Ferromagnetic thickness dependence of superconducting transition temperature in a superconductor/ferromagnet bilayer system with an inhomogeneous exchange field

• Study on the Tc of SF-bilayer with exchange fields having three components by the Usadel equations.
• The function W0 and corresponding eigenvalues and eigenvectors are shown in analytic forms.
• The monotonic, non-monotonic and reentrant behavior of Tc are found.

The superconducting transition temperature of superconductor/ferromagnet bilayer with an inhomogeneous exchange field within the framework of the Usadel equations is studied. With the geometry of superconductor/ferromagnet junction on z-axis, the exchange field rotates with constant angle ϕ respect to the z-axis and with the angle θ, θ = Qy, varying in xy-plane along the direction y that Q is a spiral wave vector. The boundary condition parameter (W0) and corresponding eigenvalues and eigenvectors are shown in analytic forms for two small angle case as measured from the xy-plane and measured from z-axis. The behavior of superconducting transition temperature versus thickness of ferromagnetic layer with varying Qξs, the transparency parameters (γb) an the proximity effect parameter (γ) are considered in our calculations. We can find monotonic, non-monotonic, and reentrant behavior of superconducting transition temperature in our calculation depending on parameters. The non-monotonic behavior is found with low γb, Qξs and the reentrant behavior is found with large γ.