  Topological magnetic textures, characterized by integer topological charge
$S$, are potential candidates in future magnetic logic and memory devices, due
to their smaller size and expected low threshold current density for their
motion. An essential requirement to stabilize them is the Dzyaloshinskii-Moriya
interaction (DMI) which promotes a particular chirality, leading to a unique
value of $S$ in a given material. However, recently coexistence of skyrmions
and antiskyrmions, with opposite topological charge, in frustrated ferromagnets
has been predicted using $J_1$--$J_2$--$J_3$ classical Heisenberg model, which
opens new perspectives, to use the topological charge as an additional degree
of freedom. In this work, we propose another approach of using a synthetic
antiferromagnetic (SAF) system, where one of the ferromagnetic (FM) layer has
isotropic and the other FM layer has anisotropic DMI to promote the existence
of skyrmions and antiskyrmions, respectively. A frustrated interaction arises
due to the coupling between the magnetic textures in the FM layers, which
enables the stabilization and coexistence of 6 novel elliptical topological
textures.
