Biskyrmions Lattices in Centrosymmetric Magnetic Films

Abstract Theoretical framework is developed that explains biskyrmion lattices observed in non-chiral magnetic films. We study films of finite thickness containing up to $1000\times 1000\times 100$ spins. Hexatic biskyrmion lattices in a pure 2D exchange model are naturally described by the Weierstrass $\mathrm{\wp }$ and $\zeta$ elliptic functions. Starting with such a lattice as an initial state we investigate how it evolves towards the minimum-energy state in the presence of perpendicular magnetic anisotropy and dipole-dipole interaction. In accordance with experiments, we find that the final state is a triangular lattice of biskyrmion bubbles containing Bloch lines.