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Ultrasonic investigations of spin-ices Dy$_2$Ti$_2$O$_7$ and Ho$_2$Ti$_2$O$_7$ in and out of equilibrium

We report ultrasound studies of spin-lattice and single-ion effects in the spin-ice materials Dy$_2$Ti$_2$O$_7$ (DTO) and Ho$_2$Ti$_2$O$_7$ (HTO) across a broad field range up to 60 T, covering phase transformations, interactions with low-energy magnetic excitations, as well as single-ion effects. In particular, a sharp dip observed in the sound attenuation in DTO at the gas-liquid transition of the magnetic monopoles is explained based on an approach involving negative relaxation processes. Furthermore, quasi-periodic peaks in the acoustic properties of DTO due to non-equilibrium processes are found to be strongly affected by {\em macroscopic} thermal-coupling conditions: the thermal runaway observed in previous studies in DTO can be suppressed altogether by immersing the sample in liquid helium. Crystal-electric-field effects having higher energy scale lead to a renormalization of the sound velocity and sound attenuation at very high magnetic fields. We analyze our observations using an approach based on an analysis of exchange-striction couplings and single-ion effects.