الفهرس 
General interest .Only 14 pages are availabe for public view
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Abstract
A Josephson junction (JJ) is made up of two superconductors sandwiching a thin, non- superconducting layer that allows electrons to tunnel through. The coherence of the wave function in a superconductor generates DC or AC currents. The DC Joseph- son current is proportional to the phase di erence between the two superconductors. The voltage applied across the junction determines the frequency of the AC Josephson current.
When the non-superconducting layer is a ferromagnet, the structure is called a superconductor−ferromagnet−superconductor (SFS) junction. A peculiar phase shift has been observed in the current−phase relation of superconductor−ferromagnet−super conductor junction. This unique class of junctions is called SFS ”ϕ0 Josephson junc- tion”. The manifestation of anomalous phase shift, which leads to a nite supercon- ducting current at zero phase di erence, is a crucial aspect of modern condensed matter physics.
The complete set of Landau−Lifshitz−Gilbert−Josephson (LLGJ) equations, which shows nonlinear behavior, describes the magnetization and phase dynamics of the SFS ϕ0 Josephson junction. The current−voltage characteristics (IVCs) and the magneti- zation dynamics of the ϕ0 Josephson junction both exhibit nonlinear behavior within the ferromagnetic resonance (FMR) region. Moreover, the dynamics of magnetization may be reduced to that of a scalar Du ng oscillator driven by Josephson oscillations at low system parameters, such as the Josephson to magnetic energy ratio, damping, and spin−orbit coupling (SOC). The spin−orbit coupling has a major role in the formation of such a nonlinear feature within the FMR region. This nonlinear behavior is respon- sible for the ferromagnetic resonant frequency shift and the reversal in its damping dependency. It also explains the increase in superconducting current within the reso- nance region. Furthermore, the relationship between the foldover e ect and negative
di erential resistance (NDR) in the IVCs has been demonstrated.