Nonlinear vortex dynamics and transient domains in ferromagnetic disks

We report a time-resolved imaging and micromagnetic simulation study of the relaxation dynamics of a magnetic vortex in the nonlinear regime. We use time-resolved photoemission electron microscopy and micromagnetic calculations to examine the emergence of nonlinear vortex dynamics in patterned ${\text{Ni}}_{80}{\text{Fe}}_{20}$ disks in the limit of long field pulses. We show for core shifts beyond $\sim 20\%–25\%$ of the disk radius, the initial motion is characterized by distortions of the vortex, a transient cross-tie wall state, and instabilities in the core polarization that influence the core trajectories.

Figure 1

(Color online) Vortex core positions parallel $\left(X\right)$ and perpendicular $\left(Y\right)$ to the applied field vs time, along with fits (red/solid lines) to damped sinusoids after (a) 1, (b) 2, and (c) 4 mT field pulses. (d) shows the time-dependent applied field profile: 75-ns-long field pulses with falling edge at $t=0$. The upper inset shows the experimental geometry indicating the relative-field $\left(\mathbf{B}\right)$ and photon-momentum $\left(\mathbf{k}\right)$ directions. The lower inset shows the $X$-deflection/$Y$-deflection amplitude ratio vs the pulse-field amplitude.

Figure 2

(Color online) (a)–(j) PEEM images at selected times after an applied field of 4 mT is removed. (b)–(d) Between 0.3 and 0.6 ns, a domain state is observed as indicated by the gray regions in the left and right lobes of the disk. (e)–(g) Between 0.9 and 1.9 ns, this domain state is not seen, possibly due to stochasticity in the domain configuration. After $\sim 2\text{ns}$, a new vortex core forms at $\sim 0.2R$ above the disk center and gyrotropic motion begins. At 8.1 ns, when the core should have its maximum shift in $X$, the image instead shows a core that is centered but broadened in the $X$ direction. The inset shows a detail of (k) the transient domain structure and (l) for an unshifted vortex.

Figure 3

(Color online) Micromagnetic simulations of the vortex dynamics. (a) Plots of $M_x$ (solid) and $M_y$ (dotted) components as a function of time show counterclockwise circular vortex motion after a 1 mT pulse and clockwise vortex motion after 2 and 4 mT pulses. Each simulation was initiated with a vortex of positive polarity. The magnetic-field pulse shape is shown as a black dashed-dotted line. (b) Images of the magnetization distribution before and after the 4 mT field pulse are shown where red/dark (blue/darker) represent the magnetization component aligned (antialigned) with $x$. Cross-sectional plots of $M_z$ along $y$ reveal that the vortex core is replaced with a complex cross-tie domain wall within 0.6 ns of the pulse consisting of spins of both positive and negative polarities. At 8 ns, $M_z$ vs $y$ shows the single new core of negative polarity.