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

Jieming Sheng^#^{1

2

3}, Jia-Wei Mei^#^{4

5

6}, Le Wang^#^{1

7}, Xiaoyu Xu⁸, Wenrui Jiang^{1

7}, Lei Xu⁹, Han Ge¹, Nan Zhao¹, Tiantian Li¹, Andrea Candini¹⁰, Bin Xi¹¹, Jize Zhao^{12

13}, Ying Fu¹⁴, Jiong Yang¹⁵, Yuanzhu Zhang¹⁵, Giorgio Biasiol¹⁶, Shanmin Wang¹, Jinlong Zhu^{1

14}, Ping Miao^{17

18}, Xin Tong^{17

18}, Dapeng Yu^{1

7}, Richard Mole¹⁹, Yi Cui⁸, Long Ma²⁰, Zhitao Zhang²⁰, Zhongwen Ouyang²¹, Wei Tong²⁰, Andrey Podlesnyak²², Ling Wang⁹, Feng Ye²², Dehong Yu²³, Weiqiang Yu^{24

25}, Liusuo Wu^{26

27

28

29}, Zhentao Wang^{30

31

32}

Affiliations

¹ Department of Physics, Southern University of Science and Technology, Shenzhen, China.
² School of Physical Sciences, Great Bay University and Great Bay Institute for Advanced Study, Dongguan, China.
³ Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, Department of Physics, Southern University of Science and Technology, Shenzhen, China.
⁴ Department of Physics, Southern University of Science and Technology, Shenzhen, China. meijw@sustech.edu.cn.
⁵ Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China. meijw@sustech.edu.cn.
⁶ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. meijw@sustech.edu.cn.
⁷ Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China.
⁸ School of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China.
⁹ School of Physics, Zhejiang University, Hangzhou, China.
¹⁰ Institute of Organic Synthesis and Photoreactivity, National Research Council of Italy, ISOF-CNR, Bologna, Italy.
¹¹ College of Physical Science and Technology, Yangzhou University, Yangzhou, China.
¹² School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou, China.
¹³ Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, China.
¹⁴ Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen, China.
¹⁵ Department of Chemistry, Southern University of Science and Technology, Shenzhen, China.
¹⁶ Laboratorio TASC, Istituto Officina dei Materiali (IOM CNR), Trieste, Italy.
¹⁷ Institute of High Energy Physics, Chinese Academy of Sciences (CAS), Beijing, China.
¹⁸ Spallation Neutron Source Science Center (SNSSC), Dongguan, China.
¹⁹ Australian Nuclear Science and Technology Organisation, Lucas Heights, New South Wales, Australia.
²⁰ Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China.
²¹ Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, China.
²² Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.
²³ Australian Nuclear Science and Technology Organisation, Lucas Heights, New South Wales, Australia. Dehong.Yu@ansto.gov.au.
²⁴ School of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China. wqyu_phy@ruc.edu.cn.
²⁵ Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, China. wqyu_phy@ruc.edu.cn.
²⁶ Department of Physics, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁷ Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, Department of Physics, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁸ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁹ Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen, China. wuls@sustech.edu.cn.
³⁰ School of Physics, Zhejiang University, Hangzhou, China. ztwang@zju.edu.cn.
³¹ School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA. ztwang@zju.edu.cn.
³² Center for Correlated Matter, Zhejiang University, Hangzhou, China. ztwang@zju.edu.cn.

^# Contributed equally.

PMID: 39833392
DOI: 10.1038/s41563-024-02071-z

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

Jieming Sheng et al. Nat Mater. 2025 Apr.

. 2025 Apr;24(4):544-551.

doi: 10.1038/s41563-024-02071-z. Epub 2025 Jan 20.

Authors

Affiliations

¹ Department of Physics, Southern University of Science and Technology, Shenzhen, China.
² School of Physical Sciences, Great Bay University and Great Bay Institute for Advanced Study, Dongguan, China.
³ Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, Department of Physics, Southern University of Science and Technology, Shenzhen, China.
⁴ Department of Physics, Southern University of Science and Technology, Shenzhen, China. meijw@sustech.edu.cn.
⁵ Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China. meijw@sustech.edu.cn.
⁶ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. meijw@sustech.edu.cn.
⁷ Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China.
⁸ School of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China.
⁹ School of Physics, Zhejiang University, Hangzhou, China.
¹⁰ Institute of Organic Synthesis and Photoreactivity, National Research Council of Italy, ISOF-CNR, Bologna, Italy.
¹¹ College of Physical Science and Technology, Yangzhou University, Yangzhou, China.
¹² School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of the MoE, Lanzhou University, Lanzhou, China.
¹³ Lanzhou Center for Theoretical Physics and Key Laboratory of Theoretical Physics of Gansu Province, Lanzhou University, Lanzhou, China.
¹⁴ Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen, China.
¹⁵ Department of Chemistry, Southern University of Science and Technology, Shenzhen, China.
¹⁶ Laboratorio TASC, Istituto Officina dei Materiali (IOM CNR), Trieste, Italy.
¹⁷ Institute of High Energy Physics, Chinese Academy of Sciences (CAS), Beijing, China.
¹⁸ Spallation Neutron Source Science Center (SNSSC), Dongguan, China.
¹⁹ Australian Nuclear Science and Technology Organisation, Lucas Heights, New South Wales, Australia.
²⁰ Anhui Key Laboratory of Low-Energy Quantum Materials and Devices, High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei, China.
²¹ Wuhan National High Magnetic Field Center and School of Physics, Huazhong University of Science and Technology, Wuhan, China.
²² Neutron Scattering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA.
²³ Australian Nuclear Science and Technology Organisation, Lucas Heights, New South Wales, Australia. Dehong.Yu@ansto.gov.au.
²⁴ School of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China. wqyu_phy@ruc.edu.cn.
²⁵ Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, China. wqyu_phy@ruc.edu.cn.
²⁶ Department of Physics, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁷ Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, Department of Physics, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁸ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. wuls@sustech.edu.cn.
²⁹ Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen, China. wuls@sustech.edu.cn.
³⁰ School of Physics, Zhejiang University, Hangzhou, China. ztwang@zju.edu.cn.
³¹ School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA. ztwang@zju.edu.cn.
³² Center for Correlated Matter, Zhejiang University, Hangzhou, China. ztwang@zju.edu.cn.

^# Contributed equally.

PMID: 39833392
DOI: 10.1038/s41563-024-02071-z

Erratum in

Publisher Correction: Bose-Einstein condensation of a two-magnon bound state in a spin-1 triangular lattice.
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. Sheng J, et al. Nat Mater. 2025 Oct 10. doi: 10.1038/s41563-025-02399-0. Online ahead of print. Nat Mater. 2025. PMID: 41073660 No abstract available.

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.

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Conflict of interest statement

Competing interests: The authors declare no competing interests.

References

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

Affiliations

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

Authors

Affiliations

Erratum in

Abstract

Conflict of interest statement

References

LinkOut - more resources

Full Text Sources