Nanoscale Near-Field Steering of Magnetic Vortices

The utility of local fields formed around a biased conductive scanning nanoscale tip is demonstrated for the trapping, tracking, and displacement of magnetic textures hosted by a substrate. The method operates at a low energy cost, is noninvasive, and is highly controllable. Detailed results are presented for the dynamic of a magnetic vortex in the sample beneath the tip. It is shown that the near-field-assisted tracking does not suffer from the usually undesirable transversal motion of magnetic vortices or skyrmions due to the topological Hall effect. Tuning the near field of the tip allows for the generation of packaged skyrmions with different topological charges. The results endorse the potential of near-field engineering for information storage and processing based on topological magnetic structure.

Figure 1

A schematic of the calculated setup. A biased conductive scanning tip is positioned in a subnanometer distance above a nanoscale-thick insulating ferrimagnetic stripe that hosts magnetic vortices. The stripe is deposited on a conductive substrate. The inhomogeneous tip-induced near field couples to the magnetic texture and allows for it to be tracked and tweezed. The enlargement shows the calculated electric field distribution around the tip.

Figure 2

The electric field distributions for a conductive tip. The radial ($E_{\rho }$) and vertical ($E_z$ dashed) electric field distributions in the middle of the YIG layer for different values of the tip radius $R$. The YIG-tip distance is $0.3\mathrm{nm}$. The tip axis defines the $z$ direction.

Figure 3

The phase diagram of the spin configurations when applying different tip-assisted near fields to the initial magnetic vortex with positive polarity and clockwise chirality. (a) A schematic diagram of the device when the near field acts on the vortex in the magnetic strip. (b) The phase diagram for a near field with $k=10$ and $k=20$: from left to right, a high-topology packaged skyrmion, packaged skyrmions ($p=1$ and $p=-1$, respectively), and magnetic vortices ($p=-1$ and $p=1$, respectively).

Figure 4

The transport process of a magnetic vortex and a packaged skyrmion. (a),(b) Snapshots of the tweezer transport of a magnetic vortex mediated by (a) the vortex itself or (b) a packaged skyrmion. The gray and black lines are the trajectory of the magnetic vortex (packaged skyrmion) centers and the near field, respectively. (c) The dynamic velocity $\mathbf{V}$ of a packaged skyrmion driven by a tip-generated near field moving along a magnetic strip ($1200\times 240\times 3{\mathrm{nm}}^3$) with a speed of $80\mathrm{m/s}$. Here, $\mathbf{V}$ is given by the LLG and Thiele equations, respectively.

Figure 5

The lateral offset as a function of the velocity. The lateral offset ${\delta }_{\perp }$ versus the longitudinal velocity of a packaged skyrmion $V_x$ in the dynamic equilibrium stage, in which the topological Lorentz force $F_y^L$ is balanced by the driving force $F_y$ due to the center offset between the acting near field of the tip and the packaged skyrmion (cf. the inset). The brown dots and black line are given by the LLG and Thiele equations, respectively. The near field is found to have a mainly Gaussian distribution with a half-width $\mathrm{\Gamma }/2$, an essential quantity for the maximum possible velocity of the packaged skyrmion.

Figure 6

The rotational motion of the packaged skyrmion. (a) The trajectories of a Gaussian electric field (${\mathbf{r}}_c^e$, red line) and a packaged skyrmion rotating with a velocity of $30\mathrm{m/s}$ (${\mathbf{r}}_{c1}^s$, blue line) and $60\mathrm{m/s}$ (${\mathbf{r}}_{c2}^s$, green line). (b) The time evolution of the polar angle ${\phi }_c^e$ (${\phi }_c^s$) of the Gaussian field (packaged skyrmion) and the magnetic energy.

Figure 7

The magnetic vortex transport mediated by the packaged skyrmion. Snapshots of the translational motion of the magnetic vortex between two YIG squares ($240\times 240\times 3{\mathrm{nm}}^3$) bridged by a YIG strip ($720\times 60\times 3{\mathrm{nm}}^3$). A Gaussian electric field with $k=20$, $R=120\mathrm{nm}$, and $E_z=15\mathrm{MV/cm}$ (topology-invariant tweezers) or $E_z=11\mathrm{MV/cm}$ (topology-switching tweezers) is applied as a driving force.