Magnetic Properties of the Intermediate State in Small Type-I Superconductors

We present simulations of the intermediate state of type-I superconducting films solving the time dependent Ginzburg-Landau equations, which include the demagnetizing fields via the Biot-Savart law. For small square samples we find that, when slowly increasing the applied magnetic field $H_a$, there is a saw-tooth behavior of the magnetization and very geometric patterns, due to the influence of surface barriers; while when slowly decreasing $H_a$, there is a positive magnetization and symmetry-breaking structures. When random initial conditions are considered, we obtain droplet and laberynthine striped patterns, depending on $H_a$.