Zeeman split Kramers doublets in spin-supersolid candidate Na₂BaCo(PO₄)₂

Na₂BaCo(PO₄)₂ is a triangular antiferromagnet that displays highly efficient adiabatic demagnetization cooling (J. Xiang et al. Nature 625, 270 (2024)) near a quantum critical point at μ₀Hc~ 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 μ₀Hc. At large fields we observe ferromagnetic fluctuations that gradually transition to being overdamped in energy below μ₀Hc 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 μ₀Hc 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.