Hidden Magnetism and Quantum Criticality in the Heavy Fermion Superconductor CeRhIn5

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With understood exceptions, conventional superconductivity does not coexist with long-range magnetic order[1]. In contrast, unconventional superconductivity develops near a boundary separating magnetically ordered and magnetically disordered phases[2,3]. A maximum in the superconducting transition temperature Tc develops where this boundary extrapolates to T=0 K, suggesting that fluctuations associated with this magnetic quantum-critical point are essential for unconventional superconductivity[4,5]. Invariably though, unconventional superconductivity hides the magnetic boundary when T < Tc, preventing proof of a magnetic quantum-critical point[5]. Here we report specific heat measurements of the pressure-tuned unconventional superconductor CeRhIn5 in which we find a line of quantum-phase transitions induced inside the superconducting state by an applied magnetic field. This quantum-critical line separates a phase of coexisting antiferromagnetism and superconductivity from a purely unconventional superconducting phase and terminates at a quantum tetracritical point where the magnetic field completely suppresses superconductivity. The T->0 K magnetic field-pressure phase diagram of CeRhIn5 is well described with a theoretical model[6,7] developed to explain field-induced magnetism in the high-Tc cuprates but in which a clear delineation of quantum-phase boundaries has not been possible. These experiments establish a common relationship among hidden magnetism, quantum criticality and unconventional superconductivity in cuprate and heavy-electron systems, such as CeRhIn5.