Here, we predict the effect of the spontaneous deformation of a flexible ferromagnetic ribbon induced by Dzyaloshinskii-Moriya interaction (DMI). The geometrical form of the deformation is determined both by the type of DMI and by the equilibrium magnetization of the stripe. We found three different geometrical phases, namely, (i) the DNA-like deformation with the stripe central line in the form of a helix, (ii) the helicoid deformation with the straight central line, and (iii) cylindrical deformation. In the main approximation the magnitude of the DMI-induced deformation is determined by the ratio of the DMI constant and the Young’s modulus. It can be effectively controlled by the external magnetic field, which can be utilized for the nanorobotics applications. All analytical calculations are confirmed by numerical simulations.
We study spin eigenexcitation of a skyrmion in a collinear uniaxial antiferromagnet by means of analytical and numerical methods. We found a discrete spectrum of modes which are localized on the skyrmion. Based on a qualitatively different dependence of the mode eigenfrequencies on the skyrmion radius R0, we divided all localized modes into two branches. Modes of the low-frequency branch are analogous to the localized magnon modes of a ferromagnetic skyrmion, their frequencies scale as R0–2 for the large radius skyrmions, while the modes of the high-frequency branch have no direct ferromagnetic counterpart and do not demonstrate the significant radius dependence and are compactly situated at the magnon continuum. All the modes, except the radially symmetrical one, are doubly degenerated with respect to the sense of rotation around the skyrmion center: clockwise or counterclockwise. An out-of-plane magnetic field removes the degeneracy (for all modes except translational), resulting in a frequency splitting, which for the small fields is linear in field. The possibility of excitation of the modes by means of the external ac magnetic fields is discussed. To explain our numerical results for the low-frequency modes, we introduce a string model for an antiferromagnetic domain wall representing boundary of the large radius skyrmion.
A new type of magnonic crystals, curvature induced ones, is realized in ferromagnetic nanowires with periodically deformed shape. A magnon band structure of such crystal is fully determined by its curvature: the developed theory is well confirmed by simulations. An application to nanoscale spintronic devises with the geometrically tunable parameters is proposed, namely, to filter elements.
The development of motility mechanisms controllable on the sub-micron length scale is crucial for both nanorobotics and shapeable magnetoelectronics. We showcase that the nanoscale shape deformation of a flexible magnet can be controlled by its magnetic attributes. Namely, we consider a problem of coupling the geometrical and magnetic degrees of freedom of an elastic loop-shaped nanowire. The minimum energy states of the system essentially depend on its geometric, magnetic, and elastic parameters. Depending on the parameters, one can distinguish two different states: a sufficiently small magnetic ring is magnetized almost uniformly, forming an `onion state’ with two magnetic domain walls. An opposite case of large, rigid magnetic rings is characterized by a flux free vortex state. These findings open new avenues of investigation with deformable, multiply connected magnetic rings for applications in multifunctional nanorobotics.
Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local curvature without any intrinsic chiral interactions. Here, we propose an alternative mechanism to stabilize chiral Néel skyrmion states relying on the gradient of curvature. We illustrate our approach with an example of a magnetic thin film with perpendicular magnetic anisotropy shaped as a circular indentation. We show that in addition to the topologically trivial ground state, there are two skyrmion states with winding numbers ±1 and a skyrmionium state with a winding number 0. These chiral states are formed due to the pinning of a chiral magnetic domain wall at a bend of the nanoindentation due to spatial inhomogeneity of the curvature-induced Dzyaloshinskii-Moriya interaction. The latter emerges due to the gradient of the local curvature at the bend. While the chirality of the skyrmion is determined by the sign of the local curvature, its radius can be varied in a broad range by engineering the position of the bend with respect to the center of the nanoindentation. We propose a general method, which enables us to reduce the magnetic problem for any surface of revolution to the common planar problem by means of proper modification of constants of anisotropy and Dzyaloshinskii-Moriya interaction.