Figure 1

(Color online) (a) Micrograph of the sample showing the gold transmission lines (yellow) and the Permalloy patterns (light green); the visible Permalloy structures are useful for alignment and for locating the nanomagnets. The circuit connections for TRMOKE measurement are also sketched, with the photoconductive switch (PCS) on one end of the transmission lines and a bias voltage on the other end $\left(V=10–15\text{V}\right)$. (b) SEM image of the Permalloy disks captured at a $45°$ tilted angle. (c) SEM top view of one of the disks shown in (b); its diameter is displayed by the SEM software, which reads “164.5 nm.”Reuse & Permissions

Figure 2

[(a)–(d)] Evolutions of $M_z$ as a function of the pump-probe optical delay time measured under different bias fields and ground states (quasisingle domain or vortex), as illustrated by the cartoons in each panel. The power spectral densities (PSD) of the time traces are shown by the insets, with the arrows marking the characteristic frequency $f_0$ as the indicator for state transitions discussed in the text.Reuse & Permissions

Figure 3

(Color online) Spin wave frequencies of the Permalloy disk. The measured data are plotted by squares, and the simulated results obtained by using the domed cylinder model and the flat cylinder model are plotted as circles and triangles, respectively. (a) Hysteresis behavior of the primary modal frequency $\left(f_0\right)$ as a function of the bias field $\left(H_0\right)$, with the arrows indicating the sweep direction of the bias field. The representative magnetization states are also sketched. The inset 3D cartoon shows the shapes of the two models. The gray curve is calculated based on Eq. (1) (for our samples, $\beta =0.375$ and $F\left(\beta \right)\approx 0.1537$, see Ref. 18 for details); the gray dashed curve gives a reference calculation based on the unmodified Kittel’s formula, i.e., $F\left(\beta \right)=0$. (b) Frequencies of the secondary modes in the vortex states. The insets show the simulated magnitude and phase distributions of the primary mode [13.1 GHz, see (a)] and the secondary mode (12.4 GHz) when $H_0=0$. The color bars (not shown) are scaled by the maximum and minimum of individual maps.Reuse & Permissions

Figure 4

(a) The solid curve shows the temporal scan of $M_z$ with an abrupt change in the precession behavior, indicating a vortex-to-quasisingle domain transition (marked by the arrow); the dashed curve shows an immediately followed scan to confirm the disk was already in the quasisingle domain state. The bias field was fixed at 67.4 kA/m during the scans. (b) Similar consecutive scans for detecting a quasisingle domain to vortex transition. The bias field was fixed at 29.1 kA/m.Reuse & Permissions

Figure 5

(Color online) The evolution of magnetization configuration in the vortex nucleation process as simulated by the flat cylinder model [(a1)–(a5)] and the domed cylinder model [(b1)–(b5)]. The disks are stabilized into equilibrium with $H_0=29.44\text{kA}/\text{m}$ (a1) and 27.85 kA/m (b1), respectively. Then, the bias fields decrease to 28.65 and 27.06 kA/m, respectively, to trigger the nucleation, representative snapshots are recorded in (a2)–(a5) and (b2)–(b5). The $\tau$ values are the “effective” time in the simulations with a large damping constant $\alpha =1.8$, so these snapshots do not reflect the real time points (in real time, the evolutions would be much slower). In each frame, the intensity of $M_z$ at the top and bottom layers of the 3D models are shown by the colored surfaces; the color bar shows a fixed minimum value ($-1$, assigned for cells outside the magnetic disk) and different maximum values for different frames. The small cones between the two surfaces represent the spins in the 3D models that are within the vortex core (the criterion $\mathit{M}$ being at least $25°$ off the disk plane); the colors of these cones are also scaled with $M_z$. For clarity, a zoom-in view of the vortex core is presented aside (b3).Reuse & Permissions