Spontaneous vortices in ferromagnet-superconductor systems

We study the interaction between superconductors and ferromagnets in two systems: a ferromagnet-superconductor bilayer, and a thin superconducting film with a periodic array of magnetic dots upon it, with spontaneous vortices appearing in the systems. We show that the superconducting phase transition is of the first order in a ferromagnet-superconductor bilayer and of the second order in the superconducting film with a periodic array of magnetic dots upon it. The shift of the transition temperature, (delta)Tc, due to the presence of a ferromagnetic layer may be positive or negative in the ferromagnet-superconductor bilayer and is always negative in the superconducting film with a periodic array of magnetic dots upon it. The dependence of (delta)Tc on geometrical factors and the external magneticfield is found. The theory is extended to multilayer structures. Next, we study the anisotropy dependence of the critical current in a thin superconducting film with a periodic array of magnetic dots with magnetization perpendicular to the film with spontaneous vortices and antivortices. The phase diagrams for the appearance of spontaneous vortices and antivortices are given for the square arrays of circular and square F dots respectively when the direction of the magnetization is parallel to the superconducting film.