  Magnetic skyrmions and antiskyrmions are topologically protected
quasiparticles exhibiting a whirling spin texture in real space. Antiskyrmions
offer some advantages over skyrmions as they are expected to have higher
stability and can be electrically driven with no transverse motion. However,
unlike the widely investigated skyrmions, antiskyrmions are rarely observed due
to the required anisotropic Dzyaloshinskii-Moriya interaction (DMI). Here we
propose to exploit the recently demonstrated van der Waals (vdW) assembly of
two-dimensional (2D) materials that breaks inversion symmetry and creates
conditions for anisotropic DMI. Using a 2D vdW magnet CrI${}_3$ as an example,
we demonstrate, based on density functional theory (DFT) calculations, that
this strategy is a promising platform to realize antiskyrmions. Polar layer
stacking of two centrosymmetric magnetic monolayers of CrI${}_3$ efficiently
lowers the symmetry, resulting in anisotropic DMI that supports antiskyrmions.
The DMI is reversible by switching the ferroelectric polarization inherited
from the polar layer stacking, offering the control of antiskyrmions by an
electric field. Furthermore, we find that the magnetocrystalline anisotropy and
DMI of CrI${}_3$ can be efficiently modulated by Mn doping, creating a
possibility to control the size of antiskyrmions. Using atomistic spin dynamics
simulations with the parameters obtained from our DFT calculations, we predict
the formation of antiskyrmions in a Cr${}_{0.88}$Mn${}_{0.12}$I${}_3$ bilayer
and switching their spin texture with polarization reversal. Our results open a
new direction to generate and control magnetic antiskyrmions in 2D vdW magnetic
systems.
