Measurements of the specific heat of antiferromagnetic CeRhIn5, to 21 kbar, and for 21 kbar to 70 kOe, show a discontinuous change from an antiferromagnetic ground state below 15 kbar to a superconducting ground state above, and suggest that it is accompanied by a weak thermodynamic first-order transition. Bulk superconductivity appears, apparently with d-wave electron pairing, at the critical pressure, 15 kbar; with further increase in pressure a residual temperature-proportional term in the specific heat disappears.
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