Two-Peak Heat Capacity Accounts for $R\ln (2)$ Entropy and Ground State Access in the Dipole-Octupole Pyrochlore Ce${}_2$Hf${}_2$O${}_7$

Abstract

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 $T_1\sim 0.065$ 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 $T_2\sim 0.025$ 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 $R\ln (2)$ 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 cross-over 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 $T\sim 0.25$ 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 $\ddot{I}€$-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 $T_2$.

Main Text (6 pages, 4 figures), Supplemental Material (14 pages, 17 figures)