Current-induced dynamics and tunable spectra of a magnetic chiral bobber

Chiral bobber (ChB) is an exotic three-dimensional topological texture in chiral magnets. It is composed of a Bloch-point singularity and a skyrmion tube; the incommensurate characteristic length scales of these two components would thus lead to novel dynamics of a ChB. Here, we report the current-induced motion and the accompanying Hall effect of a ChB. Surprisingly, we find that the Hall angle of a ChB can be tuned in a wide range from −90 ° to positive angles. A further study of spin-wave excitations identified high-frequency resonant modes, which are related to the velocity of ChB and lattice constants. The excited frequency can be two orders of magnitude higher than that of skyrmions. The broad ranges of Hall angles and frequency spectra could boost the development of spintronic devices using topological textures.

Figure 1

Cartoon representation of ChB and the BP pinned by the lattice potential. The inset illustrates spin configuration around the BP.

Figure 2

Dynamics of ChB in the presence of the electric current applied in the $x$ direction. (a), (b) The longitudinal and transverse velocities of ChB and skyrmion tube with different current density for fixed $\beta /\alpha =0.5$, 1.0, and 2.0. The insets are the magnifications of the region at low current density. (c) The dependence of ChB Hall angle on the current density for fixed $\beta /\alpha =0.5$, 1.0, and 2.0. The dots represent the results of simulation, and the solid lines represent the calculated results by Thiele's equation. Values of other parameters, $\mathcal{G}=-4\pi ,\mathcal{D}=9.4\pi ,\mathrm{and}\lambda =0.04$. The inset is the magnification of the region at low current density. (d) The schematics of the current-driven ChB trajectories at $\beta /\alpha =2$. The curved arrow indicates the evolution of ChB trajectory with current density increasing. The inset shows the ChB size before current applied.

Figure 3

(a) Time dependence of $x$, $y$, and $z$ positions of BP in the 3D Cartesian coordinate system with the current density $5\times {10}^7\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$. Insets: the magnification in the range of 10 to 12 ns; the cyan curve is a guide for the eyes of the period related to the $y$ component of the lattice potential. (b) The FFT for the $z$ position of BP and the $z$ component of the total magnetization over time. (c) Schematic diagram of ChB motion process: (c1) the initial state before the current is applied; (c2) the intermediate state in which the ChB is stretched; and (c3) the final state in which the BP relaxes back.

Figure 4

(a) The frequency spectra of ChB at different current densities for the fixed cell size $3\times 3\times 3\mathrm{n}{\mathrm{m}}^3$. (b) The current-density dependence of frequency: the dashed lines are the linear fittings. (c) The frequency spectra of ChB for different cell size with the fixed current density $5\times {10}^7\mathrm{A}/\mathrm{c}{\mathrm{m}}^2$. The dashed line indicates the peak position of the low-frequency SS mode. (d) The dependence of frequency on the 1/cell size: the dashed lines are the linear fittings; the black balls are the SS mode with frequency $f=0.4\mathrm{GHz}$.