It has long been suspected that spin fluctuations in ${\mathrm{ZrZn}}_2$ may lead to a triplet superconductivity. We point out another possibility, an inhomogeneous singlet (Fulde-Ferrell) state. We calculated the electronic structure, as well as the zone center phonons and their coupling with electrons. We find that the exchange splitting is nonuniform and the Fermi surface exhibits substantial nesting. Both factors favor a Fulde-Ferrell state at parts of the Fermi surface. We find a substantial coupling of Zr rattling modes with electrons, which can provide the necessary pairing in the $s$-channel.

• Received 27 July 2001

DOI:https://doi.org/10.1103/PhysRevLett.88.187004