Competition and/or Coexistence of Antiferromagnetism and Superconductivity in CeRhIn${}_5$ and CeCoIn${}_5$

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 $p_{\mathrm{c}}^{\star }\approx 2$ GPa. Above $p_{\mathrm{c}}^{\star }$ 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 $H_{\mathrm{c}2}$. 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 superconductivity.