Boundary conditions for the N\'{e}el order parameter in a chiral antiferromagnetic slab

Understanding of the interaction of antiferromagnetic solitons including domain walls and skyrmions with boundaries of chiral antiferromagnetic slabs is important for the design of prospective antiferromagnetic spintronic devices. Here, we derive the transition from spin lattice to micromagnetic nonlinear $\sigma$-model with the corresponding boundary conditions for a chiral cubic G-type antiferromagnet and analyze the impact of the slab boundaries and antisymmetric exchange (Dzyaloshinskii--Moriya interaction) on the vector order parameter. We apply this model to evaluate modifications of antiferromagnetic domain walls and skyrmions upon interaction with boundaries for different strengths of the antisymmetric exchange. Due to the presence of the antisymmetric exchange, both types of antiferromagnetic solitons become broader when approaching the boundary and transform to a mixed Bloch--N\'{e}el structure. Both textures feel the boundary at the distance of about 5 magnetic lengths. In this respect, our model provides design rules for antiferromagnetic racetracks, which can support bulk-like properties of solitons.