Dynamic Origin of Vortex Core Switching in Soft Magnetic Nanodots

The magnetic vortex with in-plane curling magnetization and out-of-plane magnetization at the core is a unique ground state in nanoscale magnetic elements. This kind of magnetic vortex can be used, through its downward or upward core orientation, as a memory unit for information storage, and thus, controllable core switching deserves some special attention. Our analytical and micromagnetic calculations reveal that the origin of vortex core reversal is a gyrotropic field. This field is induced by vortex dynamic motion and is proportional to the velocity of the moving vortex. Our calculations elucidate the physical origin of the vortex core dynamic reversal, and, thereby, offer a key to effective manipulation of the vortex core orientation.

Figure 1

Geometry of the model and scheme of the VC reversal in a cylindrical magnetic nanodot. The in-plane $\mathbf{M}$ distribution is marked by different colors, as indicated by the color wheel. The spikes correspond to the core magnetization: the switching occurs from the “upward” (left) to the “downward” orientation (right). The oscillating in-plane magnetic field amplitude is $H_0=50\mathrm{Oe}$, and the field frequency is $\omega /2\pi =580\mathrm{MHz}$.

Figure 2

Snapshot images at the selected moments of the spatial $\mathbf{M}$ distribution and of the gyrofield distribution for a moving vortex. The color of the surfaces indicates the local out-of-plane normalized magnetization $m_z$ in the first row and the local out-of-plane component $h_z$ in the second row. The streamlines with the small arrows indicate the in-plane $\mathbf{M}$ direction. The VC magnetization [solid (red) line] and the gyrofield $z$ component [dashed (green) line] profiles along the line crossing the VC and the nanodot center are shown in the third row. The static vortex profile [dotted (black) line] was intentionally shifted for direct comparison with the dynamic vortex profile [solid (red) line].

Figure 3

(a) The simulated trajectories of the VC motion under an oscillating magnetic field during the time periods $t=0–8\mathrm{ns}$ for the upper panel (shaded circle) and $t=8–16\mathrm{ns}$ for the lower panel. The small circles (green) indicate the VC positions at the times indicated for the snapshot images in Fig. 2. The velocity $\upsilon$ and the amplitude $|\mathbf{X}|$ of the moving VC are plotted vs time in (b) and (c), respectively. VC orientation reversal occurs at the maximum velocity (${\upsilon }_c$) and amplitude values. The extreme minimum value of the local $h_z$ for the upward core orientation and its maximum value for the downward core orientation and the local $m_z$ are shown vs time in (d) and (e), respectively. The solid (red) and dashed (blue) lines correspond to the upward ($p=+1$) and downward ($p=-1$) core orientations, respectively. The vertical lines indicate the times when the extreme values of the local $h_z$ have infinite values, which correspond to the singularity of the gyrofield Eq. (2) at the points $m_z=-p$.