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Motivated by the recent experiment on the size and helicity control ofskyrmions in Mn$_{1-x}$Fe$_x$Ge [K. Shibata et al., Nature Nanotechnology 8,732 (2013)], we study how the Dzyaloshinskii-Moriya (DM) interaction changesits size and sign in metallic helimagnets. By means of first-principlescalculations, we successfully reproduce the non-trivial sign change of the DMinteraction observed in the experiment. While the DM interaction sensitivelydepends on the carrier density or the detail of the electronic structure suchas the size of the exchange splitting, its behavior can be systematicallyunderstood in terms of the distribution of anticrossing points in the bandstructure. By following this guiding principle, we can even induce giganticanisotropy in the DM interaction by applying a strain to the system. Theseresults pave the new way for skyrmion crystal engineering in metallichelimagnets.

Control of Dzyaloshinskii-Moriya interaction in Mn$_{1-x}$Fe$_x$Ge: a first-principles study