# Biskyrmions Lattices in Centrosymmetric Magnetic Films

## TL;DR

This paper develops a theoretical framework explaining the formation and evolution of biskyrmion lattices in non-chiral magnetic films, matching experimental observations of their structure and stability.

## Contribution

It introduces a mathematical model using elliptic functions to describe biskyrmion lattices and studies their evolution under realistic magnetic interactions.

## Key findings

- Biskyrmion lattices are described by elliptic functions in a 2D exchange model.
- The evolution leads to a stable triangular lattice of biskyrmion bubbles with Bloch lines.
- The model aligns with experimental observations of non-chiral magnetic films.

## Abstract

Abstract Theoretical framework is developed that explains biskyrmion lattices observed in non-chiral magnetic films. We study films of finite thickness containing up to $1000\times1000\times100$ spins. Hexatic biskyrmion lattices in a pure 2D exchange model are naturally described by the Weierstrass $\wp$ 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.