Three-dimensional shape dependence of spin-wave modes in single FePt nanomagnets

We report the dependence of the intrinsic spin-wave spectra on the three-dimensional shape in single FePt nanomagnetic elements. In contrast to the well-known center and edge modes in flat, circular nanodisks, curved nanomagnets with identical nominal thickness and footprint exhibit a rich multimode spectrum with qualitatively different dependence on applied field, such as a low-frequency “pinned” mode. Dynamic micromagnetic modeling shows that the experimentally observed modes originate from different sections of the nanomagnet with vastly different demagnetization fields. Thus, controlled shaping of a nanomagnet in all three dimensions creates the possibility of magnetization dynamics by design.

Figure 1

SEM images of (a) an individual flat nanodot and (b) a nanosphere after ion-beam milling isolation (cartoon cross sections shown above). Experimental TR-MOKE data for a $d$ $=$ 100 nm (c) flat disk and (d) spherical cap at three applied field strengths (listed above each trace). The left columns show the background-subtracted time traces, and the right columns display the corresponding FFT spectra with the Gaussian peak fits included (gray lines).

Figure 2

Peak frequencies as a function of applied field for a $d$ $=$ 100 nm (a) flat disk and (b) spherical cap. The symbols with error bars represent the experimental data, while the solid lines correspond to micromagnetic simulation.

Figure 3

Simulated Fourier amplitude spectra of 100 nm spherical cap at an applied field of ${\mu }_0{H}_{\mathrm{app}}=0.54$ T. The cross section of the cap shows the $x$ component of the simulated demagnetizing field, with the applied field direction and color bar shown. The cap is broken up into four sections, and the frequency spectra show their respective oscillation frequencies.

Figure 4

Demagnetizing field (a, c) and mode images (b, d) for a $d$ $=$ 100 nm (a, b) flat disk and (c, d) spherical cap (${\mu }_0{H}_{\mathrm{app}}=0.41$ T). The $x$ component of $H_d$ is shown for both side and top-down views with the applied field direction and color scale indicated in the center. The graph in (c) plots the average magnitude of $H_d$ for the four spherical cap regions. The mode images in (b) and (d) (numbers correspond to the frequency branches in Fig. 2) are shown with the applied AC field frequencies listed, and are normalized from black (minimum oscillation amplitude) to white (maximum).