# Spin Vortices and Skyrmions of a Single Electron in Inhomogeneous Magnetic Fields

## TL;DR

This paper investigates how inhomogeneous magnetic fields influence the spin textures of a single electron in two dimensions, revealing the formation of vortices and skyrmions, including topologically trivial fields inducing topological configurations.

## Contribution

It demonstrates that quantum effects can induce topological spin textures in a single electron, even under trivial magnetic field conditions, through analytical, approximation, and numerical methods.

## Key findings

- In-plane spin components form vortices.
- Total spin field can become a skyrmion.
- Topologically trivial fields can induce topological spin textures.

## Abstract

We study the spin textures of a confined two-dimensional electron in inhomogeneous magnetic fields. These fields can either be external or effective fields due to a background magnetic texture in the plane in which the electron resides. By analytical considerations, WKB-type approximations, and by performing numerical diagonalizations we show that the in-plane spin field components of a single electron can form vortices while the total spin field can become a skyrmion. Most interestingly, we find that topological trivial magnetic fields can induce topological spin field configurations in the eigenstates of the electron due to quantum effects.