and wait times. Therefore to ensure the sample was heated above 900 mK, two AQP were used, separated by 300 seconds, which explains why the starting temperature for [Ho$_{2}$Ti$_{2}$O$_{7}$]{} was higher in Fig. 2 (see Supplementary Note 2 and Supplementary Fig. 3 for further discussions).

A schematic of the AQP used for the preparation of the samples is shown in Fig. 3d. First a field of $-0.3$ T was applied and the sample was allowed to cool to base temperature for 20 minutes. The field was then reversed at 2.2 T s$^{-1}$ to $+ 0.3$ T for 4 s then reduced to zero. After a wait period ranging from 10 to 50,000 s, a field of 0.08 T was applied and the relaxation of the magnetization was recorded. The field $B= 0.08$ T was chosen because it is large enough to get sizeable relaxation, but small compared to the avalanche fields shown in Fig. 4. In this way, when applying the magnetic fields, the relaxation is well behaved and the sample does not heat.

The AQP used for the data of Fig. 4 was similar to the above, except the avalanche field was $\pm 0.4$ T. After the wait period 