Interplay of Magnetism and Superconductivity in CeM(In$_{1-x}$Hg$_x$)$_5$*

The CeMIn$_5$ (M=Co, Rh, Ir) heavy fermion superconductors have attracted interest in recent years due to their high superconducting transition temperatures (e.g., $T_c$=2.3 K in CeCoIn$_5$), unconventional superconductivity, and magnetic- field induced exotic ground states. In particular, field- induced quantum criticality at the upper critical field H$_{c2} $=5 T in CeCoIn$_5$ and a possible field-induced magnetic state within the superconducting state suggests close proximity to antiferromagnetism.$^1$ The exciting discovery of slight changes in the electronic structure of CeMIn$_5$ with Cd or Hg substitution$^2$ at the percent level in CeCoIn$_5$ appears to have ``uncovered'' the hidden magnetism in this material. Therefore, substitution of Hg in CeMIn$_5$ offers yet another way to probe the proximity to magnetism in CeCoIn$_5$, the field-induced magnetic state under pressure in CeRhIn$_5$, and the coexistence of magnetism and superconductivity. The physical properties of CeM(In$_{1-x}$Hg$_x$)$_5$ system will be discussed and contrasted with those found with isoelectronic substitutions. $^1$ {J. Paglione {\textit{et al.}} Phys. Rev. Lett. {\textbf {91}} 246405 (2003); A. Binachi {\textit{et al.}} Phys. Rev. Lett. {\textbf{91}} 257001 (2003)} $^2$ {L.D. Pham {\textit{et al.}} Phys. Rev. Lett. {\textbf {97}} 056404 (2006)}