Spontaneous vortex phase and pinning in ferromagnetic-superconducting systems

Heterogeneous ferromagnetic-superconducting systems such as a regular array of ferromagnetic nano dots deposited on the top of a superconducting thin film have attracted many research teams both experimental and theoretical. The interest in these systems does not only stem from being good candidates for technological applications, but also because they represent a new class of physical systems where two competing order parameters can coexist. This work focuses on the theoretica laspects of these systems by studying the static and dynamics of few model systems. In the first part, the static properties of a superconducting thin film interacting with a ferromagnetic texture are considered within the London approximation. In particular, the ferromagnetic textures considered here are a circular dot of submicrometer size with in-plane magnetization, an elliptical dot magnetized in the direction perpendicular to the superconductor, and a ferromagnetic dot magnetized in the direction normal to the superconducting film and containing non magnetic cavities. I also consider the interaction of vortices in the superconductor with a ferromagnetic columnar defect which penetrates the supercondcting film. In each case the vector potential and magnetic field of the ferromagnet in the presence of the superconductor are calculated. Afterward the presence of vortices in the superconductor is assumed and the energy of vortex-texture system is found. The pinning potential and force supplied by the texture are then derived from the energy of interaction between the ferromagnet and superconductor. I show that if the magnetization of the ferromagnet exceeds a critical value then vortices are spontaneously created in the ground state of the system. Such spontaneous creation of vortices is possible mostly in a close vicinity of the superconducting transition temperature Ts. For every case, the threshold value of the magnetization at which vortices start to be spontaneously created in the SC is calculated as a function of the parameters of the texture geometry. The phase diagrams for transitions from vortexless regime to regimes with one or more vortices are determined for all cases. In the second problem, the transport properties of a ferromagnetic superconducting bilayer with alternating magnetization and vortex density are studied within a phenomenological model. I show that pinning forces do not appear for continuous distribution of vortices, so a discrete model for the bilayer system is constructed. Afterward, I calculate the pinning forces acting on vortices and antivortices resulting from highly inhomogeneous distribution of flux lines and prove that this system has strong transport anisotropy. In the absence of random pinning, the system displays a finite resistance for the current in the direction perpendicular to the domains while its resistance vanishes for the parallel current. The transport anisotropy strongly depends on temperature. I study this dependence and show that the ratio of parallel to perpendicular critical current is largest close to the superconducting transition temperature Ts and the vortex disappearance temperature Tv while it has a minimum in between them.