Spin dynamics and mode structure in nanomagnet arrays: Effects of size and thickness on linewidth and damping

We use frequency resolved magneto-optic Kerr effect to probe the spin dynamics and mode structure in 50–200-nm-diameter ${\text{Ni}}_{80}{\text{Fe}}_{20}$ nanomagnets ranging from 3 to 10 nm in thickness. We find that the intrinsic Gilbert damping parameter is largely unaffected by the nanopatterning process despite a large linewidth dependence on the size of the nanomagnets. In the larger nanomagnets, both end and center modes are observed. The linewidth of these two modes differ considerably, which is most likely the result of the sensitivity of the end mode to small variations and imperfection of the shape and edge materials. We show that this effect can be exploited as a means to separately characterize the magnetic properties of the nanomagnets as well as the size and shape variations within the array.

Figure 1

(Color online) SEM images of (a) nominally 200 nm nanomagnets with 20% ellipticity and (b) nominally 50 nm circular nanomagnets. (c) Schematic diagram of a nanomagnet sample structure.

Figure 2

(Color online) Schematic diagram of the FR-MOKE experimental setup. The inset shows the sample geometry and coordinate system from the perspective of the charge-couple device camera.

Figure 3

(Color online) (a) An example of an FR-MOKE spectrum of an array of 100 nm nanomagnets. The fit to the data is included and shows the asymmetry of the peaks due to a nonzero phase relationship between the two resonances. (b) A simulated spectrum of a 100 nm nanomagnet reproducing the asymmetry in the peaks and showing a significantly narrower linewidth for the lower frequency peak.

Figure 4

(Color online) Contour plots of spectra for 10-nm-thick ${\text{Ni}}_{80}{\text{Fe}}_{20}$ for the (a) thin film, (b) 50-nm-diameter, (c) 100-nm-diameter, and (d) 200-nm-diameter nanomagnet arrays. The scale bar represents the normalized amplitude.

Figure 5

(Color online) Contour plots of spectra for 5-nm-thick ${\text{Ni}}_{80}{\text{Fe}}_{20}$ for the (a) thin film, (b) 50-nm-diameter, (c) 100-nm-diameter, and (d) 200-nm-diameter nanomagnet arrays. The scale bar represents the normalized amplitude.

Figure 6

(Color online) Contour plots of spectra for 3-nm-thick ${\text{Ni}}_{80}{\text{Fe}}_{20}$ for the (a) thin film, (b) 50-nm-diameter, (c) 100-nm-diameter, and (d) 200-nm-diameter nanomagnet arrays. The scale bar represents the normalized amplitude.

Figure 7

(Color) Plots of $f_0$ vs $H_b$ for 10-nm-thick ${\text{Ni}}_{80}{\text{Fe}}_{20}$ for (a) 50-, (b) 100-, and (c) 200-nm-diameter nanomagnet arrays. Fits of Eq. (1) to the experimental data (▲) are included as the red solid line. Simulations performed for single nanomagnets of the same size (blue line) show reasonable agreement with the experimental data. The insets in each figure show the relative amplitude of precession across the nanomagnet for each mode obtained from the simulations. The horizontal plane in the insets indicates where the amplitude is zero.

Figure 8

(Color online) $\Delta H_0$ vs $f_0$ for the 5-nm-thick ${\text{Ni}}_{80}{\text{Fe}}_{20}$ with (a) the thin film, (b) 75-nm-diameter, and (c) 200-nm-diameter arrays. Both the end (△) and center (○) modes are observed in the 200-nm-diameter sample. Fits to Eq. (5) are included that were used to separate the contribution of $\alpha$ and $\Delta H_0$ to the total mode linewidth. The insets show the respective Kittel plots used to convert from $\Delta f$ to $\Delta H$.

Figure 9

(Color online) Values of (a) $\alpha$ and (b) $\Delta H_0$ as a function of thin-film thickness, and the diameter dependence of (c) $\alpha$ and (d) $\Delta H_0$ for the 5-nm-thick patterned samples. The vertical dashed line indicates the boundary between regions where single and multiple modes are observed.

Figure 10

(Color online) Plots of $f_0$ vs $H_b$ for a 110-nm-diameter nanomagnet array showing the frequency shift in the modes as the nominal ellipticity of the nanomagnets are varied between 0% and 20%.

Figure 11

(Color online) Plot of $\Delta H_0$ vs $f_0$ 5-nm-thick $220\times 202{\text{nm}}^2$ nanomagnet array along with data taken from the size distribution model with (a) the size fluctuation measured in SEM analysis, and (b) a best fit of the size fluctuations to the end mode data.

Figure 12

(Color) (a) Images of the nanomagnet shape used to simulate the effect of egglike shape distortion obtained for values of $c=0$, 0.1, and 0.2. (b) The simulated frequency versus applied field angle for these three nanomagnet shapes. The insets show the amplitude of precession across the nanomagnet structure for each mode where yellow is the highest amplitude and dark blue represents zero amplitude. (c) SEM image of a $220\times 202{\text{nm}}^2$ nanomagnet that has been enhanced to show the edge boundary. An ellipse is overlaid to show the deviation of the sample from the nominal shape.