# Magnetic Vortex induced by Nonmagnetic Impurity in Ferromagnets: Magnetic Multipole and Toroidal around the Vacancy

## TL;DR

This paper theoretically investigates how nonmagnetic impurities induce magnetic vortices in ferromagnets through asymmetric Dzyaloshinskii-Moriya interactions, revealing their magnetic multipole and toroidal characteristics.

## Contribution

It introduces a novel mechanism for vortex nucleation around impurities via asymmetric interactions, supported by spin-wave analysis and Monte Carlo simulations.

## Key findings

- Magnetic vortices with vorticity l=+1 are stabilized without external fields.
- Vortices exhibit magnetic multipole moments based on vorticity and helicity.
- Potential realization in monolayer ferromagnets on nonmagnetic substrates.

## Abstract

We report our theoretical study on nucleation of a magnetic vortex around a nonmagnetic impurity doped into ferromagnets. The mechanism lies in the asymmetric Dzyaloshinskii-Moriya interaction arising from the breaking of spatial inversion symmetry by the impurity. By using the spin-wave analysis and Monte Carlo simulations, we show that the asymmetric interaction induces a magnetic vortex with nonzero vorticity $l=+1$. The vortex is stabilized even for less frustration in exchange interactions and in the absence of an external magnetic field. We also find that the magnetic vortex is characterized by magnetic multipoles according to its vorticity and helicity. We demonstrate a potential realization of such a magnetic vortex by considering a monolayer ferromagnet on a nonmagnetic substrate, which results in the magnetic monopole and toroidal dipole.