Rotational transition, dislocations and domain formation in vortex systems with combined six- and 12-fold anisotropic interactions*

We introduce a model of vortices in type-II superconductors with a combined 6- and 12-fold anisotropy in the interaction potential, motivated by the vortex lattice (VL) phase diagram in MgB₂ and UPt₃. Using numerical simulations we show that the VL undergoes a continuous rotational transition as the ratio of the 6- and 12-fold anisotropy is changed, causing the VL to fracture into domains. We explore the structure of domain boundaries, and isolated dislocations present with single VL domains. Furthermore, we calculate the stress field associated with both dislocations and domain boundaries. The simulations provide a real space complement to results obtained from small-angle neutron scattering studies. We discuss how our simulations may be extended to model metastable VL phases observed experimentally, and the kinetics of the metastable-to-equilibrium transition. Finally we compare our numerical results to similar work on graphene lattices, skyrmions and colloids.