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 sawtooth 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 ${H}_{a}$.

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