  We formulate and study the general boundary conditions dictating the
magnetization profile in the vicinity of an interface between magnets with
dissimilar properties. Boundary twists in the vicinity of an edge due to
Dzyaloshinskii-Moriya interactions have been first discussed in [Wilson et al.,
Phys. Rev. B 88, 214420 (2013)] and in [Rohart and Thiaville, Phys. Rev. B 88,
184422 (2013)]. We show that in general case the boundary conditions lead to
the magnetization profile corresponding to the N\'eel, Bloch, or intermediate
twist. We explore how such twists can be utilized for creation of skyrmions and
antiskyrmions, e.g., in a view of magnetic memory applications. To this end, we
study various scenarios how skyrmions and antiskyrmions can be created from
interface magnetization twists due to local instabilities. We also show that a
judicious choice of Dzyaloshinskii-Moriya tensor (hence a carefully designed
material) can lead to local instabilities generating certain types of skyrmions
or antiskyrmions. The local instabilities are shown to appear in solutions of
the Bogoliubov-de-Gennes equations describing ellipticity of magnon modes bound
to interfaces. In one considered scenario, a skyrmion-antiskyrmion pair can be
created due to instabilities at an interface between materials with properly
engineered Dzyaloshinskii-Moriya interactions. We use micromagnetics
simulations to confirm our analytical predictions.
