Specific heat ofCeRhIn5: Pressure-driven evolution of the ground state from antiferromagnetism to superconductivity

Resistivity measurements on ${\mathrm{CeRhIn}}_5$ have suggested an unusual “first-order-like” transition from antiferromagnetism to superconductivity at a critical pressure $P_c,$ ∼15 kbar: At pressures below $P_c$ the magnetic ordering temperature is approximately independent of pressure. At $P_c$ antiferromagnetism disappears abruptly and is replaced by superconductivity, with a critical temperature that is also approximately independent of pressure. Here we report measurements of the low-temperature specific heat of ${\mathrm{CeRhIn}}_5$ at pressures to 21 kbar, and for 21 kbar in magnetic fields to 70 kOe. They confirm, by measurement of a bulk thermodynamic property, the unusual relation between magnetism and superconductivity, and permit an estimate of the discontinuity in entropy at $P_c.$ They also give insight into the natures of the antiferromagnetic and superconducting states and their changes with pressure: With increasing pressure the zero-field specific-heat anomaly changes from one typical of antiferromagnetic ordering at ambient pressure to one more characteristic of the formation of a Kondo singlet ground state at 21 kbar. The change in general shape of the anomaly is gradual, but at $P_c,$ where the data suggest a weak thermodynamic first-order transition, there is a discontinuous change from an antiferromagnetic ground state to a superconducting ground state. Below $P_c$ the quasiparticle density of states increases and the spin-wave stiffness decreases with increasing pressure. At $P_c$ the low-energy magnetic excitations disappear and are replaced by excitations that are characteristic of superconductivity with line nodes in the energy gap. The quasiparticle density of states is continuous at $P_c,$ but decreases with increasing pressure, to zero at 21 kbar. These features suggest the possibility of superconductivity with d-wave pairing and, at intermediate pressures, “extended gaplessness.” At 21 kbar except for the line nodes, the Fermi surface is fully gapped. The specific-heat data also show the existence of a second-order transition in the 11–12-kbar region, where features in the magnetic susceptibility and resistivity have been observed.