Skyrmion oscillations in magnetic nanorods with chiral interactions

We report that in cylindrical nanorods with chiral interactions spin textures corresponding to spatial skyrmion oscillations can be stabilized depending on the initial state, as revealed by micromagnetic calculations. The skyrmion oscillation, or skyrmion-chain state, occurs when the diameter of the rod is larger than the helical pitch length of the material, and the number of skyrmions on the chain is proportional to the length of the nanorod. The topological charge is localized, breaking translational symmetry, but in the presence of a uniaxial anisotropy, or upon the application of an external field, the localization disappears and a single skyrmion line is formed. These findings provide a deeper understanding of the interplay between geometry and topology, and show how spatial confinement specifically in curved solids can stabilize skyrmionic spin textures.

Figure 1

Simulated ultrathin nanodisks with diameter of 120 nm after an external field of 1 T has been applied (a) in-plane and (b) out-of-plane. In (b) a skyrmion core forms.

Figure 2

Spin configurations in cylindrical nanowires with a length of 500 nm and a diameter of 120 nm showing (a) the helicoid state and (b) the skyrmion state with oscillating spin texture. The two slices and their respective magnetization profile show the two modes of oscillation. The dashed line is a fit with the $\pi$ domain wall profile (see text). (c) A contour plot of the $z$ component of the magnetization inside the nanowire shown in (b) and the oscillation of the topological charge [see Eq. (1)] $Q$ along the wire.

Figure 3

(a) Snapshot of simulation performed on a FeGe cone, showing the possible spin textures at each range of diameters, starting with a conical spin structure for thin rods $d\le 60$ nm, then a helicoid spin structure for $60<d\le 100$ nm, entering the skyrmion-chain state for $100<d\le 140$ nm, then again a helicoid structure for $140<d\le 160$ nm, which then transforms to a ring state for $d>160$ nm. (b) Comparison between three systems with different DMI strength and (c) diameter ($d_{\mathrm{sc}}$) at which the skyrmion-chain state becomes stable as a function of DMI strength; circles are simulation results and solid lines are fits using $d_{\mathrm{sc}}\propto 1/D$: $d_{\mathrm{sc}}$ is proportional to the characteristic pitch length [inset to (c)].

Figure 4

Cross section of cylindrical nanowires with diameter 120 nm and length 500 nm with (a) a uniaxial anisotropy ($K_{\mathrm{u}}$), and (b) an external field. The spin structure corresponds to that of a single skyrmion line, characterized by the absence of oscillations in $Q$. The dashed line is a fit with the $\pi$ domain wall profile.