  Quantum magnetic materials can provide explicit realizations of paradigm
models in quantum many-body physics. In this context, SrCu$_2$(BO$_3$)$_2$ is a
faithful realization of the Shastry-Sutherland model (SSM) for ideally
frustrated spin dimers, even displaying several of its quantum magnetic phases
as a function of pressure. We perform inelastic neutron scattering (INS)
measurements on SrCu$_2$(BO$_3$)$_2$ at 5.5 GPa and 4.5 K, observing spin waves
that characterize the high-pressure antiferromagnetic phase. The experimental
spectra are well described by linear spin-wave calculations on a SSM with an
inter-layer interaction, which is determined accurately as $J_c = 0.053(3)$
meV. The presence of $J_c$ indicates the need to account for the
three-dimensional nature of SrCu$_2$(BO$_3$)$_2$ in theoretical models, also at
lower pressures. We find that the ratio between in-plane interactions, $J'/J =
1.8(2)$, undergoes a dramatic change compared to lower pressures that we deduce
is driven by a sharp drop in the dimer coupling, $J$. Our results underline the
wide horizons opened by high-pressure INS experiments on quantum magnetic
materials.
