Magnetic heat capacity measurements of a high-quality single crystal of the dipole-octupole pyrochlore ${\mathrm{Ce}}_2{\text{Hf}}_2{\mathrm{O}}_7$ down to a temperature of $T=0.02\mathrm{K}$ are reported. These show a two-peaked structure, with a Schottky-like peak at $T_1\sim 0.065\mathrm{K}$, similar to what is observed in its sister Ce pyrochlores ${\mathrm{Ce}}_2{\text{Zr}}_2{\mathrm{O}}_7$ and ${\mathrm{Ce}}_2{\text{Sn}}_2{\mathrm{O}}_7$. However, a second sharper peak is observed at $T_2\sim 0.025\mathrm{K}$, signifying the entrance to the ground state. The ground state appears to have gapped excitations, as even the most abrupt extrapolation to $C_P=0$ at $T=0\mathrm{K}$ fully accounts for the $R\ln (2)$ entropy associated with the pseudospin-$1/2$ doublet for ${\mathrm{Ce}}^{3+}$ in this environment. The ground state could be conventionally ordered, although theory predicts a much larger anomaly in $C_P$ at much higher temperatures than the measured $T_2$ for expectations from an all-in, all-out ground state of the XYZ Hamiltonian for ${\mathrm{Ce}}_2{\text{Hf}}_2{\mathrm{O}}_7$. The sharp low-temperature peak could also signify a crossover from a classical spin liquid to a quantum spin liquid (QSL). For both scenarios, comparison of the measured $C_P$ with NLC calculations suggests that weak interactions beyond the nearest-neighbor XYZ Hamiltonian become relevant below $T\sim 0.25\mathrm{K}$. The diffuse magnetic neutron scattering observed from ${\mathrm{Ce}}_2{\text{Hf}}_2{\mathrm{O}}_7$ at low temperatures between $T_2$ and $T_1$ resembles that observed from ${\mathrm{Ce}}_2{\text{Zr}}_2{\mathrm{O}}_7$, which is well established as a $\pi$-flux quantum spin ice (QSI). Together with the peak in the heat capacity at $T_2$, this diffuse scattering from ${\mathrm{Ce}}_2{\text{Hf}}_2{\mathrm{O}}_7$ is suggestive of a classical spin liquid regime above $T_2$ that is distinct from the zero-entropy quantum ground state below $T_2$.

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• Frustrated magnetism
• Quantum spin liquid
• Spin ice
• Pyrochlores
• Cluster expansion
• Neutron scattering
• Quantum Monte Carlo
• Specific heat measurements