Magnons are the elementary excitations of typical magnetically ordered systems, and their interactions often lead to a plethora of emergent phenomena. In his seminal work, physicist Hans Bethe pointed out the possibility of forming two-magnon bound states in a spin chain. Later, this concept was generalized to higher dimensions by Wotis and Hanus. As an analogue of Cooper pairs in superconductors, it has been predicted theoretically that the BEC of two-magnon bound states corresponds to a quantum phase transition into a new state of matter, often termed as the spin nematic (SN) state. The SN state is a type of “hidden order” that breaks the spin rotational symmetry while having zero dipolar magnetic moments.

To date, multi-magnon bound states have been observed in several systems, including one-dimensional (1D) spin chains, triangular lattices (TLs), and cold atoms. However, affirmative experimental evidence of two-magnon condensation and the associated SN phase remains elusive. While the application of a magnetic field appears to be one of the most promising paths to tune the system through this QCP, it is a challenging task due to the high saturation fields or rather complicated magnetic exchanges involved for the known candidate materials.

A collaborative research team, including Associate Professors Liusuo Wu and Jiawei Mei from the Department of Physics at the Southern University of Science and Technology (SUSTech), researcher Zhentao Wang from Zhejiang University, Professor Weiqiang Yu from Renmin University of China, Professor Dehong Yu from the Australian Nuclear Science and Technology Organisation (ANSTO), along with other collaborators from Huazhong University of Science and Technology, the High Magnetic Field Laboratory (Hefei), and Oak Ridge National Laboratory (ORNL), has achieved substantial progress in this field.

Their research, titled “Bose-Einstein condensation of a two-magnon bound state in a spin-one triangular lattice”, has been published in Nature Materials.

These achievements build upon systematic research into low-dimensional quantum magnetic materials in recent years. Through investigations of spin dynamics in two-dimensional (2D) frustrated spin systems, the researchers revealed 2D quantum criticality associated with single magnon condensation. Additionally, they successfully determined the spin Hamiltonian and conducted a comprehensive theoretical and experimental analysis of the spin continuous excitation spectrum using inelastic neutron scattering. Previous findings have been published in the Proceedings of the National Academy of Sciences (PNAS) and The Innovation.

In this latest study, the team found clear evidence of a two-dimensional BEC of a two-magnon bound state in the recently discovered spin-1 TL insulating antiferromagnet Na2BaNi(PO4)2. The small magnetic exchanges of this compound result in a low saturation field (∼1.8T), that allows an accurate extraction of the model parameters by an inelastic neutron scattering (INS) experiment in the fully polarized (FP) phase. They found two-magnon bound states to be stable from the exact solution of the Lippmann-Schwinger equation. Confirmation via electron spin resonance (ESR) and nuclear magnetic resonance (NMR) measurements demonstrated that the QCP at saturation field originates from the BEC of a two-magnon bound state, responsible for the SN phase below saturation.

Figure 1. Solution of the spin-1 model with the simulated energy dispersions of the one-magnon excitation, two-magnon continuum, and two-magnon bound state, along with the experimental (neutron, ESR, and NMR) data.

Dr. Jieming Sheng, who is currently an assistant professor at the Great Bay University, is the first author of the paper. Jiawei Mei, Weiqiang Yu, Dehong Yu, Liusuo Wu and Zhentao Wang serve as the corresponding authors.

Paper link in Nature Materials: https://doi.org/10.1038/s41563-024-02071-z

Related links:

PNAS: https://doi.org/10.1073/pnas.2211193119

The Innovation: https://doi.org/10.1016/j.xinn.2024.100769

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