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The Ce compounds CeCoIn 5  and CeRhIn 5  are ideal model systems to study the competition of antiferromagnetism (AF) and superconductivity (SC). Here we discuss the pressure–temperature and magnetic field phase diagrams of both compounds. In CeRhIn 5  the interesting observation is that in zero magnetic field a coexistence AF + SC phase exist inside the AF phase below the critical pressure  $p_{\rm c}^{\rm *} \approx 2$  GPa. Above  $p_{\rm c}^{\rm *} $  AF is suppressed in zero field but can be re‐induced by applying a magnetic field. The collapse of AF under pressure coincides with the abrupt change of the Fermi surface. In CeCoIn 5  a new phase appears at low temperatures and high magnetic field (LTHF) which vanishes at the upper critical field  H  c2 . In both compounds the paramagnetic pair breaking effect dominates at low temperature. We discuss the evolution of the upper critical field under high pressure of both compounds and propose a simple picture of the glue of reentrant magnetism to the upper critical field in order to explain the interplay of antiferromagnetic order and SC.

Competition and/or coexistence of antiferromagnetism and superconductivity in CeRhIn 5 and CeCoIn 5