Upper critical fields of ferromagnet/superconductor layered structures

The temperature dependence of the upper critical fields, both perpendicular Hc2⊥ and parallel Hc2∥ to layer planes of ferromagnet/superconductor bi- and multilayers, is theoretically investigated. The secular equation of the superconducting order parameter for determining the phase diagram (H, T) is obtained by solving exactly the linearized Usadel equations in the multimode method taking into account the material parameter values. For the bilayers system, the influence of the boundary resistivity on the critical fields, and the dimensional crossover behavior of Hc2∥(T) are studied in details. For the multilayered structure, the effects of the π-phase state on both the superconducting transition temperature Tc and the upper critical fields (Hc2⊥, and Hc2∥) are also considered. The nonmonotonic Tc behaviors are predicted. The interplay between 0- and π-phases leading to the strong oscillations of Tc as well as the temperature dependence of the zero temperature critical fields on the ferromagnetic layer thickness are investigated theoretically.