Chiral Magnetic Skyrmions with Arbitrary Topological Charge (skyrmionic sacks)

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 particle-like states which may occur in various chiral magnets including atomic layers, e.g., PdFe/Ir(111), rhombohedral GaV$_4$S$_8$ semiconductor, B20-type alloys as Mn$_{1-x}$Fe$_x$Ge, Mn$_{1-x}$Fe$_x$Si, Fe$_{1-x}$Co$_x$Si, Cu$_2$OSeO$_3$, acentric tetragonal Heusler compounds.