The interaction between a superconducting vortex and an out-of-plane magnetized ferromagnetic disk: influence of the magnet geometry

TL;DR

This paper theoretically explores how the shape and size of a ferromagnetic disk with out-of-plane magnetization influence the interaction energy and vortex positioning in a superconducting film, revealing potential qubit applications.

Contribution

It provides analytic models and vector plots of the SC-FM interaction for various geometries, highlighting the impact of magnet shape on vortex behavior and qubit potential.

Findings

Different magnet geometries create unique vortex energy landscapes.

Disks with cavities can host multiple vortex minima for qubit design.

Sharp-edged magnets like squares and triangles attract vortices to corners.

Abstract

The interaction between a superconducting vortex in a type II superconducting film (SC) and a ferromagnet (FM) with out-of-plane magnetization is investigated theoretically within the London approximation. The dependence of the interaction energy on the FM-vortex distance, film thickness and different geometries of the magnetic structures: disk, annulus(ring), square and triangle are calculated. Analytic expressions and vectorplots of the current induced in the SC due to the presence of the FM are presented. For a FM disk with a cavity, we show that different local minima for the vortex position are possible, enabling the system to be suitable to act as a qubit. For FMs with sharp edges, like e.g. for squares and triangles, the vortex prefers to enter its equilibrium position along the corners of the magnet.