Evolution of interorbital superconductor to intraorbital spin-density wave in layered ruthenates

Abstract

The ruthenate family of layered perovskites has been a topic of intense interest, with much work dedicated to the superconducting state of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Another long-standing puzzle is the lack of superconductivity in its sister compound, ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$, which constrains the possible mechanisms of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$. Here we address a microscopic mechanism that unifies the orders in these materials. Beginning from a model of ${\mathrm{Sr}}_{2}{\mathrm{RuO}}_{4}$ featuring interorbital spin-triplet pairing via Hund's and spin-orbit couplings, we find that bilayer coupling alone enhances, while staggered rotations destroy interorbital superconductivity. A magnetic field then shifts van Hove singularities, allowing intraorbital spin-density wave order to form in ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$. Our theory predicts that ${\mathrm{Sr}}_{3}{\mathrm{Ru}}_{2}{\mathrm{O}}_{7}$ without staggered rotations exhibits interorbital superconductivity with a possibly higher transition temperature.