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# Three-state nematicity in the triangular lattice antiferromagnet Fe1/3NbS2

## Abstract

Nematic order is the breaking of rotational symmetry in the presence of translational invariance. While originally defined in the context of liquid crystals, the concept of nematic order has arisen in crystalline matter with discrete rotational symmetry, most prominently in the tetragonal Fe-based superconductors where the parent state is four-fold symmetric. In this case the nematic director takes on only two directions, and the order parameter in such ‘Ising-nematic’ systems is a simple scalar. Here, using a spatially resolved optical polarimetry technique, we show that a qualitatively distinct nematic state arises in the triangular lattice antiferromagnet Fe1/3NbS2. The crucial difference is that the nematic order on the triangular lattice is a $$Z_3$$ or three-state Potts-nematic order parameter. As a consequence, the anisotropy axes of response functions such as the resistivity tensor can be continuously reoriented by external perturbations. This discovery lays the groundwork for devices that exploit analogies with nematic liquid crystals.

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## Data availability

The data represented in Figs. 1b,c, 2a,b,c, 3a,b and 5b,c,e,f are provided with the paper as source data. All other data that support results in this Article are available from the corresponding author upon reasonable request.

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## Acknowledgements

We thank D. H. Lee and J. E. Moore for useful discussions and N. Tamura for support at the Advanced Light Source. Optical measurements were performed at the Lawrence Berkeley National Laboratory in the Quantum Materials programme supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under contract no. DE-AC02- 05CH11231. A.L. and J.O. received support for optical measurements from the Gordon and Betty Moore Foundation’s EPiQS Initiative through grant no. GBMF4537 to J.O. at University of California, Berkeley. Work by J.G.A., E.M., C.J. and S.D. was supported as part of the Center for Novel Pathways to Quantum Coherence in Materials, an Energy Frontier Research Center funded by the US Department of Energy, Office of Science, Basic Energy Sciences. Synthesis of Fe1/3NbS2 was supported by Laboratory Directed Research and Development Program of Lawrence Berkeley National Laboratory under contract no. DE-AC02-05CH11231. J.G.A. and N.L.N. received support from the Gordon and Betty Moore Foundation’s EPiQS Initiative grant no. GBMF9067 to J.G.A. at University of California, Berkeley. R.M.F. was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award DE-SC0012336 and, during completion of the work, under award DE‐SC0020045. X-ray diffraction to register crystal orientation was carried out at beamline 12.3.2 at the Advanced Light Source, which is a Department of Energy User Facility, under contract no. DE-AC02-05CH11231.

## Author information

Authors

### Contributions

A.L. and C.L. performed and contributed equally to the birefringence microscopy measurements and data analysis. C.J., S.D. and E.M. grew and characterized the crystals. E.M., N.L.N. and J.G.A. discovered the switching effect that motivated this project. J.W.F.V. and R.M.F. developed the theoretical model. W.C. performed the simulation of depth profiling. D.R. assisted with optical measurements. J.O., A.L., C.L., J.W.F.V. and R.M.F. wrote the manuscript. All authors commented on the manuscript.

### Corresponding author

Correspondence to Joseph Orenstein.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–7.

## Source data

### Source Data Fig. 1

Source data for Fig. 1b,c

### Source Data Fig. 2

Source data for Fig. 2a,b,c

### Source Data Fig. 3

Source data for Fig. 3a,b

### Source Data Fig. 5

Source data for Fig. 5b,c,e,f

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Little, A., Lee, C., John, C. et al. Three-state nematicity in the triangular lattice antiferromagnet Fe1/3NbS2. Nat. Mater. 19, 1062–1067 (2020). https://doi.org/10.1038/s41563-020-0681-0

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• DOI: https://doi.org/10.1038/s41563-020-0681-0

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