Zeeman split Kramers doublets in spin-supersolid candidate Na${}_2$BaCo(PO${}_4$)${}_2$

Abstract

Na${}_2$BaCo(PO${}_4$)${}_2$ is a triangular antiferromagnet that displays highly efficient adiabatic demagnetization cooling (J. Xiang $\text{et al.}$ Nature $625$, 270 (2024)) near a quantum critical point at $\hat{I}{¼}_0{H}_c\sim 1.6$ T, separating a low-field magnetically disordered from a high-field fully polarized ferromagnetic phase. We apply high resolution backscattering neutron spectroscopy in an applied field to study the magnetic excitations near $\hat{I}{¼}_0{H}_c$. At large fields we observe ferromagnetic fluctuations that gradually transition to being overdamped in energy below $\hat{I}{¼}_0{H}_c$ where the magnetism is spatially disordered. We parameterize the excitations in the high field polarized phase in terms of coupled Zeeman split Kramers doublets originating from the presence of spin-orbit coupling. On reducing the field, the splitting between the Kramers doublets is reduced and if done adiabatically, provides a mechanism for reducing temperature. On lowering the applied field through the $\hat{I}{¼}_0{H}_c$ the excitations characterize a textured phase that we suggest is inefficient for cooling. Low temperature disordered frustrated magnets built on Kramers doublets with nearby quantum critical points provide a route for efficient magnetocalorics.

(main text - 5 pages, 4 figures; supplementary information - 7 pages, 7 figures, to be published in Physical Review Letters)