Single-ion properties of the transverse-field Ising model materialCoNb2O6

$\mathrm{Co}{\mathrm{Nb}}₂{\mathrm{O}}₆$ is one of the few materials that is known to approximate the one-dimensional transverse-field Ising model (1D-TFIM) near its quantum critical point. It has been inferred that ${\mathrm{Co}}²⁺$ acts as a pseudospin $1/2$ with anisotropic exchange interactions that are largely Ising-like, enabling the realization of the TFIM. However, the behavior of $\mathrm{Co}{\mathrm{Nb}}₂{\mathrm{O}}₆$ is known to diverge from the ideal TFIM under transverse magnetic fields that are far from the quantum critical point, requiring the consideration of additional anisotropic, bond-dependent (Kitaev-like) terms in the microscopic pseudospin-$1/2$ Hamiltonian. These terms are expected to be controlled in part by single-ion physics, namely the wave function for the pseudospin-$1/2$ angular momentum doublet. Here, we present the results of both inelastic neutron scattering measurements and electron paramagnetic resonance spectroscopy on $\mathrm{Co}{\mathrm{Nb}}₂{\mathrm{O}}₆$, which elucidate the single-ion physics of ${\mathrm{Co}}²⁺$ in $\mathrm{Co}{\mathrm{Nb}}₂{\mathrm{O}}₆$ for the first time. We find that the system is well-described by an intermediate spin-orbit coupled Hamiltonian, and the ground state is a well-isolated Kramers doublet with an anisotropic $g$ tensor. We provide the approximate wave functions for this doublet, which we expect will be useful in theoretical investigations of the anisotropic exchange interactions.