Driven Dynamic Mode Splitting of the Magnetic Vortex Translational Resonance

A magnetic vortex in a restricted geometry possesses a nondegenerate translational excitation that corresponds to circular motion of its core at a characteristic frequency. For 40-nm thick, micron-sized permalloy elements, we find that the translational-mode microwave absorption peak splits into two peaks that differ in frequency by up to 25% as the driving field is increased. An analysis of micromagnetic equations shows that for large driving fields two stable solutions emerge.

Figure 1

(a) Microwave spectra (real part, scaled) for sample $A$, $H=60\mathrm{Oe}$, as a function of $h_{\mathrm{ac}}$. (b) Spectra showing dynamic splitting as a function of excitation power for $H=20–140\mathrm{Oe}$ applied along the ellipse minor axis.

Figure 2

(a) Calculated vortex core motion amplitude as a function of $\omega$ for a circular disk with $\beta >0$ shows a foldover effect when $h_{\mathrm{ac}}$ (values in legend) is increased. Arrows indicate the hysteretic path and the dashed line shows the $\beta =0$ result for $h_{\mathrm{ac}}=1.5\mathrm{Oe}$. (b) $A_x$ vs $\omega /2\pi$ using a large $C_2$ value shows a crossover effect for $h_{\mathrm{ac}}=5\mathrm{Oe}$.

Figure 3

Micromagnetic simulations for a $300\times 150\mathrm{nm}$ ellipse, 20-nm thick, for $h_{\mathrm{ac}}$ of (a) 0.1 Oe, (b) 10 Oe, and inset of (b) 20 Oe. The frequency was increased [dark (blue)] or decreased [light (green)] at $31.8\mathrm{kHz}/\mathrm{ns}$, and the $x$ axis converted from time to $\omega /2\pi$.