Zeeman Split Kramers Doublets in Spin-Supersolid Candidate Na_2⁢BaCo⁢(PO₄)₂

Na_2⁢BaCo⁢(PO₄)₂ is a triangular antiferromagnet that displays highly efficient adiabatic demagnetization cooling [Junsen Xiang et al., Nature (London) 625, 270 (2024)] 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 𝜇₀⁢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 𝜇₀⁢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.