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Metastable states of sub-micron scale ferromagnetic periodic antidot arrays

The magnetic textures on nanoscale possess topological features due to the continuity of the magnetization vector field and its boundary conditions. In thin planar nanoelements, where the dependence of the magnetization across the thickness is inessential, the textures can be represented as a soup of 2-d topological solitons, corresponding to magnetic vortices and antivortices, which are the solutions of Skyrme's model. Topology of the element (of the boundary conditions) then imposes the restrictions on properties and locations of these objects. Periodic arrays of magnetic antidots have topology with infinite connectivity. In this work we classify and build an approximate analytical representation of metastable magnetization textures in such arrays and prove the conservation of their topological charge.