Structure of the magnetic order induced by Ti-doping in Sr₂RuO₄

Replacing less than one percent of Ru atoms by non-magnetic Ti⁴⁺ is sufficient to induce incommensurate spin density wave order in Sr₂RuO₄. The ordering wave vector Q ∼ (2π/3, 2π/3) coincides with the nesting vector of two out of three Fermi surface sheets. We consider a microscopic model for these two bands and explore the formation of magnetic order through doping with non-magnetic impurities. For this purpose we develop a spatially resolved mean field theory for the microscopic model including spin-orbit coupling and a phenomenological Ginzburg-Landau formulation. The different approaches, which are connected by an effective field theory derived from the microscopic model, deliver consistent results and allow us to examine the inhomogeneous magnetic order. Extending the field theory into a gauge field theory in both charge and spin channels reveals several more features of the system due to spin-orbit coupling, such as impurity induced spin currents and the connection between charge currents and spin polarization. Our findings allow a more detailed analysis of the experimental data for Sr₂Ru_1-xTi_xO₄. In particular, we find that the available measurements are consistent with our theoretical predictions.