Biskyrmion lattices in centrosymmetric magnetic films

A theoretical framework is developed that permits construction of biskyrmion lattices observed in nonchiral magnetic films. Skyrmion and antiskyrmion configurations are discussed. We study films of finite thickness containing up to 1000 × 1000 × 100 spins. Hexatic biskyrmion lattices in a pure two-dimensional (2D) exchange model are naturally described by the Weierstrass and ζ elliptic functions. Starting with such a lattice as an initial state, we investigate how it evolves toward a minimum-energy state in a zero magnetic field in the presence of perpendicular magnetic anisotropy (PMA) and dipole-dipole interaction. Metastable biskyrmion lattices exist at low PMA. At higher PMA, we observe stable triangular lattices of biskyrmion bubbles containing Bloch lines, whose energies are lower than the energy of the uniformly magnetized state.