The investigation of geometrically frustrated systems with antiferromagnetically (AFM) ordered spins attracts attention due to their potential to stabilize exotic quantum states, such as a spin liquid state, which holds promise for applications in quantum computing. Here we present our study of the triangular AFM compound Na₂BaMn(PO₄)₂ [1,2], which has an unusually high spin S = 5/2. In contrast, the isostructural compound with Co (S = 1/2) [3] has been studied extensively, as lower spin systems are typically more favourable for the formation of quantum spin liquids. We use single crystal neutron diffraction and inelastic neutron scattering to determine the magnetic structures and spin excitations for magnetic fields applied in the basal plane and along the c-axis of the trigonal symmetry. At zero magnetic field, the system undergoes two magnetic transitions at around 1.25 K (AFM2) and 1.1 K (AFM1). The out-of-plane incommensurate component k of the magnetic propagation vector (1/3, 1/3, k) changes significantly in these two AFM phases, which suggests non-negligible interlayer couplings. Depending on the direction of the magnetic field, Na₂BaMn(PO₄)₂ shows several field-induced transitions. These transitions cause changes in the magnetic propagation vector before the system reaches the spin-polarized state. By combining neutron diffraction, low-temperature specific heat, and dc magnetization, we establish temperature–magnetic field phase diagrams for both field directions. Using ab initio calculations and Monte Carlo simulations, we determine the exchange interactions, anisotropy parameters, and the phase diagrams. Our combined experimental and theoretical study shows that Na₂BaMn(PO₄)₂ is mainly a 2D system, with very weak 3D coupling that only acts as a "witness" to what happens in two dimensions. The separation between the two zero-field transitions (AFM1 and AFM2) depends on the XXZ nature of the anisotropy and the 3D coupling. The gap in the dispersion of the fully polarized phase is influenced by the XXZ anisotropy, single-ion anisotropies, and the magnetic field. Finally, we compare our results with the Co (S = 1/2) and Ni (S = 1) [4] counterparts and discuss their similarities and differences. 

Our findings are summarized in the recent preprint: Biniskos, N., ...D. Sviták, ... and P. Čermák. arXiv:2508.21021 (2025).

References

[1] J. Kim, et. al., Journal of Physics: Condensed Matter, 34, p. 475803 (2022).

[2] C. Zhang, et. al., Phys. Rev. B, 110, p. 214405 (2024).

[3] N. Li, Q. Huang, et. al. Nature Communications, 11, p. 4216 (2020).

[4] N. Li, Q. Huang, et. al. Phys. Rev. B, 104, p. 104403 (2021).