  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.
