Bifurcations of the superconductor–ferromagnet–superconductor φ0 Josephson junction

Abstract

A general method is presented to study the bifurcations that occur in models of anomalous ${\phi }_0$ Josephson junctions. To demonstrate the method, a bifurcation analysis is made of the superconductor–ferromagnet–superconductor ${\phi }_0$ Josephson junction, in which the Josephson to magnetic energy ratio and the direct current bias are used as the two control parameters. The recently developed embedding technique facilitates the use of standard numerical continuation techniques for the analysis. It reveals that the stability limit can be disrupted through either a Neimark–Sacker or period-doubling bifurcation. The corresponding one-parameter bifurcation manifolds delineate the regions in which further destabilisation occurs, finally leading to chaos. Furthermore, it is shown that the Floquet multipliers along the Neimark–Sacker bifurcation curve signal the synchronisation on the torus. Bi-stability also occurs in the system and is shown to originate from the generalised period-doubling and Chenciner bifurcations. The identification of regions in the parameter space where bi-stability occurs is important for applications which exploit such bi-stability to achieve controlled reorientation of the magnetisation and/or the switching from one voltage state to another.