Excitation Spectrum and Spin Hamiltonian of the Frustrated Quantum Ising Magnet Pr$_3$BWO$_9$

We present a thorough experimental investigation on single crystals of the rare-earth based frustrated quantum antiferromagnet Pr$_3$BWO$_9$, a purported spin-liquid candidate on the breathing kagome lattice. This material possesses a disordered ground state with an unusual excitation spectrum involving a coexistence of sharp spin-waves and broad continuum excitations. Nevertheless, we show through a combination of thermodynamic, magnetometric and spectroscopic probes with detailed theoretical modeling that it should be understood in a completely different framework. The crystal field splits the lowest quasi-doublet states into two singlets moderately coupled through frustrated superexchange, resulting in a simple effective Hamiltonian of an Ising model in a transverse magnetic field. While our neutron spectroscopy data do point to significant correlations within the kagome planes, the dominant interactions are out-of-plane, forming frustrated triangular spin-tubes through two competing ferro-antiferromagnetic bonds. The resulting ground state is a simple quantum paramagnet, but with significant modifications to both thermodynamic and dynamic properties due to small perturbations to the transverse field Ising model in the form of hyperfine enhanced nuclear moments and weak structural disorder.