High Frequency Modes in Vortex-State Nanomagnets

The magnon mode excitation spectrum is obtained from a linearized set of Landau-Lifshitz equations for vortex ground state cylindrical nanomagnets in an external magnetic field. It is shown that there is a rich spectrum of doublet states, and the splitting can be amplified in an external magnetic field.

Figure 1

Frequency of the $m=0$, $m=\pm 1$, and $|m|=2$ modes versus $\sqrt{L/R}$ for permalloy dots. Here and in Fig. 2 the straight lines are guides to indicate deviations from linearity.

Figure 2

Frequency of the low-frequency gyrotropic mode ${\omega }_{PM}$ and the magnitude of the $m=\pm 1$ doublet splitting $\Delta \omega$ as a function of $L/R$ for permalloy dots.

Figure 3

Frequencies of the $m=\pm 1$ and $m=\pm 2$ modes versus magnetic field for the $R=200\mathrm{n}\mathrm{m}$ permalloy magnetic dot of thickness $L=50\mathrm{n}\mathrm{m}$. In Figs. 3, 4 the triangle symbols are used to distinguish between these curves.

Figure 4

Frequencies of the $m=\pm 1$ and $m=\pm 2$ modes versus magnetic field for the permalloy magnetic ring with inner and outer radii $R_i=100\mathrm{n}\mathrm{m}$ and $R_o=200\mathrm{n}\mathrm{m}$, and thickness $L=50\mathrm{n}\mathrm{m}$.