Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice

Jieming Sheng; Jia Wei Mei; Le Wang; Xiaoyu Xu; Wenrui Jiang; Lei Xu; Han Ge; Nan Zhao; Tiantian Li; Andrea Candini; Bin Xi; Jize Zhao; Ying Fu; Jiong Yang; Yuanzhu Zhang; Giorgio Biasiol; Shanmin Wang; Jinlong Zhu; Ping Miao; Xin Tong; Dapeng Yu; Richard Mole; Yi Cui; Long Ma; Zhitao Zhang; Zhongwen Ouyang; Wei Tong; Andrey Podlesnyak; Ling Wang; Feng Ye; Dehong Yu; Weiqiang Yu; Liusuo Wu; Zhentao Wang

doi:10.1038/s41563-024-02071-z

Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice

Jieming Sheng, Jia Wei Mei, Le Wang, Xiaoyu Xu, Wenrui Jiang, Lei Xu, Han Ge, Nan Zhao, Tiantian Li, Andrea Candini, Bin Xi, Jize Zhao, Ying Fu, Jiong Yang, Yuanzhu Zhang, Giorgio Biasiol, Shanmin Wang, Jinlong Zhu, Ping Miao, Xin TongDapeng Yu, Richard Mole, Yi Cui, Long Ma, Zhitao Zhang, Zhongwen Ouyang, Wei Tong, Andrey Podlesnyak, Ling Wang, Feng Ye, Dehong Yu, Weiqiang Yu, Liusuo Wu, Zhentao Wang

Research output: Contribution to journal › Article › peer-review

Abstract

In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose–Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman coupling to a magnetic field is able to tune the particle density through a quantum critical point, beyond which a ‘hidden order’ is predicted to exist. Here we report direct observation of the Bose–Einstein condensation of the two-magnon bound state in Na₂BaNi(PO₄)₂. Comprehensive thermodynamic measurements confirmed the two-dimensional Bose–Einstein condensation quantum critical point at the saturation field. Inelastic neutron scattering experiments were performed to establish the microscopic model. An exact solution revealed stable two-magnon bound states that were further confirmed by electron spin resonance and nuclear magnetic resonance experiments, demonstrating that the quantum critical point is due to the pair condensation, and the phase below the saturation field is likely the long-sought-after spin nematic phase.

Original language	English
Journal	Nature Materials
DOIs	https://doi.org/10.1038/s41563-024-02071-z
State	Accepted/In press - 2025

Funding

We thank C. D. Batista, R. M. Fernandes, A. V. Chubukov, I. A. Zaliznyak and Y. P. Cai for helpful discussions. We thank L. Sorba (NANO-CNR, Italy) for support with the Hall sensor magnetometer substrate; X. F. Xiao and J. Y. Zhu from Quantum Design for support with the low-temperature measurements; and G. Davidson for great support in setting up and operating the superconducting magnet and the dilution insert throughout the experiment on Pelican. The research was supported by the National Key Research and Development Program of China (grant nos 2021YFA1400400, 2022YFA1402704, 2023YFA1406500 and 2024YFA1408303), the National Natural Science Foundation of China (grant nos 12134020, 11974157, 12104255, 12047501, 11874188, 12047501, 12005243, 11874080, 12374124, 12204223, 12474143 and 12374150), the Guangdong Basic and Applied Basic Research Foundation (grant nos 2021B1515120015, 2022B1515120014, 2023B0303000003 and 2023B1515120060) and the Shenzhen Fundamental Research Program (grant nos JCYJ20220818100405013 and JCYJ20230807093204010). The Major Science and Technology Infrastructure Project of the Material Genome Big-science Facilities Platform was supported by the Municipal Development and Reform Commission of Shenzhen. A portion of this research used resources at the Spallation Neutron Source, a US Department of Energy Office of Science User Facility operated by the Oak Ridge National Laboratory. Z.W.\u2019s theoretical calculations at the University of Minnesota were supported by the US Department of Energy through the University of Minnesota Center for Quantum Materials under award no. DE-SC-0016371. During the writing of the paper, Z.W. was supported by the National Key Research and Development Program of China (grant no. 2022YFA1402200) and the Key Research and Development Program of Zhejiang Province, China (grant no. 2021C01002). We also acknowledge the beam time awarded by Australia\u2019s Nuclear Science and Technology Organisation (ANSTO) through proposal no. P9955, and by the Spallation Neutron Source, Oak Ridge National Laboratory through proposal no. 29333.

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10.1038/s41563-024-02071-z

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Sheng, J., Mei, J. W., Wang, L., Xu, X., Jiang, W., Xu, L., Ge, H., Zhao, N., Li, T., Candini, A., Xi, B., Zhao, J., Fu, Y., Yang, J., Zhang, Y., Biasiol, G., Wang, S., Zhu, J., Miao, P., ... Wang, Z. (Accepted/In press). Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice. Nature Materials. https://doi.org/10.1038/s41563-024-02071-z

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title = "Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice",

abstract = "In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose–Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman coupling to a magnetic field is able to tune the particle density through a quantum critical point, beyond which a {\textquoteleft}hidden order{\textquoteright} is predicted to exist. Here we report direct observation of the Bose–Einstein condensation of the two-magnon bound state in Na2BaNi(PO4)2. Comprehensive thermodynamic measurements confirmed the two-dimensional Bose–Einstein condensation quantum critical point at the saturation field. Inelastic neutron scattering experiments were performed to establish the microscopic model. An exact solution revealed stable two-magnon bound states that were further confirmed by electron spin resonance and nuclear magnetic resonance experiments, demonstrating that the quantum critical point is due to the pair condensation, and the phase below the saturation field is likely the long-sought-after spin nematic phase.",

author = "Jieming Sheng and Mei, {Jia Wei} and Le Wang and Xiaoyu Xu and Wenrui Jiang and Lei Xu and Han Ge and Nan Zhao and Tiantian Li and Andrea Candini and Bin Xi and Jize Zhao and Ying Fu and Jiong Yang and Yuanzhu Zhang and Giorgio Biasiol and Shanmin Wang and Jinlong Zhu and Ping Miao and Xin Tong and Dapeng Yu and Richard Mole and Yi Cui and Long Ma and Zhitao Zhang and Zhongwen Ouyang and Wei Tong and Andrey Podlesnyak and Ling Wang and Feng Ye and Dehong Yu and Weiqiang Yu and Liusuo Wu and Zhentao Wang",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Nature Limited 2025.",

year = "2025",

doi = "10.1038/s41563-024-02071-z",

language = "English",

journal = "Nature Materials",

issn = "1476-1122",

publisher = "Nature Research",

}

Sheng, J, Mei, JW, Wang, L, Xu, X, Jiang, W, Xu, L, Ge, H, Zhao, N, Li, T, Candini, A, Xi, B, Zhao, J, Fu, Y, Yang, J, Zhang, Y, Biasiol, G, Wang, S, Zhu, J, Miao, P, Tong, X, Yu, D, Mole, R, Cui, Y, Ma, L, Zhang, Z, Ouyang, Z, Tong, W, Podlesnyak, A, Wang, L, Ye, F, Yu, D, Yu, W, Wu, L & Wang, Z 2025, 'Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice', Nature Materials. https://doi.org/10.1038/s41563-024-02071-z

TY - JOUR

T1 - Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice

AU - Sheng, Jieming

AU - Mei, Jia Wei

AU - Wang, Le

AU - Xu, Xiaoyu

AU - Jiang, Wenrui

AU - Xu, Lei

AU - Ge, Han

AU - Zhao, Nan

AU - Li, Tiantian

AU - Candini, Andrea

AU - Xi, Bin

AU - Zhao, Jize

AU - Fu, Ying

AU - Yang, Jiong

AU - Zhang, Yuanzhu

AU - Biasiol, Giorgio

AU - Wang, Shanmin

AU - Zhu, Jinlong

AU - Miao, Ping

AU - Tong, Xin

AU - Yu, Dapeng

AU - Mole, Richard

AU - Cui, Yi

AU - Ma, Long

AU - Zhang, Zhitao

AU - Ouyang, Zhongwen

AU - Tong, Wei

AU - Podlesnyak, Andrey

AU - Wang, Ling

AU - Ye, Feng

AU - Yu, Dehong

AU - Yu, Weiqiang

AU - Wu, Liusuo

AU - Wang, Zhentao

PY - 2025

Y1 - 2025

N2 - In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose–Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman coupling to a magnetic field is able to tune the particle density through a quantum critical point, beyond which a ‘hidden order’ is predicted to exist. Here we report direct observation of the Bose–Einstein condensation of the two-magnon bound state in Na2BaNi(PO4)2. Comprehensive thermodynamic measurements confirmed the two-dimensional Bose–Einstein condensation quantum critical point at the saturation field. Inelastic neutron scattering experiments were performed to establish the microscopic model. An exact solution revealed stable two-magnon bound states that were further confirmed by electron spin resonance and nuclear magnetic resonance experiments, demonstrating that the quantum critical point is due to the pair condensation, and the phase below the saturation field is likely the long-sought-after spin nematic phase.

AB - In ordered magnets, the elementary excitations are spin waves (magnons), which obey Bose–Einstein statistics. Similarly to Cooper pairs in superconductors, magnons can be paired into bound states under attractive interactions. The Zeeman coupling to a magnetic field is able to tune the particle density through a quantum critical point, beyond which a ‘hidden order’ is predicted to exist. Here we report direct observation of the Bose–Einstein condensation of the two-magnon bound state in Na2BaNi(PO4)2. Comprehensive thermodynamic measurements confirmed the two-dimensional Bose–Einstein condensation quantum critical point at the saturation field. Inelastic neutron scattering experiments were performed to establish the microscopic model. An exact solution revealed stable two-magnon bound states that were further confirmed by electron spin resonance and nuclear magnetic resonance experiments, demonstrating that the quantum critical point is due to the pair condensation, and the phase below the saturation field is likely the long-sought-after spin nematic phase.

UR - http://www.scopus.com/inward/record.url?scp=85217248804&partnerID=8YFLogxK

U2 - 10.1038/s41563-024-02071-z

DO - 10.1038/s41563-024-02071-z

M3 - Article

AN - SCOPUS:85217248804

SN - 1476-1122

JO - Nature Materials

JF - Nature Materials

ER -

Bose–Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice

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