Two-Peak Heat Capacity Accounts for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>R</mml:mi> <mml:mi>ln</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mn>2</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:math> Entropy and Ground State Access in the Dipole-Octupole Pyrochlore <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi>Ce</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> <mml:msub> <mml:mrow> <mml:mtext>Hf</mml:mtext> </mml:mrow> <mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="normal">O</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>7</mml:mn> </mml:mrow> </mml:msub> </mml:mrow> </mml:math>

Magnetic heat capacity measurements of a high-quality single crystal of the dipole-octupole pyrochlore Ce_{2}Hf_{2}O_{7} down to a temperature of T=0.02 K are reported. These show a two-peaked structure, with a Schottky-like peak at T_{1}∼0.065 K, similar to what is observed in its sister Ce pyrochlores Ce_{2}Zr_{2}O_{7} and Ce_{2}Sn_{2}O_{7}. However, a second sharper peak is observed at T_{2}∼0.025 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 K fully accounts for the Rln(2) entropy associated with the pseudospin-1/2 doublet for 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 Ce_{2}Hf_{2}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∼0.25 K. The diffuse magnetic neutron scattering observed from Ce_{2}Hf_{2}O_{7} at low temperatures between T_{2} and T_{1} resembles that observed from Ce_{2}Zr_{2}O_{7}, which is well established as a π-flux quantum spin ice (QSI). Together with the peak in the heat capacity at T_{2}, this diffuse scattering from Ce_{2}Hf_{2}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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