Magnetism and superconductivity inC15compounds from self-consistent band calculations

All-atom—all-electron self-consistent semirelativistic linear muffin-tin orbital energy-band studies are reported for Ti${\mathrm{Be}}_2$, Zr${\mathrm{Zn}}_2$ (at ambient and high pressures), the high-$T_c$ superconductor Zr${\mathrm{V}}_2$, and the ultralow-$T_c$ superconductor Y${\mathrm{Al}}_2$. Total and partial (by atom type and $l$ values) density of states, Stoner-like parameters, electron-phonon coupling parameter $\lambda$ and superconducting transition temperatures $T_c$ (determined within the rigid muffin-tin approximation and McMillan's strong coupling theory with and without paramagnon contributions), and their behavior under applied pressure are used to discuss the origin of their observed magnetism and/or superconductivity. From an analysis of the results, we suggest possible high-$T_c$ superconductivity at high pressure for Zr${\mathrm{Zn}}_2$, and its unlikely occurrence for Ti${\mathrm{Be}}_2$ unless dominant soft phonon modes exist.