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# Spin-excitation anisotropy in the nematic state of detwinned FeSe

## Abstract

The origin of the electronic nematicity in FeSe is one of the most important unresolved puzzles in the study of iron-based superconductors. In both spin- and orbital-nematic models, the intrinsic magnetic excitations at Q1 = (1, 0) and Q2 = (0, 1) of twin-free FeSe are expected to provide decisive criteria for clarifying this issue. Although a spin-fluctuation anisotropy below 10 meV between Q1 and Q2 has been observed by inelastic neutron scattering at low temperature, it remains unclear whether such an anisotropy also persists at higher energies and associates with the nematic transition Ts. Here we use resonant inelastic X-ray scattering to probe the high-energy magnetic excitations of detwinned FeSe. A prominent anisotropy between the magnetic excitations along the H and K directions is found to persist to E ≈ 200 meV, which decreases gradually with increasing temperature and finally vanishes at a temperature around Ts. The measured high-energy spin excitations are dispersive and underdamped, which can be understood from a local-moment perspective.Taking together the large energy scale far beyond the dxz/dyz orbital splitting, we suggest that the nematicity in FeSe is probably spin-driven.

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## Data availability

All data that support the plots in this paper are available from the corresponding author upon reasonable request. Source data are provided with this paper. The data can also be found at Figshare public repository65.

## Code availability

All relevant source code is available from the corresponding author upon reasonable request.

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## Acknowledgements

The work at Beijing Normal University is supported by National Key Projects for Research and Development of China with Grant No. 2021YFA1400400 and the National Natural Science Foundation of China (grants nos. 11922402 and 11734002;) (X.L.). The RIXS experiments were carried out at the ADRESS beamline of the Swiss Light Source at the Paul Scherrer Institut (PSI). The work at PSI is supported by the Swiss National Science Foundation through project no. 200021_178867 and the Sinergia network Mott Physics Beyond the Heisenberg Model (MPBH; projects nos. CRSII2 160765/1 and CRSII2 141962; T.S.). The work at Renmin University was supported by the Ministry of Science and Technology of China, National Program on Key Research Project grant no. 2016YFA0300504 and Research Funds of Remnin University of China grant no. 18XNLG24 (R.Y.). The experimental work at Rice University is supported by the US Department of Energy, Basic Energy Sciences, under grant no. DE-SC0012311 (P.D.). The single-crystal synthesis work at Rice is supported by the Robert A. Welch Foundation grant no. C-1839 (P.D.). The theoretical work at Rice was supported by the US Department of Energy, Office of Science, Basic Energy Sciences, under award no. DE-SC0018197, and the computational part by the Robert A. Welch Foundation grant no. C-1411 (Q.S.). Q.S. acknowledges the hospitality of the Aspen Center for Physics, which is supported by NSF grant no. PHY-1607611.

## Author information

Authors

### Contributions

X.L. conceived this project and developed the detwinning strategy. X.L. and T.S. wrote the beamtime proposals and coordinated the experiments as well as all other project phases. X.L., W.Z., Y.T., E.P., R.L., Z.T. and T.S. carried out the RIXS experiments with the support of V.N.S. X.L. analysed the data with assistance from Y.S. P.L., R.L. and Z.T. prepared the BaFe2As2 single crystals. T.C. and P.D. provided the FeSe single crystals. R.Y. and Q.S. carried out theoretical and computational analyses. X.L., P.D. and T.S. wrote the manuscript with input from R.Y. and Q.S. All authors made comments.

### Corresponding authors

Correspondence to Xingye Lu, Pengcheng Dai or Thorsten Schmitt.

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### Competing interests

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## Supplementary information

### Supplementary Information

Supplementary Figs. 1–6 and discussions.

## Source data

### Source Data Fig. 1

Incident energy-dependent XAS and RIXS.

### Source Data Fig. 2

Summary of RIXS results on detwinned FeSe and BaFe2As2.

### Source Data Fig. 3

Energy dispersions and damping rates for the spin excitations of detwinned FeSe and BaFe2As2.

### Source Data Fig. 4

Anisotropic magnetic excitations in detwinned FeSe and BaFe2As2.

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Lu, X., Zhang, W., Tseng, Y. et al. Spin-excitation anisotropy in the nematic state of detwinned FeSe. Nat. Phys. (2022). https://doi.org/10.1038/s41567-022-01603-1

• Accepted:

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• DOI: https://doi.org/10.1038/s41567-022-01603-1

• ### Spin-excitation anisotropy in the nematic state of detwinned FeSe

• Xingye Lu
• Wenliang Zhang
• Thorsten Schmitt

Nature Physics (2022)

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• Laura Fanfarillo

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