Helicity of magnetic vortices and skyrmions in soft ferromagnetic nanodots and films biased by stray radial fields

Abstract

Static magnetization configurations of thin soft ferromagnetic films and nanodots, coupled to a hard antidot matrix with out-of-plane magnetization, are studied by micromagnetic simulations and analytical calculations. When the antidot matrix produces sufficient stray fields, having radial symmetry, these nanostructures support the formation of topologically nontrivial magnetic configurations---vortices and skyrmions in nanodots and films, respectively. It is demonstrated that the studied nanostructure reveals an additional degree of freedom---the helicity of the vortex or skyrmion---which can be tuned on demand by a variation of the material parameters and geometry. The variation of helicity $\ensuremath{\gamma}$ is not abrupt. In addition to Neel-like (radial) vortices and skyrmions $(\ensuremath{\gamma}=0,\ensuremath{\pi})$, it is possible to achieve unconventional configurations with an intermediate helicity $\ensuremath{\gamma}\ensuremath{\ne}0,\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2,\ensuremath{\pi}$, which transform to common Bloch-like configurations $(\ensuremath{\gamma}=\ifmmode\pm\else\textpm\fi{}\ensuremath{\pi}/2)$ in the limit of negligible stray fields from the matrix. We present an analytical model, which allows us to calculate the stability region of pure Neel-like states, outside which unconventional magnetization states with intermediate helicity are realized.