Local and Nonlocal Effects of Geometry in Curvilinear Magnetic Nanoarchitectures

Interplay between the geometry and behavior of magnetic textures in statics and dynamics has been traditionally considered regarding planar confined samples and their boundaries (vortices in nanodisks, interaction of skyrmions and domain walls with notches etc.). Recent developments of experimental techniques on fabrication of freestanding 3D nanostructures gave a possibility to access and validate theoretical predictions of behavior of magnetic textures, related to the intrinsic geometric properties of extended films and complex sample topologies [1].

Properties of energy functionals in both, ferro- and antiferromagnetic samples reflect geometric symmetries in curvature-driven Dzyaloshinskii-Moriya interaction and anisotropies, which are proportional to the first and second powers of the curvatures, respectively [1]. Magnetostatics is also sensitive to the breaks of the geometric symmetries. In thin films, it is possible to tease out an interplay between the out-of-surface magnetization component and mean curvature of the film [2]. Furthermore, for such non-local textures as vortices hosted by asymmetric Py caps, it enables complex magnetochiral effects pronounced in twisting of the vortex string in a helix and coupling of this helix chirality with the vorticity of the whole texture [3].

Antiferromagnetic curvilinear nanoarchitectures provide more intrinsic material symmetries. In spin chains, the dipolar interaction provides the hard-axis shape anisotropy, with the anisotropy axis along the tangential direction to the chain. This makes the geometry-driven helimagnetic phase transition to be possible for any finite curvature and torsion of the chain [4]. The locally broken spatial translation symmetry of antiferromagnetic dimers in bipartite chains leads to the micromagnetic energy term of the non-chiral longitudinal Dzyaloshinskii energy symmetry and enables local weak ferromagnetic response related to the spatial inhomogeneity of the Neel vector [5]. The geometry-driven easy axis of anisotropy is present even if the material anisotropy is of the hard-axis type, which enables spin-flop transition governed by the chain shape. In a particular case of the ring with the hard-tangential anisotropy and uniform ground state, the helimagnetic phase transition appears in spin-flop phase and the intermediate canted phase for the case of strong Dzyaloshinskii-Moriya interaction [6].

References
1. D. Makarov, O. Volkov, A. Kakay et al., Adv. Mat. 34, 2101758 (2022)
2. D. Sheka, O. Pylypovskyi, P. Landeros et al., Commun. Phys. 3, 128 (2020)
3. O. Volkov, D. Wolf, O. Pylypovskyi, et al., Nat. Commun. In press (2023)
2. O. Pylypovskyi, D. Kononenko, K. Yershov et al., Nano Lett. 20, 8157 (2020)
5. O. Pylypovskyi, Y. Borysenko, J. Fassbender et al., Appl. Phys. Lett. 118, 182405 (2021)
6. Y. Borysenko, D. Sheka, J. Fassbender, et al., Phys. Rev. B 106, 174426 (2022)