Towards control of the size and helicity of skyrmions in helimagnetic alloys by spin-orbit coupling

Chirality - that is, left- or right-handedness - is an important concept in a broad range of scientific areas. In condensed matter, chirality is found not only in molecular or crystal forms, but also in magnetic structures. A magnetic skyrmion1-8 is a topologically stable spin vortex structure, as observed in chiral-lattice helimagnets, and is one example of such a structure. The spin swirling direction (skyrmion helicity) should be closely related to the underlying lattice chirality via the relativistic spin-orbit coupling. Here, we report on the correlation between skyrmion helicity and crystal chirality in alloys of helimagnets Mn_1-x Fe_x Ge with varying compositions by Lorentz transmission electron microscopy and convergent-beam electron diffraction over a broad range of compositions (x = 0.3-1.0). The skyrmion lattice constant shows non-monotonous variation with composition x, with a divergent behaviour around x = 0.8, where the correlation between magnetic helicity and crystal chirality changes sign. This originates from continuous variation of the spin-orbit coupling strength and its sign reversal in the metallic alloys as a function of x. Controllable spin-orbit coupling may offer a promising way to tune skyrmion size and helicity.