Spin wave dynamics in elliptical dots

We investigate the ferromagnetic resonance modes of the magnetic vortex states on ${\mathrm{Ni}}_{81}{\mathrm{Fe}}_{19}$ ellipses using broadband ferromagnetic resonance measurements and micromagnetic simulations. Experiments show a rich structure of modes in the resonance absorption spectra, with absorption peak amplitudes dependent on the direction of the probing radio-frequency field. The evolution of the resonant modes is observed to be symmetric around zero field, due to the reversibility of the vortex core motion. The simulated absorption spectra reproduce the main features of the experimental results. A detailed analysis of the resonant modes at zero field shows that the observed absorption profiles result from the overlap of resonant modes which have an increasing complexity with the frequency. Besides, the simplest resonant modes are not those that exhibit the larger absorption amplitudes. Furthermore, the observed frequency splitting of some of the oscillation modes with the external field is correlated to the symmetry breaking during the vortex motion.

Figure 1

Main figure: Scanning electron microscope image of the $2.4\mu \mathrm{m}\times 1.4\mu \mathrm{m}$ elliptical elements. Inset: Magnetic force microscopy image, showing the vortex configuration.

Figure 2

(a) Magnetization curve. (b) and (c) Experimental absorbed power spectra for $H\perp h_{\mathrm{rf}}$ and $H\parallel h_{\mathrm{rf}}$, respectively. The vertical dotted lines correspond to the transition fields described in the text and the arrows indicate the field sweep direction.

Figure 3

Experimental and simulated absorbed power spectra for $H\perp h_{\mathrm{rf}}$ and $H\parallel h_{\mathrm{rf}}$.

Figure 4

Calculated absorbed power of one ellipse, as a function of frequency and $h_{\mathrm{rf}}$ direction, for $H=0$ and $0.5\mathrm{Oe}$ $h_{\mathrm{rf}}$ amplitude.

Figure 5

Main modes' in-plane component of the magnetization oscillations at $H=0\mathrm{Oe}$. Top: $h_{\mathrm{rf}}$ along the major axis. Bottom: $h_{\mathrm{rf}}$ and along the minor axis.

Figure 6

Vortex core motion and frequency splitting of the $1.5\text{−}\mathrm{GHz}$ mode due to an applied external field.