excitations [@CMS]. This is made possible by the fact that the emergent excitations of the system – the monopoles – are objects localised in direct space that move through flipping spins. As well as illustrating this generic point, our result may also have practical consequences. We have established how coupling with nuclear spins controls the magnetic monopole current and the spectacular magnetothermal avalanches: hence any experimental handle on the nuclear spins of the system would also be a rare experimental handle on the monopole current. Any future application of magnetic monopoles in spin ice will surely rely on the existence of such experimental handles.

Methods {#methods .unnumbered}
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[*Samples.* ]{}Single crystals were grown by the floating zone method for all samples, the natural $^{\rm nat}$[Dy$_{2}$Ti$_{2}$O$_{7}$]{} and [Ho$_{2}$Ti$_{2}$O$_{7}$]{}  samples (DTO, HTO) were prepared at the Institute of Solid State Physics, University of Tokyo, Japan, and $^{162}$[Dy$_{2}$Ti$_{2}$O$_{7}$]{}, $^{163}$[Dy$_{2}$Ti$_{2}$O$_{7}$]{} at Warwick University and Oxford University respectively.

[*Measurements.* ]{} Measurements were made using a low temperature SQUID magnetometer developed at the Institut Néel in Grenoble. The magnetometer is equipped with a miniature dilution refrigerator with a base temperature of 65 mK. The fast dynamics after a field change were measured in a relative mode, 