Magneto-elastic induced vibronic bound state in the spin ice pyrochlore Ho${}_2$Ti${}_2$O${}_7$

The single ion physics of Ho${}_2$Ti${}_2$O${}_7$ is well-understood to produce strong Ising anisotropy, which is an essential ingredient to its low-temperature spin ice state. We present inelastic neutron scattering measurements on Ho${}_2$Ti${}_2$O${}_7$ that reveal a clear inconsistency with its established single ion Hamiltonian. Specifically, we show that a crystal field doublet near 60~meV is split by approximately 3~meV. Furthermore, this crystal field splitting is not isolated to Ho${}_2$Ti${}_2$O${}_7$ but can also be found in its chemical pressure analogs, Ho${}_2$Ge${}_2$O${}_7$ and Ho${}_2$Sn${}_2$O${}_7$. We demonstrate that the origin of this effect is a vibronic bound state, resulting from the entanglement of a phonon and crystal field excitation. We derive the microscopic Hamiltonian that describes the magneto-elastic coupling and provides a quantitative description of the inelastic neutron spectra.