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Unconventional magnetization processes and thermal runaway in spin-ice Dy$_2$Ti$_2$O$_7$

We investigate the non-equilibrium behavior of the spin-ice material Dy$_2$Ti$_2$O$_7$ by studying its magnetization as a function of the rate at which an external field is swept. At temperatures below the enigmatic "freezing" temperature $T_{\rm equil}\approx600$ mK, we find that even the slowest sweeps fail to yield the equilibrium magnetization curve and instead give a smooth, initially much flatter curve. For higher sweep rates, the magnetization develops sharp steps accompanied by similarly sharp peaks in the temperature of the sample. We ascribe the former behavior to the energy barriers encountered in the magnetization process, which proceeds via flipping of spins on filaments traced out by the field-driven motion of the gapped, long-range interacting magnetic monopole excitations. In contrast, the peaks in temperature result from the released Zeeman energy not being carried away efficiently into the bath, with the resulting heating triggering a chain reaction.