Attractive interaction between superconducting vortices in tilted magnetic fields

Practical applications of superconductors need layered very anisotropic or two-dimensional materials and magnetic fields applied on an arbitrary direction with respect to the layers. Then, Cooper pair currents can only circulate either fully within or perpendicular to the layers. In tilted magnetic fields this creates mutually perpendicular circular currents, leading to Josephson and pancake vortices, with quantized circulation across and within layers. Vortices form intertwined lattices that have been visualized mostly using non-invasive magnetic imaging techniques, but no direct manipulation has been achieved. Here we present magnetic force microscopy experiments in tilted magnetic fields in $Bi_{2}Sr_{2}CaCu_{2}O_{8}$. We trigger pancake vortex motion in between Josephson vortices, and find that the Josephson vortex lattice is highly manipulable, such that Josephson vortices in different layers can be crossed by the combined action of the tip's force and the rotating magnetic field. This unprecedented malleabilty originates in an attractive component of the interaction between Josephson vortices in tilted magnetic fields caused by an out of equilibrium arrangement of pancake vortices and might be characteristic of strongly anisotropic superconductors in tilted magnetic fields.