Fig. 3 |. High-field magnetic susceptibility and heat capacity data.

a, ${\chi }^{\prime }\left(H\right)$ data collected at 330 mK showing the phase boundary (dashed line) between the quantum disordered (QD) ground state and magnetically ordered $\mathbf{q}=(1/3,1/3,0)$ state near 3 T. A second transition back into the quantum disordered state or a quantum paramagnetic phase begins at higher fields. b, ${\chi }^{\prime }\left(T\right)$ data collected under a series of magnetic fields that traverse the ordered state; 4 T and 5 T ${\chi }^{\prime }\left(T\right)$ data illustrate the onset of the ordered phase below 1 K, while 6 T and 7 T data suggest partial re-entry into a disordered magnetic state. c, Specific heat of NaYbO₂ measured down to 80 mK under zero field and overplotted with the non-magnetic NaLuO₂ analogue. The resulting magnetic entropy $\mathrm{\Delta }{S}_M$ approaches 95% of $R\text{ln}\left(2\right)$. d, Values of $C_p\left(T\right)$ under varying magnetic fields. The lower peak centred around 1K develops a sharp anomaly at 5 T, indicative of the phase transition into the $\mathbf{q}=(1/3,1/3,0)$ state that is suppressed by 9 T. The inset shows the low-temperature portion of the $0\mathrm{T}{C}_p\left(T\right)$ data fit to a power law. The resulting fit to $T^{2.04}$ is shown as a solid yellow line through the data. Error bars denote one standard deviation of the data.