for the the longest $t_{\rm w}$. This is again consistent with the conclusion that that the larger the nuclear spin moment, the more effective the spontaneous monopole recombination. The measurements were performed primarily at 200 mK, but the same conclusion follows from measurements at 80 mK. [Ho$_{2}$Ti$_{2}$O$_{7}$]{} also exhibits some unusual behaviour suggesting that the monopole density and magnetization do not approach equilibrium in a simple way. First, the magnetization jumps fall short of the $M$ vs $H$ equilibrium curve taken at 900 mK, even though thermometers placed on the sample indicate that the sample does indeed heat above 900 mK (see Supplementary Note 2 and Supplementary Fig. 3 for more details). Secondly, in contrast to the behaviour of [Dy$_{2}$Ti$_{2}$O$_{7}$]{} discussed above, the CC curve of [Ho$_{2}$Ti$_{2}$O$_{7}$]{} falls in the middle of the distribution of $H_{\rm ava}$($t_{\rm w}$) indicating, unusually, that waiting long enough at low temperature is an equally efficient way of approaching equilibrium as slow cooling.

Discussion {#discussion .unnumbered}
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The experimental result demonstrated here is that magnetic monopole dynamics in the frozen regime of spin ice are greatly enhanced by the hyperfine coupling of the electronic and nuclear moments. We now argue that this observation finds a 