Vortex-antivortex molecules in superconducting films with magnetic dot arrays

Following earlier works [Milosevic and Peeters, PRB (2003), PRL (2004)], we studied the vortex-antivortex stabilization in a superconducting film under a square array of magnetic dots of variable size. The theoretical side of the investigation was done within the Ginzburg-Landau theory, and main findings comprise: (i) multi-shell vortex-antivortex structures, (ii) the profound interaction between neighboring vortex-antivortex molecules through exchange of ``valence'' antivortices, and (iii) dual interaction of stabilized vortex-antivortex pairs and magnetic dots with excess flux-lines of the applied homogeneous magnetic field. On experimental side, the results are corroborated by scanning Hall probe measurements, performed on a 80nm thick Pb film, on top of a square array (period 5$\mu $m) of magnetic dots of four sizes - R=0.522, 0.738, 0.808, and 0.902$\mu $m, etched out of a [2nm Pt] [0.6nm Co/1.0nm Pt]$_{10}$ multilayer film with perpendicular magnetization. A 20nm thick Ge layer was evaporated on top of the dots to avoid the proximity effect. In measurements performed at T=5K, direct SHPM images showed the structure of antivortices between the magnetic dots, whereas the successive difference images revealed the positioning of additional vortices in applied homogeneous magnetic field.