Figure 2: Zero-field (ZF) muon spin relaxation (μSR) experiments on RENiO₃ and V₂O₃.

(a) ZF time spectra taken at 2 K for four compounds of RENiO₃ near the quantum phase transition. The coloured dots represent the data, the solid curves the fits. The three magnetically ordered compounds show nearly identical oscillation frequencies (hence identical moment sizes) but very different oscillation amplitudes (hence different ordered volume fractions). (b) Temperature dependence of the oscillation frequencies for RENiO₃ compounds with first-order thermal phase transitions. Filled (open) circles represent data taken in a cooling (warming) sequence. All magnetically ordered compounds have two or three frequencies lying along two common bands (shaded grey regions), indicating that the ordered moment size does not change along the horizontal axis of the phase diagram. The large grey circle with the neighbouring vertical bar indicates the average estimated standard deviation (ESD) of the refined frequency produced from the least-squares minimization compared to the symbol size. The coloured dashed lines are guides to the eye showing the approximate transition temperature for each composition. (c) ZF spectra for YNiO₃ taken at various temperatures through the thermal phase transition. (d) Temperature dependence of the oscillation frequencies for RENiO₃ compounds with second-order-like thermal phase transitions, revealing the continuous development of the ordered moment size. (e,f) Plots for pressure-tuned V₂O₃ corresponding to (a,b).