Simulations of the dynamic switching of vortex chirality in magnetic nanodisks by a uniform field pulse

We present a possibility to switch the chirality of a spin vortex occurring in a magnetic nanodisk by applying a uniform in-plane field pulse, based on optimizing its strength and duration. The related spin-dynamical process, investigated by micromagnetic simulations, consists of several stages. After applying the field, the original vortex is expelled from the disk, after which two C-shaped states oscillate between each other. The essence of the method is based on turning the field off at a suitably chosen moment for which the orientation of the C-state will evolve into the nucleation of a vortex with the desirable chirality. This idea simply uses the information about the original chirality present inside the nanodisk during the dynamic process before losing it in saturation, and can thus be regarded as analogous to the recent studies on the polarity switching.

Figure 1

(Color online) Selected trajectories of the vortex core plotted inside the top-viewed contour of the Py nanodisk (a) for applied fields $B_x=45$, 51, and 57 mT. For the case of 45 mT (dashed curve) the trajectory corresponds to a spiral motion, whereas for 51 and 57 mT (solid and dotted curves) the trajectory leads the vortex core out of the disk. The chart (b) classifies all processes according to the size of the field.

Figure 2

(Color online) Time evolution of magnetization distribution after applying a pulse of magnetic field $B_x=51\text{mT}$ with two examples of temporal duration of 836 and 988 ps. The color scale of $M_y$, the geometric orientation, and the field pulse are displayed in the bottom-left corner. The top part of the figure demonstrates the evolution during the nonzero field, applied from $t=0$ until a stable, saturated state at 5 ns. The blue (gray solid) frame displays the evolution after turning the field off at $t_{\text{off}}=836\text{ps}$ (shorter pulse). The red (gray dashed) frame displays the evolution after turning the field off at $t_{\text{off}}^{\prime }=988\text{ps}$ (longer pulse).

Figure 3

(Color online) Analyzing the dynamic processes. (a) Time evolution of fluidlike vorticity $\omega ={\left[\nabla \times \mathit{m}\right]}_z$ (averaged over the nanodisk) after applying the pulse $B_x=51\text{mT}$ (the $\omega$ curve) and after two examples of turning the field off at $t_{\text{off}}=836\text{ps}$ (the ${\omega }_{\text{A}}$ curve) and $t_{\text{off}}^{\prime }=988\text{ps}$ (the ${\omega }_{\text{B}}$ curve). (b) The top inset shows the Fourier transform of a selected range of the vorticity function $\omega \left(t\right)$; the selection is depicted by the quotation arrows. The space distribution of magnetization oscillations during the nonzero field for the peak frequency ${\Omega }_0$ are displayed in the bottom insets corresponding to the (c) amplitudes and the (d) phases of the oscillations.

Figure 4

(Color online) Time evolution of energies. (a) The evolution of the total, exchange, demagnetizing, and external-field energies during the externally applied field $B_x=51\text{mT}$. The two quotation arrows show two examples of turning the field off. (b) The evolution of the energies after turning the field off at $t_{\text{off}}=836\text{ps}$. (c) The analogous evolution for $t_{\text{off}}^{\prime }=988\text{ps}$. The trajectories of the cores of nucleated vortices, corresponding to the two cases [(b) and (c)], are displayed in (d) and (e), respectively.