with three-state Potts character. Here we demonstrate strain control of three-state Potts nematicity as a vestigial order of zigzag antiferromagnetism in FePSe3. Optical linear dichroism measurements reveal the nematic state and demonstrate the rotation of the nematic director by uniaxial strain. We show that the nature of the nematic phase transition can also be controlled by strain, inducing a smooth crossover transition between a Potts nematic transition and an Ising nematic flop transition. Elastocaloric measurements demonstrate the signatures of two coupled phase transitions, indicating that the vestigial nematic transition is separated from the antiferromagnetic transition. This establishes FePSe3 as a system to explore three-state Potts vestigial nematicity.
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Data availability
The datasets generated during and/or analysed during this study are available from the corresponding authors upon reasonable request. Source data are provided with this paper.
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Acknowledgements
We thank Q. Zhang for substantial insights. This work was mainly supported by the Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division (DE-SC0012509). Strain devices were partially supported by the Air Force Office of Scientific Research (AFOSR) Multidisciplinary University Research Initiative (MURI) program, grant no. FA9550-19-1-0390. Bulk crystal growth and EC measurements were supported by NSF MRSEC DMR-2308979 and the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant no. GBMF6759 (to J.-H.C.). We also acknowledge the use of facilities and instrumentation supported by NSF MRSEC DMR-1719797. X.X. and J.-H.C. acknowledge support from the State of Washington-funded Clean Energy Institute.
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X.X., K.H., J.-H.C., H.W. and E.R. conceived the experiment. K.H. fabricated the samples and performed the optical measurements. J.C. designed and built the strain cell for atomically thin flakes. E.R. performed the EC measurement, and Q.J. synthesized and characterized the bulk crystals under the supervision of J.-H.C. D.X. constructed the domain population model. All authors contributed to the data analysis and interpretation. K.H., X.X., E.R. and J.-H.C. wrote the paper with input from all authors. All authors discussed the results and commented on the paper.
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Extended data
Extended Data Fig. 1 Linear dichroism spectrum.
Linear dichroism signal as a function of incident photon energy for a thin-bulk FePSe3 sample at 5 K. The spectrum shows a broad LD response centered around 2 eV. The photon energy dependent LD response is possibly due to a resonance effect with a d-d electronic transition. Previous measurements on FePS3 showed similar enhancement of LD response at known d-d transitions.
Extended Data Fig. 2 Strain apparatus and crystal response to strain.
Schematic of the strain cell used for the strain measurements and optical image of a representative strain sample. The crystal zigzag direction was aligned along the strain direction.
Extended Data Fig. 3 Strain calibration using Si phonon mode and Thermal calibration.
a, Raman spectra of the silicon Raman mode centered around 525 cm−1 with −80 V (blue) and 80 V (red) applied to the strain cell. b, Raman shift of the silicon Raman mode as a function of the piezo voltage. c, Linear dichroism versus temperature for a non-strained, thin bulk FePSe3 flake on the strainer setup, showing the shift (~10 K) in the transition temperature due to the increased thermal load of the strainer. The x-axis shows the nominal thermocouple reading.
Extended Data Fig. 4 Linear dichroism spatial mapping.
a, Nematic directors (represented by the white arrows) at each sampled point overlaid on top of the reflection raster map for various piezo voltages. The raster map was scanned over 28 μm × 14 μm area with 1 μm step sizes. The maximally negative voltage corresponds to the highest compressive strain applied. Scale bar: 5 μm. The absence of distinct nematic domains, which are separated by 2π/3, across the sample demonstrates that the results of Fig. 2a, b are not a product of our probe beam concomitantly sampling adjacent nematic domains. b, Optical image of the measured strain sample. The red box represents the area which the LD mapping was measured, and the black arrow shows the strain direction. Scale bar: 5 μm.
Extended Data Fig. 5 Polarization-resolved Raman spectroscopy of the strain FePSe3 sample.
a, Raman response of a thin-bulk flake at two thermal points. Labelled peaks (P1, P2, and P3) correspond to Raman modes associated with the zigzag AFM order. b, c, Co-linearly polarized Raman scattering as the incident polarization is rotated for compressive (−120 V) and tensile (90 V) strain, respectively. d, e, Polar plot of the integrated intensity of the Raman mode labelled P1 superimposed onto zigzag orders at compressive (d) and tensile (e) strain. P1 Raman mode exhibits a four-fold symmetry that is rotationally separated by π/4 with respect to the zigzag order. Thus, a 2π/3-shift in the zigzag order would result in a π/6-shift in the incident polarization dependence of the Raman mode.
Extended Data Fig. 6 Polarization-dependent intensity of Raman mode at ~73 cm−1.
a, Polarization dependence of the integrated intensity of Raman mode labelled P1 in Extended Data Fig. 5 as strain is swept from compressive (blue curves) to tensile (red curves) side. b, Incident polarization angle values where the Raman peak reaches the maximum value. There is near 30-degree rotation as strain is swept from compressive to tensile strain.
Extended Data Fig. 7 Raw data and background subtraction.
a,b, Polarization-dependent LD responses at 35 K and 160 K, respectively. The black curves represent the background LD response from the sample at 295 K. The pink curves represent the raw LD response observed from the sample. The blue curves are the LD response after subtracting the background response from the raw data.
Extended Data Fig. 8 Domain Population Model Fitting.
a, Polarization-dependent LD response shown in Fig. 2a. b,c, LD responses and corresponding fit to function, \(LD(\theta )=f(\varepsilon )\,\cos (2\theta )+[1-f(\varepsilon )]\cos (2(\theta +2\pi /3))\), to extract f(ε) at −0.033% and 0% strain, respectively. d, f(ε) versus strain for LD response shown in Fig. 2a.
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Hwangbo, K., Rosenberg, E., Cenker, J. et al. Strain tuning of vestigial three-state Potts nematicity in a correlated antiferromagnet. Nat. Phys. 20, 1888–1895 (2024). https://doi.org/10.1038/s41567-024-02653-3
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DOI: https://doi.org/10.1038/s41567-024-02653-3