Vortex Lattices in Stripe Domains of Ferromagnet/Superconductor Bilayer

TL;DR

This paper investigates the discrete vortex lattice configurations in stripe domains of ferromagnet/superconductor bilayers, especially when the domain size is comparable to the effective penetration depth, using a London-Maxwell based approach.

Contribution

It introduces a detailed analysis of vortex chain arrangements in stripe domains, extending beyond continuum models to account for discrete vortex effects.

Findings

Vortices in neighboring domains are shifted by half a period.

Multiple vortex chains can spontaneously form depending on system parameters.

Equilibrium vortex positions and domain sizes are calculated using London-Maxwell equations.

Abstract

The continuum theory of domain structures in ferromagnetic/superconducting bilayers fails when the equilibrium domain size becomes comparable with effective penetration depth $\Lambda$. Instead, a lattice of discrete vortices must be considered. Here, we report our results on the discrete vortex lattices in stripe domain structures of ferromagnetic/superconducting bilayers. The vortices are assumed to be situated periodically on chains in stripe domains. We study the configurations containing up to three chains per domain, and calculate their equilibrium energies, equilibrium domain size and vortex positions through a method based on London-Maxwell equations. In equilibrium, the vortices in the neighbor domains are half-way shifted while they are next to each other in the same domain. Additionally, more vortex chains per domain appear spontaneously depending on magnetization and domain wall energy.