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 $\textit{et al.}$ Nature ${\bf{625}}$, 270 (2024)) near a quantum critical point at $μ_{0}H_{c}\sim 1.6$ 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 $μ_{0}H_{c}$. 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 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 $μ_{0}H_{c}$ 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.

Figures (4)

• Figure 1: $(a)$ Structure of Na$_{2}$BaCo(PO$_{4}$)$_{2}$ (NBCP) with octahedral CoO$_6$. $(b)$ Co$^{2+}$ single-ion energies under spin-orbit, distortion and molecular field with an overall applied octahedral crystalline electric field. The dipole active quantum levels with finite neutron cross section from the ground state (blue) are highlighted in red. $(c)$ Constant momentum slice (MAPS) at T=10 K of the first spin-orbit level $j_{eff}=3/2$. We note that given the direction of the integration, the spectral intensities found at zero on the $x$-axis describe a sum over (0,0,$\pm$0.5) rather than data strictly at the $|\vec{Q}|$=0 origin.
• Figure 2: Constant energy slices (OSIRIS) taken at 4 T from (a) the measured data between $\Delta E=[0.62,0.67]$ meV, (c) RPA calculations with the inclusion of the term $\kappa$ taken at E=0.645 meV and (e) RPA theory excluding $\kappa$. Constant momentum slices are also presented with (b) data cuts along the (-H$\pm$0.1, 2H$\pm$0.1, 0) direction. Additional RPA theoretical dispersion plots taken at H=0 along the (-H,2H,0) direction (d) including the parameter $\kappa$ and (f) excluding it.
• Figure 3: Constant momentum slices (OSIRIS) along (-H$\pm$0.1, 2H$\pm$0.1, 0) for $(a)$$\mu_0\mathit{H}$ = 3.0 T, (c) 2.0 T, (e) 1.0 T, (f) 0.5 T. RPA calculations for (b) $\mu_0\mathit{H}$=3.0 T and (d) 2.0 T.
• Figure 4: Folded constant-$E$ slices (OSIRIS) at $(a)$ E=[0.32,0.37] meV (3 T) and $(c)$ [0.01,0.015] meV (0 T). RPA calculations at $(b)$ E=0.325 meV (3 T) and $(d)$ 0.085 meV (0 T). $(e)$ Constant-$\vec{Q}$ slice (OSIRIS) at $\mu_{0}H$= 0 T. $(f)$ Obtained parameters as a function of $\mu_{0}H$ with guiding lines.