Competition between d-wave superconductivity and magnetism in uniaxially strained Sr2RuO4

The pairing symmetry of Sr_2RuO_4 is a long-standing fundamental question in the physics of superconducting materials with strong electronic correlations. We use the functional renormalization group to investigate the behavior of superconductivity under uniaxial strain in a two-dimensional realistic model of Sr_2RuO_4 obtained with density functional theory and incorporating the effect of spin-orbit coupling. We find a dominant d_x^2-y^2 superconductor mostly hosted by the d_xy-orbital, with no other closely competing superconducting state. Within this framework we reproduce the experimentally observed enhancement of the critical temperature under strain and propose a simple mechanism driven by the density of states to explain our findings. We also investigate the competition between superconductivity and spin-density wave ordering as a function of interaction strength. By comparing theory and experiment, we discuss constraints on a possible degenerate partner of the d_x^2-y^2 superconducting state.