Conventional magnetic superconductors

•(Pseudo)binary superconducting materials exhibit short-range magnetic order.•Exchange interaction suppresses TcTc in (pseudo)binary materials containing RE ions.•We discuss ternary RERh4B4 and REMo6(S, Se)8 and quaternary RENi2B2C compounds.•Long-range magnetic order exists in some RE (qua)ternary superconductors.•Reentrant superconductivity, MFIS, and exotic magnetic states are observed.

We discuss several classes of conventional magnetic superconductors including the ternary rhodium borides and molybdenum chalcogenides (or Chevrel phases), and the quaternary nickel-borocarbides. These materials exhibit some exotic phenomena related to the interplay between superconductivity and long-range magnetic order including: the coexistence of superconductivity and antiferromagnetic order; reentrant and double reentrant superconductivity, magnetic field induced superconductivity, and the formation of a sinusoidally-modulated magnetic state that coexists with superconductivity. We introduce the article with a discussion of the binary and pseudobinary superconducting materials containing magnetic impurities which at best exhibit short-range “glassy” magnetic order. Early experiments on these materials led to the idea of a magnetic exchange interaction between the localized spins of magnetic impurity ions and the spins of the conduction electrons which plays an important role in understanding conventional magnetic superconductors. These advances provide a natural foundation for investigating unconventional superconductivity in heavy-fermion compounds, cuprates, and other classes of materials in which superconductivity coexists with, or is in proximity to, a magnetically-ordered phase.