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The antiferromagnetic pyrochlore material NaCaCo$_2$F$_7$ is a thermal spinliquid over a broad temperature range (~ 140 K down to $T_F = 2.4 $K), in whichmagnetic correlations between Co$^{2+}$ dipole moments explore a continuousmanifold of antiferromagnetic XY states. The thermal spin liquid is interruptedby spin freezing at a temperature that is ~ 2 % of the mean field interactionstrength, leading to short range static XY clusters with distinctive relaxationdynamics. Here we report the low energy inelastic neutron scattering responsefrom the related compound NaSrCo$_2$F$_7$, confirming that it hosts the samestatic and dynamic spin correlations as NaCaCo$_2$F$_7$. We then present thesingle-ion levels of Co$^{2+}$ in these materials as measured by inelasticneutron scattering. An intermediate spin orbit coupling model applied to anensemble of trigonally distorted octahedral crystal fields accounts for theobserved transitions. The single-ion ground state of Co$^{2+}$ is a Kramersdoublet with a strongly XY-like $g$-tensor ($g_{xy}/g_{z}$ ~ 3). The localdisorder inherent from the mixed pyrochlore $A$ sites (Na$^{+}$/Ca$^{2+}$ andNa$^{+}$/Sr$^{2+}$) is evident in these measurements as exaggerated broadeningof some of the levels. A simple model that reproduces the salient features ofthe single-ion spectrum produces approximately 8.4 % and 4.1 % variation in the$z$ and $xy$ components of the $g$-tensor, respectively. This study confirmsthat an $S_{eff} =1/2$ model with XY antiferromagnetic exchange and weakexchange disorder serves as a basic starting point in understanding the lowtemperature magnetic behavior of these strongly frustrated magnets.

Single-ion properties of the $S_{eff}$ = 1/2 XY antiferromagnetic pyrochlores, Na$A^{\prime}$Co$_2$F$_7$ ($A^{\prime} = $ Ca$^{2+}$, Sr$^{2+}$)