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High fraction of the surface atoms considerably enhances the influence of size and shape on the magnetic and electronic properties of nanoparticles. Shape effects in ferromagnetic nanoparticles are well understood and allow to set and control the parameters of a sample that affect its magnetic anisotropy during production. In the present paper we study the shape effects in the other widely used magnetic materials -- antiferromagnets, -- which possess vanishingly small or zero macroscopic magnetization. We take into account the difference between the surface and bulk magnetic anisotropy of a nanoparticle and show that the effective magnetic anisotropy depends on the particle shape and crystallographic orientation of its faces. Corresponding shape-induced contribution to the magnetic anisotropy energy is proportional to the particle volume, depends on magnetostriction, and can cause formation of equilibrium domain structure. Crystallographic orientation of the nanoparticle surface determines the type of domain structure. The proposed model allows to predict the magnetic properties of antiferromagnetic nanoparticles depending on their shape and treatment., Comment: 15 pages, 6 figures, to be submitted to Journal of Physics Condensed Matter

The Dzyaloshinskii-Moriya interaction (DMI) is at the heart of many modern developments in the research field of spintronics. DMI is known to generate noncollinear magnetic textures, and can take two forms in antiferromagnets: homogeneous or inter-sublattice, leading to small, canted moments and inhomogeneous or intra-sublattice, leading to formation of chiral structures. In this work, we first determine the strength of the effective field created by the DMI, using SQUID based magnetometry and transport measurements, in thin films of the antiferromagnetic iron oxide hematite, $\alpha$-Fe$_2$O$_3$. We demonstrate that DMI additionally introduces reconfigurability in the long distance magnon transport in these films under different orientations of a magnetic field. This arises as a hysteresis centred around the easy-axis direction for an external field rotated in opposing directions whose width decreases with increasing magnetic field as the Zeeman energy competes with the effective field created by the DMI.