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We consider localized topologically nontrivial magnetic textures (skyrmions, antiskyrmions, and bimerons) in a thin magnetic film with anisotropic interfacial Dzyaloshinskii-Moriya interaction (iDMI). We use micromagnetic simulations and analytical consideration for studying the internal magnetic structure and stability of these textures. Skyrmion and antiskyrmion become elliptic and orient along the main axes of the iDMI tensor even for small anisotropy. In contrast, bimeron (antibimeron) orientation changes fluently with varying the iDMI anisotropy. Depending on the iDMI anisotropy the bimeron may consist of a vortex and antivortex pair or of ``hedgehog'' state and antivortex. In experiment the considered iDMI anisotropy can be induced by a strain applied to a magnetic film. We develop a phenomenological approach to establish the strain-iDMI relation.
Udalov et al. (Thu,) studied this question.