Chiral magnetic skyrmions with arbitrary topological charge

Abstract

We show that continuous and spin-lattice models of chiral ferro- and antiferromagnets provide the existence of an infinite number of stable soliton solutions of any integer topological charge. A detailed description of the morphology of new skyrmions and the corresponding energy dependencies are provided. The considered model is general, and is expected to predict a plethora of particlelike states which may occur in various chiral magnets including ultrathin films, e.g., PdFe/Ir(111), rhombohedral ${\mathrm{GaV}}_{4}{\mathrm{S}}_{8}$ semiconductor, B20-type alloys as ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Ge}$, ${\mathrm{Mn}}_{1\ensuremath{-}x}{\mathrm{Fe}}_{x}\mathrm{Si}$, ${\mathrm{Fe}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x}\mathrm{Si}$, ${\mathrm{Cu}}_{2}{\mathrm{OSeO}}_{3}$, and acentric tetragonal Heusler compounds.