Skyrmions in 3D soft magnetic nanodots with no Dzyaloshinskii-Moriya interactions

Abstract

Skyrmions typically appear in systems with perpendicular magnetic anisotropy (PMA) and Dzyaloshinskii-Moriya interactions (DMI). Bloch skyrmion states can be stabilized in magnetic dots with no need of DMI [1]. However, PMA is typically considered to be necessary. Nanoparticle geometry is an additional important factor for the skyrmion stabilization due to the influence of magnetostatic energy. Therefore, the sample shape (e.g. spherical) can result in stabilization of the skyrmions [2]. Recently, stabilization of the half-hedgehog skyrmions in soft magnetic (Permalloy) hemispherical dots by the MFM tip was demonstrated [3].Here we conduct micromagnetic simulations in 3D soft magnetic dots with planar (cylindrical) or curved (spherical cap) geometry with neither PMA nor DMI. The geometries of both magnetic elements correspond to the base radius 60-120 nm and the aspect ratio thickness/ radius ranged from 0.4 to 2 and magnetic parameters of permalloy. In a wide range of the dot sizes, we observed the co-existence of multiple magnetic states. Particularly, in the spherical caps we stabilized for the same geometry, the in-plane, the out-of-plane (flower-like), the 3D vortex-like (Bloch skyrmion), the 3D Néel skyrmion –like (see Fig.1) and the Bloch point-like states. The Bloch skyrmion is characterized by a vortex configuration in the basal plane while the Neel-like skyrmon – by the radial vortex configuration and is similar to the half hedgehog structure.The existence of magnetic skyrmions without DMI or PMA in cylindrical nanodots was demonstrated by analytical calculations using the Belavin-Polyakov ansatz [4]. Both Néel and Bloch (vortex-like) skyrmions structures have been proven to be metastable or stable states in some range of dot sizes. The Néel skyrmion always has larger energy than the Bloch skyrmion. Direct micromagnetic simulations confirm the co-existence of both types of skyrmions, although in a smaller range of geometrical parameters than predicted by analytical calculations. In spherical caps, the curved geometry provides an additional factor for the Néel skyrmion stabilization which was obtained for a wide range of geometrical parameters. Typically, the Néel skyrmion has the largest energy of all structures, however its energy decreases as a function of the cap basal diameter and aspect ratio. Consequently, for some geometrical parameters we found a Néel skyrmion having smaller energy than that of the Bloch skyrmion. The spherical geometry also leads to a coupling between the skyrmion polarization and radial magnetization components, so that only the skyrmions with positive Polarity (P) and outward chirality (Q) or negative polarity and inward chirality are possible, see Fig. 1Finally, we present the state diagram for skyrmions in soft magnetic caps and nanopillars. We have also calculated 2D topological charges and the gyrovector values, both depending on the geometrical parameters. **