Extended Data Fig. 9: Summary of heat capacity measurements.

a Top view of the sample holder for specific heat measurements, showing the silver sample stage suspended by NbTi wires from the silver frame that was directly screwed to the mixing chamber of the cryostat, as well as the gold wire serving as thermal link to the bath. b Bottom view of the sample holder showing the thermometer (left) and heater (right) chips that are glued to the sample stage with GE varnish. c Single-crystalline sample of Ce₂Zr₂O₇ used for specific heat measurements. d Comparison of the specific heat data of Ce₂Zr₂O₇ obtained in this work with published results^39,42,67. The grey line is a guide to the eyes. e Same data as in a, except for the data measured on powder down to only 0.4 K⁶⁷, rescaled to the average of the data points of Smith et al.⁴² and Gao et al.³⁹ at 100 mK, which is deemed to be the most precise estimate of the absolute magnitude of the specific heat of Ce₂Zr₂O₇ at this temperature. The grey line is a cubic-in-temperature fit to data below 50 mK. f Magnetic specific heat data on Ce₂Zr₂O₇ as a function of temperature on double-logarithmic scales, compared to power-law fits, \(A{T}^{\alpha }\), with fixed powers \(\alpha\) of 3 (grey), and 2.5 (red) and 3.5 (blue) for comparison, illustrating that \(\alpha =3\) describes the data best. A minimization procedure with open α yields the \({\chi }_{v}^{2}(\alpha)\) dependence shown in the inset, confirming that, within the error bars, α = 3 is the best description of the data. g Arrhenius plot of the magnetic specific heat together with a linear fit to the data (grey line), showing that the low-temperature specific heat of Ce₂Zr₂O₇ could also be accounted for by a thermally activated behavior, with a gap of 0.1 K (inset). Both fits yield similar minimal \({\chi }_{v}^{2}\), preventing discrimination between the two on purely statistical grounds. h Magnetic entropy release as function of temperature obtained by integrating our C_mag/T data (full black symbols) together with previously published C_mag/T data³⁹ (open symbols), both scaled as done in e. Within the error of the measurements, the full entropy of \(\bar{R}\mathrm{ln}2\) is reached at 10 K (grey shaded area). The vertical error bars in d-g are estimated to be at a maximum 10 % at 100 mK and up to 20 % at the lowest temperatures. Horizontal error bars represent maximal errors in the temperatures of the sample, which amount to 10 % on average (depending on whether a larger or smaller heater power was used).