Self-consistent full-potential linearized-augmented-plane-wave local-density electronic-structure studies of magnetism and superconductivity in C15 compounds: ${\mathrm{ZrZn}}_2$ and ${\mathrm{ZrV}}_2$

The electronic structure and properties of the cubic Laves phase (C15) compounds ${\mathrm{ZrZn}}_2$ and ${\mathrm{ZrV}}_2$ have been determined using our all-electron full-potential linearized-augmented-plane-wave (FLAPW) method for bulk solids. The computations were performed in two stages: (i) self-consistent warped muffin tin and (ii) self-consistent full potential. Spin-orbit coupling was included after either stage. The effects of the inclusion of the nonspherical terms inside the muffin tins on the eigenvalues is found to be small (of order 1 mRy). However, due to the fact that some of the bands near the Fermi level are flat, this effect leads to a much higher value of the density of states at $E_F$ in ${\mathrm{ZnZr}}_2$. The most important difference between the materials ${\mathrm{ZrZn}}_2$ and ${\mathrm{ZrV}}_2$ is the position of the d bands derived from the Zr and V atoms. Consequently, these materials have completely different Fermi surfaces. We have investigated the magnetic properties of these compounds by evaluating their generalized Stoner factors and found agreement with experiment. Our results for the superconducting transition temperature for these materials is found to be strongly dependent on the spin fluctuation parameter ${\mu }_{\mathrm{sp}}$. Of course, because of the magnetic transition, superconductivity cannot be observed in ${\mathrm{ZnZr}}_2$.