Longitudinal Spin Fluctuations and Superconductivity in Ferromagnetic ${\mathrm{ZrZn}}_2$ from Ab Initio Calculations

The recent discovery of superconductivity coexisting with weak itinerant ferromagnetism in the $d$-electron intermetallic compound ${\mathrm{ZrZn}}_2$ strongly suggests spin-fluctuation mediated superconductivity. Ab initio electronic structure calculations of the Fermi surface and generalized susceptibilities are performed to investigate the viability of longitudinal spin-fluctuation-induced spin-triplet superconductivity in the ferromagnetic state. The critical temperature is estimated to be of the order of 1 K. Additionally, it is shown that in spite of a strong electron-phonon coupling ( ${\lambda }_{\mathrm{ph}}=0.7\mathrm{}$), conventional $s$-wave superconductivity is inhibited by the presence of strong spin fluctuations.