probed by neutrons in the time domain and magnetometry in the frequency domain*

We describe an experimental investigation of classical spin ice dynamics in a new class of high quality Ho₂Ti₂O₇ single crystals. Employing a pump-probe method with microsecond time resolution, we have tracked neutrons diffracted from the (002) pinch point in response to an Oe range step changes in field applied along <110>. The relaxation time rises acutely from 10ms to over 10 ks upon cooling from 1.3K to 0.6K. Similar characteristic timescales were obtained from SQUID-based AC susceptibility measurements down to 1mHz on similar crystals. There are major quantitative differences between the present result and previously published works that we ascribe to our ultra-pure crystals. In addition, our simultaneous study of the Fourier-transform-related responses in time and frequency allows detailed mathematical scrutiny of the non-Debye relaxation process in spin ice.