Magnetism and superconductivity in rare-earth ternary borides

The observation of magnetism and superconductivity in both the ternary rare-earth rhodium borides (MRh₄B₄) and the Chevrel phase ternaries M_xMo₆S₈ (with x close to 1) and most recently (i) the discovery of re-entrant magnetism accompanying a transition to a normal metallic state at T<T^s_c (the superconducting transition temperature) and (ii) the coexistence of magnetism and superconductivity have generated considerable excitement as to the origin of these phenomena. We discuss the origin of magnetism and superconductivity in the MRh₄B₄ compounds and re-entrant magnetism in ErRh ₄B₄ using the results of ab initio self-consistent LMTO energy band calculations. The total and separate l-decomposed contributions to the density of states (DOS) arising from the two M, eight Rh and eight B atoms per unit cell are used to estimate their various contributions to magnetic ordering (via the 4f-5d RKKY interaction) and/or superconductivity (using a Gaspari-Gyorffy model to obtain the electronic contributions to λ, the electron-phonon coupling parameter, and McMillan strong coupling theory to obtain T^s_c). Comparisons are made with recent experimental results and several experimental speculations about the re-entrant magnetism state are presented including the possibility of a mixed (ferromagnetic and superconducting) state.