Modeling of microwave-assisted switching in micron-sized magnetic ellipsoids

The microwave-assisted magnetization reversal is modeled in a permalloy micron-sized magnetic ellipsoid. Our simulations confirm that this process requires less field than magnetization reversal under a static field. This is due to a different reversal mode which in the case of the microwave-assisted process is always a ripple structure. During the magnetization reversal, two stages, nucleation and relaxation, are distinguished. The nucleation process is governed by spin-wave instabilities. The relaxation process is related to the domain expansion through domain-wall propagation determined by the precessional motion of magnetic moments in the center of the domain walls. As a consequence, the switching time is a complex oscillating function of the microwave frequency.

Figure 1

(Color online) Geometry of the simulated system.

Figure 2

Simulated descending branch of the hysteresis cycle for the permalloy ellipsoid with static applied field only (full circles) and with simultaneously applied static and mw field with $H_{\text{ac}}=25.1\text{Oe}$, and two frequencies (open symbols). The dc field is applied along the long ellipsoid axis $Y$. The average ellipsoid magnetization $⟨M_y⟩$ is normalized to the total saturation value.

Figure 3

Amplitude of the critical field necessary for magnetization switching as a function of the maximum field angle with the anisotropy axis for static field and microwave-assisted switching.

Figure 4

(Color online) Magnetization configurations during the static-field hysteresis process at different time moments (a) initial state at the coercive field, (b) intermediate state, showing the vortices propagation, and (c) the final state at the coercive field. The field is applied at $45°$ with the $Y$ axis.

Figure 5

Dynamical configurations: $M_x$ (left) and $M_z$ (right) components (gray scale) during the mw-assisted magnetization reversal for applied fields $H_{\text{dc}}=-31.41\text{Oe}$ and $H_{\text{ac}}=18.84\text{Oe}$ and for two different frequencies $\nu =1\text{GHz}$ [(a), (c)] and $\nu =6\text{GHz}$ [(b), (d)]. For the dynamics of the reversal process, see the supplemental material (Ref. 37).

Figure 6

Number of domains in the ellipsoid nucleated during the first two nanoseconds as a function of mw frequency for applied fields $H_{\text{dc}}=-31.41\text{Oe}$ and $H_{\text{ac}}=25.13\text{Oe}$.

Figure 7

Domain size in the ellipsoid along the $y$ coordinate as a function of the position of its center for two time snapshots, corresponding to the first nucleation-expansion stage of the mw-assisted reversal processes and for $H_{\text{dc}}=-31.41\text{Oe}$ and $H_{\text{ac}}=25.13\text{Oe}$. Note that after approximately $t>2.5\text{ns}$ the domain size expansion is suppressed.

Figure 8

(Color online) More detailed magnetization configuration in the upper part of the ellipsoid showing the occurrence of domain walls and vortices. $H_{\text{dc}}=-31.41\text{Oe}$, $H_{\text{ac}}=25.13\text{Oe}$, and $\nu =0.1\text{GHz}$.

Figure 9

Switching time of the magnetization as a function of the mw frequency for various values of the mw-field amplitude $H_{\text{ac}}$ and $H_{\text{dc}}=-31.41\text{Oe}$

Figure 10

Contour plot for the switching time of the ellipsoid for applied field $H_{\text{dc}}=-31.41\text{Oe}$.

Figure 11

Temporal evolution for the average $⟨M_y⟩$ magnetization component (normalized to the saturation value) during the microwave-assisted switching process at $H_{\text{dc}}=-31.41\text{Oe}$ and $H_{\text{ac}}=25.13\text{Oe}$.

Figure 12

Temporal evolution for the average $⟨M_z^2⟩$ magnetization component (normalized to the saturation value) during the microwave-assisted switching process at $H_{\text{dc}}=-31.41\text{Oe}$ and $H_{\text{ac}}=25.13\text{Oe}$.

Figure 13

Switching time of the magnetization as a function of the mw frequency for two values of the stationary field $H_{\text{dc}}$ and the mw-field amplitude $H_{\text{ac}}=25.13\text{Oe}$.