Static and dynamic magnetic properties of ${\text{Ni}}_{80}{\text{Fe}}_{20}$ square antidot arrays

We have investigated both static and dynamic magnetic properties of square antidot arrays in a ferromagnetic thin-film structure of Au (2 nm)/${\text{Ni}}_{80}{\text{Fe}}_{20}$ (27.6 nm) on a ${\text{SiO}}_2$ 500 nm/Si substrate using magneto-optic Kerr effect magnetometry, Brillouin light scattering (BLS), and micromagnetic simulations. The antidot patterns were $1\mu \text{m}$ square holes arranged in two separate square lattices of dot separations $d=0.6\mu \text{m}$ and $1.0\mu \text{m}$. The introduction of antidots induced an in-plane fourfold magnetic anisotropy with hard axes on the two nearest-antidot-neighbor directions. The coercive field, $H_c$, was increased by the presence of antidots. Fixed-frequency modes were observed in spin-wave dispersion relations in remanent spin configurations. These modes correspond to spin-wave confinement by antidot edges, which were seen as a series of nodal lines parallel to the edges in simulated spin-wave mode spatial mappings. Domains in remanent states, some of which were responsible for the existence of dipole-exchange backward volume modes seen in BLS spectra, were also found to confine spin waves in simulations.

Figure 1

SEM images and schematic of antidot samples. The square antidot area is $1\times 1\mu {\text{m}}^2$. (a) and (b) are antidots in square lattices with separations $d=1.0\mu \text{m}$ and $d=0.6\mu \text{m}$, respectively. (c) shows a close up of an antidot taken with the sample tilted at $75°$, and hence the side wall inside the antidot could be seen. The image was analyzed line by line, and the total thickness of the film was found to be $29.6\pm 0.2\text{nm}$. (d) is a schematic of the antidot pattern. It shows the geometry and parameters defined for MOKE and BLS measurements as well as for OOMMF simulations.

Figure 2

Hysteresis loops of antidot patterns and a continuous film obtained by MOKE measurements and static OOMMF simulations. ${\mathbf{H}}_{\left(\text{ext}\right)}$ was applied at either $\Phi =0°$ or $\Phi =45°$ w.r.t. the edge of antidot. (a) and (b) are results from antidot patterns of separations $d=0.6\mu \text{m}$ and $d=1.0\mu \text{m}$, respectively. (c) is the MOKE result for the continuous film.

Figure 3

OOMMF simulated spin configurations in antidot patterns at various points along the upper part of their hysteresis loops, i.e., $H_{\left(\text{ext}\right)}$ being changed from $+500\text{Oe}$ in steps of 1 Oe to $-500\text{Oe}$.

Figure 4

External field, $H_{\left(\text{ext}\right)}$, dependent spin-wave frequency measured by BLS from antidot structures and a continuous film at $k_y=1.73\times {10}^5{\text{cm}}^{-1}$. (a) shows the whole range of continuous film data which were fitted to Eq. (4) with $M_s$ and $\gamma$ as parameters. ● are data from BLS measurements and (– – –) is the fitted curve. (b) and (c) are results from antidot patterns of $d=0.6\mu \text{m}$ at $\Phi =0°$ and $45°$, respectively. (d) and (e) are results from antidot patterns of $d=1.0\mu \text{m}$ at $\Phi =0°$ and $45°$, respectively. In (b)–(e), ● are data from BLS measurements and ○ are calculated frequencies from OOMMF simulations. Only the mode with frequency closest to that of the DE mode in the continuous film is shown here for clearer comparisons. (– – –) is the fitted curve for the continuous film.

Figure 5

Spin-wave dispersions in antidot structures at $H_{\left(\text{ext}\right)}=0\text{Oe}$. (a) and (b) are dispersion data from antidot patterns of $d=0.6\mu \text{m}$ at $\Phi =0°$ and $45°$, respectively. (c) and (d) are dispersion data from antidot patterns of $d=1.0\mu \text{m}$ at $\Phi =0°$ and $45°$, respectively. (– – –) is the dispersion curve calculated for a continuous film using Eq. (4). (—) are standing-wave frequencies as observed in micromagnetic simulations. These lines cover the range of $k_y$ in which these fixed-frequency modes are found in simulations. $(\cdots )$ are fitted dispersion curves for dipole-exchange backward volume modes using Eq. (6).

Figure 6

Spatial mappings of spin-wave modes in antidot structures at $H_{\left(\text{ext}\right)}=0\text{Oe}$ obtained from OOMMF simulations. $n$ is the number of nodes found across the edges of the pattern.