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Nonlinear Dynamics in a Magnetic Josephson Junction

We theoretically consider a Josephson junction formed by a ferromagnetic spacer with a strong spin-orbit interaction or a magnetic spin valve, i.e., a bilayer with one static and one free layer. Electron spin transport facilitates a nonlinear dynamical coupling between the magnetic moment and charge current, which consists of normal and superfluid components. By phenomenologically adding reactive and dissipative interactions (guided by structural and Onsager symmetries), we construct magnetic torques and charge pumping, whose microscopic origins are also discussed. A stability analysis of our coupled nonlinear systems generates a rich phase diagram with fixed points, limit cycles, and quasiperiodic states. Our findings reduce to the known phase diagrams for current-biased nonmagnetic Josephson junctions, on the one hand, and spin-torque driven magnetic films, on the other, in the absence of coupling between the magnetic and superconducting order parameters.