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

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