Competing symmetries in superconducting vortex–antivortex “molecular crystals”

Hybrid structures composed of superconducting films deposited on ordered arrays of magnetic ‘dots’ have attracted enormous interest in recent years. Dots with sufficiently large magnetic moments may generate one or more spontaneous vortex–antivortex (V–AV) pairs in the superconducting film which can either remain associated with individual nanomagnets as V–AV “molecules” in dilute arrays or organise themselves into an ‘ionic’ crystal in dense arrays. Exactly how V–AV molecules transform into lattices and how they interact with (anti)fluxons induced by external magnetic fields remain challenging questions for both theory and experiment. We have used high resolution scanning Hall probe microscopy to image V–AV “molecules” induced in superconducting Pb films by the stray fields from square arrays of ferromagnetic Co/Pt dots. We have directly observed spontaneous V–AV pairs and studied how they interact with added “free” (anti)fluxons in an applied magnetic field. We observe a rich variety of subtle phenomena arising from competing symmetries in our system which can either drive added antivortices to join AV shells around nanomagnets or stabilise the translationally symmetric AV lattice between the dots. Added vortices annihilate AV shells, leading eventually to a stable ‘nulling state’ with no free fluxons, which should exhibit a strongly field-enhanced critical current. At higher densities we actually observe vortex shells around the magnets, stabilised by the asymmetric anti-pinning potential. Our experimental findings are in good agreement with Ginzburg–Landau calculations.