Cage-related crystal-field effects in the paramagnetic range of PrB$_6$

New insights into the paramagnetic range of PrB$_6$ below 50 K are revealed through specific-heat, thermal-expansion and magnetic measurements. The latent heats of the two successive magnetic transitions, together with an improved description of the lattice contribution, enable a detailed determination of the thermal variation of the magnetic entropy. Immediately above the first-order magnetic ordering temperature ($T_N = 6.7$ K), the magnetic entropy per Pr$^{3+}$ is close to that of a doublet, instead of the triplet crystal-field ground state identified by inelastic neutron scattering. Temperatures in excess of 30 K are required to reach the entropy of the threefold-degenerate ground state. This is reminiscent of the CeB$_6$ case and, similarly, strongly suggests a dynamical splitting of the crystal-field ground state within the boron cage. Further evidence of this splitting is provided by the analysis of the low-temperature paramagnetic susceptibility, which resembles that of a non-magnetic ground state. In addition, a large thermal-expansion anomaly is observed below 20 K, consistent with the expected centrifugal Jahn-Teller effect.