Influence of Boundaries and Geometrical Curvatures on Antiferromagnetic Textures

A complex structure of magnetic subsystem in antiferromagnets (AFMs) determines challenges and technological perspectives for both, fundamental
research and their applications for spintronic and spin-orbitronic devices [1]. In this respect, properties of the confined samples are of key interest because
of the possibility to tune magnetic responses via effects of boundary and geometrical curvature [2]. Here, we consider textures in (i) AFM slabs with the
Dzyaloshniskii-Morya interaction (DMI) of bulk symmetry [3] and (ii) the intrinsically achiral curvilinear spin chains arranged along space curves [4].
We derive a transition from spin lattice of G-type AFM to the sigma-model with the respective boundary conditions for the AFM order parameter [3]. The
DMI influences a texture via boundary conditions modifying the ground state, domain wall shape and skyrmion profiles. Approaching the boundary in the
slab with easy-axis anisotropy, the domain wall becomes broader and of mixed Bloch-Neel type near the top surface. Near the edges of the sample, the
domain wall plane possesses and additional twist. Note, that the edge twists appear in achiral AFMs as well if the domain wall plane lies at an angle to the
side faces [5]. Similarly, skyrmions of any radius become of the Bloch-Neel type approaching the top/bottom surfaces of the sample. The radius of narrow
skyrmions changes up to 10% due to the boundary effects.
AFM spin chains arranged along space curves can model the simplest curvilinear nanoarchitectures. Their geometry is described by the curvature and
torsion, determining local bends and twists of the curve. The geometry-driven anisotropy and inhomogeneous DMI render them as chiral helimagnets [6].
In addition, the exchange interaction generates the weakly ferromagnetic response, scaling linearly with curvature and torsion. The inter- and single-ion
anisotropies in curvilinear AFM chains lead to the additional anisotropic contributions, scaling with curvature. The single-ion anisotropy leads to the
homogeneous DMI mixing normal and tangential components of ferro- and antiferromagnetic vector order parameters. Both anisotropy models contribute
to the additional easy axes, which determine the direction of the order parameters in spin-flop phase [4].
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[3] O. V. Pylypovskyi et al, Phys. Rev. B 103, 134413 (2021)
[4] O. V. Pylypovskyi et al, Appl. Phys. Lett. 118, 182405 (2021)
[5] N. Hedrich et al, Nat. Phys. 17, 574 (2021)
[6] O. V. Pylypovskyi, D. Y. Kononenko et al, Nano Lett. 20, 8157 (2020)