Symmetry Violation in a Superconducting Film with a Square Array of Ferromagnetic Dots

We study the equilibrium state of a superconducting film covered with a regular square array of perpendicularly magnetized magnetic dots. The dots induce vortices in the film directly under them and antivortices between the dots. We show that the symmetry of the dot array is spontaneously violated by the vortices. The positions of the vortices and the antivortices depend on the magnetization and the size of the dots.