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

Nat Mater. 2025 Jan 20. doi: 10.1038/s41563-024-02071-z. Online ahead of print.

Authors

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. [email protected].
⁵ Shenzhen Institute for Quantum Science and Engineering, Shenzhen, China. [email protected].
⁶ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. [email protected].
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. [email protected].
²⁴ School of Physics and Beijing Key Laboratory of Optoelectronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, China. [email protected].
²⁵ Key Laboratory of Quantum State Construction and Manipulation (Ministry of Education), Renmin University of China, Beijing, China. [email protected].
²⁶ Department of Physics, Southern University of Science and Technology, Shenzhen, China. [email protected].
²⁷ Guangdong Provincial Key Laboratory of Advanced Thermoelectric Materials and Device Physics, Department of Physics, Southern University of Science and Technology, Shenzhen, China. [email protected].
²⁸ Shenzhen Key Laboratory of Advanced Quantum Functional Materials and Devices, Southern University of Science and Technology, Shenzhen, China. [email protected].
²⁹ Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area (Guangdong), Shenzhen, China. [email protected].
³⁰ School of Physics, Zhejiang University, Hangzhou, China. [email protected].
³¹ School of Physics and Astronomy, University of Minnesota, Minneapolis, MN, USA. [email protected].
³² Center for Correlated Matter, Zhejiang University, Hangzhou, China. [email protected].

^# Contributed equally.

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

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.