The number of vortices representing the best compromise for a superconductor depends on both the temperature and the applied magnetic field. However, vortices are not always very mobile; their mobility depends on how the superconducting material was manufactured. When the vortices can easily move in and out of the superconductor, pinning is very weak. When the vortices are completely frozen in their position, though, pinning is very strong. Multiple factors determine the pinning force of vortices: the presence of impurities, flaws, the crystallographic quality of the material, the value of the critical current…
If you cool a type II superconducting sample with a magnet millimetres from its surface, the magnetic field of the magnet going through the sample will concentrate in the heart of the vortices created when superconductivity appears. If the superconductor strongly pins the vortices, then the vortices that appeared in front of the magnet will become a magnetic fingerprint of the magnet and will hold it in place. If you try to remove the magnet, you will feel a strong resistance, strong enough in some cases to be able to turn the superconductor upside down and see the magnet suspended beneath it.
If you pull hard enough to remove the magnet, the vortices will remain in place and the magnetic image of the magnet will be pinned in the superconductor. You can show that the magnetic image is pinned in the superconductor if you bring paperclips or a ferrofluid near the superconductor. These ferrous objects will be attracted by the magnetic field going through the vortices and will stick on the sample where the magnet had been. If you bring the magnet back, it will return to its original position exactly adapting to the magnetic fingerprint, as if it had a memory. The magnet will float in the air, a few millimetres from the superconductor, levitating in a stable way. It is even possible to make the magnet levitate under the superconductor using vortex pinning, as can be seen in the following video:
Pattern showing an experiment of strong pinning: a superconductor (in grey) is cooled while a magnet (in blue) is maintained millimetres from the surface by a non magnetic plastic wedge. When the green wedge is removed, the magnet remains in position and levitates. If the magnet is removed, the magnetic field in the volume of the superconductor, now in the form of vortices, remains pinned. If you return the magnet, it will levitate again in the same position.
