  Motivated by the recent experiment on the size and helicity control of
skyrmions in Mn$_{1-x}$Fe$_x$Ge [K. Shibata et al., Nature Nanotechnology 8,
732 (2013)], we study how the Dzyaloshinskii-Moriya (DM) interaction changes
its size and sign in metallic helimagnets. By means of first-principles
calculations, we successfully reproduce the non-trivial sign change of the DM
interaction observed in the experiment. While the DM interaction sensitively
depends on the carrier density or the detail of the electronic structure such
as the size of the exchange splitting, its behavior can be systematically
understood in terms of the distribution of anticrossing points in the band
structure. By following this guiding principle, we can even induce gigantic
anisotropy in the DM interaction by applying a strain to the system. These
results pave the new way for skyrmion crystal engineering in metallic
helimagnets.
