  To understand emergent magnetic monopole dynamics in the spin ices
Ho$_2$Ti$_2$O$_7$ and Dy$_2$Ti$_2$O$_7$, it is necessary to investigate the
mechanisms by which spins flip in these materials. Presently there are thought
to be two processes: quantum tunneling at low and intermediate temperatures and
thermally activated at high temperatures. We identify possible couplings
between crystal field and optical phonon excitations and construct a strictly
constrained model of phonon-mediated spin flipping that quantitatively
describes the high-temperature processes in both compounds, as measured by
quasielastic neutron scattering. We support the model with direct experimental
evidence of the coupling between crystal field states and optical phonons in
Ho$_2$Ti$_2$O$_7$.
