Structural Transitions in Vortex Systems with Anisotropic Interactions*

We introduce a model of vortices in type-II superconductors with an anisotropic vortex-vortex interaction potential. Using numerical simulations we show that the vortex lattice (VL) undergoes structural transitions as the anisotropy is increased. For a four-fold anisotropy we reproduce the well-known VL evolution from a triangular lattice at low anisotropy, to a rhombic intermediate state, and finally a square lattice for high anisotropy. In some cases a multi-q state is observed, consisting of an Archimedean tiling that combines square and triangular local ordering.
Simulations with a combined 6- and 12-fold anisotropy leads to a continuous rotation of triangular domains, consistent with the VL phase diagram observed in MgB₂. This allow us to explore the effect of VL domain boundaries, expected to be responsible for the metastable VL phases observed in this material. The simulations provide a real space complement to the reciprocal space results obtained from small-angle neutron scattering studies.