Pinning Forces in Superconductors from Periodic Ferromagnetic Dot Array

Using the London equation, we derive a formula by which the pinning force from magnetic dots can be calculated. We numerically calculate the interaction between ferromagnetic dots and vortices in type II superconductors under various conditions. It is found that the pinning force of the magnetic dot with 50 nm thickness reaches 3.5 × 10 N that is one order magnitude stronger than the intrinsic pinning force in cuprate at 77 K. We investigate various parameter dependences of the pinning force. It is found that the most effective way to increase the pinning force is to increase the thickness of the dot. The pinning force is weakly dependent on both the size and magnetic permeability of the dots. When temperature increases, the pinning force linearly decreases. And when the magnetic field increases, the attraction force increases linearly in the low field region.