Ground state configurations of vortices in superconducting film with magnetic dot

TL;DR

This paper analyzes the configurations of vortices in a superconducting film with a magnetic dot, revealing how vortex states depend on magnetization and dot size through analytical and numerical methods.

Contribution

It provides a detailed analytical and numerical study of vortex and antivortex configurations in superconducting films with magnetic dots, including phase diagrams and field calculations.

Findings

Single vortex appears at high magnetization

Antivortices emerge with increased magnetization

Total vorticity is mostly zero or one for small dots

Abstract

We consider a thin superconducting film with a magnetic dot with permanent magnetization (normal to the film) placed on it by a method based on London-Maxwell equations. For sufficiently high dot magnetization a single vortex appears in the ground state. Further increase of magnetization is accompanied with the appearance of antivortices and more vortices in the film. We study analytically conditions for the appearance of a vortex--antivortex pair for a range of parameters. The phase diagram with diversity of vortex--antivortex states is calculated numerically. When appear in the ground state, antivortices are at distances comparable to the dot radius. For not too large dot radii the total vorticity in the ground state is predominantly zero or one. Magnetic field due to the dot and vortices everywhere in space is calculated analytically.