Zeeman Split Kramers Doublets in Spin-Supersolid Candidate Na_{2}BaCo(PO_{4})_{2}.

Na_{2}BaCo(PO_{4})_{2} is a triangular antiferromagnet that displays highly efficient adiabatic demagnetization cooling [Junsen Xiang et al., Nature (London) 625, 270 (2024)NATUAS0028-083610.1038/s41586-023-06885-w] near a quantum critical point at μ_{0}H_{c}∼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 μ_{0}H_{c}. At large fields we observe ferromagnetic fluctuations that gradually transition to being overdamped in energy below μ_{0}H_{c} where the magnetism is spatially disordered. We parametrize 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 μ_{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.