^{1}and D. V. Berkov

^{1,a)}

### Abstract

In this paper, we present a detailed numerical micromagnetic study of the spin wave propagation in a thin magnetic film where several columns of circular antidots (holes) are cut out. We determine the transmission coefficient of such a system as the function of the spin wave frequency (transmission spectrum), and study the absorption and transmission frequency regions in dependence on the interdot distances and on the number of antidot columns. It turns out that already several antidot columns are sufficient to obtain nearly perfect gaps in the transmission spectrum of spin waves, so that already a system of a few such columns can be used as a very effective magnonic filter. Next, we establish a close relation between the transmission spectrum of our system and the spectrum of eigenmodes of the corresponding infinite antidot lattice. Finally, we demonstrate that transmission and absorption bands can be easily tuned (for the given antidot arrangement) by changing the external magnetic field. Importantly, the transmission spectrum exhibits a universal scaling when the external field is changed, when this spectrum is plotted as the function of the magnon wave vector.

Authors greatly acknowledge the European Community's Seventh Framework Programme (FP7/2007-2013) under Grant Agreement No. 228673 (MAGNONICS). The authors also thank S. Erokhin, D. Grundler, G. Gubbiotti and V. Kruglyak for useful discussions.

I. INTRODUCTION

II. SIMULATED SYSTEM AND SIMULATION METHODOLOGY

III. SIMULATION RESULTS FOR ANTIDOT SYSTEMS AND DISCUSSION

A. Dependence of the transmission spectrum on the geometry of an antidot system

B. Relation between the filter transmission spectrum and the antidot lattice eigenmodes

C. Scaling of the transmission spectrum with the external field

IV. CONCLUSION

### Key Topics

- Spin waves
- 37.0
- Magnons
- 22.0
- External field
- 17.0
- Normal modes
- 14.0
- Magnetic films
- 10.0

## Figures

Dispersion f(λ) for the unpatterned magnetic film used in our simulations. Inset: the same dispersion relation plotted within the narrow frequency region 9.2–9.3 GHz to show the existence of the minimal frequency f min ≈ 9.23 GHz at λ min ≈ 760 nm.

Dispersion f(λ) for the unpatterned magnetic film used in our simulations. Inset: the same dispersion relation plotted within the narrow frequency region 9.2–9.3 GHz to show the existence of the minimal frequency f min ≈ 9.23 GHz at λ min ≈ 760 nm.

(a) Simulation geometry for an unpatterned film and (b) oscillation power spectrum of the my -component computed along the measurement line (see (a)) at the distance Lx = 500 nm from the “excitation” line (note the logarithmic scale of the ordinate axis).

(a) Simulation geometry for an unpatterned film and (b) oscillation power spectrum of the my -component computed along the measurement line (see (a)) at the distance Lx = 500 nm from the “excitation” line (note the logarithmic scale of the ordinate axis).

Geometry of the antidot filter with definitions of corresponding geometric parameters.

Geometry of the antidot filter with definitions of corresponding geometric parameters.

Transmitted power spectra P(f) (left column) and transmission ratio T(f) (right column) for various distances between the antidot rows ay as shown in the legend. The number of the antidot columns for all systems shown here is N col = 4, the distance between the columns is ay = 200 nm. Spectra are calculated for the oscillations of the in-plane magnetization projection perpendicular to the external field direction (my -projection), averaged along the (green) measurement line positioned at the distance 500 nm on the right from the last antidot column shown in Fig. 3 .

Transmitted power spectra P(f) (left column) and transmission ratio T(f) (right column) for various distances between the antidot rows ay as shown in the legend. The number of the antidot columns for all systems shown here is N col = 4, the distance between the columns is ay = 200 nm. Spectra are calculated for the oscillations of the in-plane magnetization projection perpendicular to the external field direction (my -projection), averaged along the (green) measurement line positioned at the distance 500 nm on the right from the last antidot column shown in Fig. 3 .

Transmission ratio T(f) for various numbers of antidot columns N col as shown in the legend, calculated at the distance of 500 nm from the last antidot column. The distance between the antidot columns is equal to the distance between their rows: ay = ax = 200 nm.

Transmission ratio T(f) for various numbers of antidot columns N col as shown in the legend, calculated at the distance of 500 nm from the last antidot column. The distance between the antidot columns is equal to the distance between their rows: ay = ax = 200 nm.

Oscillation power maps (on the logarithmic scale) for propagating modes in a system of N col = 8 antidot columns with ay = ax = 200 nm. Letters to the left of each map denote the transmission bands indicated in Fig. 8 . A qualitatively different propagating character for the ground mode (upper image) and all other modes can be clearly recognized.

Oscillation power maps (on the logarithmic scale) for propagating modes in a system of N col = 8 antidot columns with ay = ax = 200 nm. Letters to the left of each map denote the transmission bands indicated in Fig. 8 . A qualitatively different propagating character for the ground mode (upper image) and all other modes can be clearly recognized.

Geometry for the calculation of spectra in-between the excitation line and the antidot filter (upper scheme) and magnetization oscillation spectra at various distances from the filter (as shown in the legend at the lower graph). Typical interference patterns observed for frequencies within the gap in the transmission spectra of the same filter (compare to Fig. 5 , spectra for N col = 8) prove the strong reflection of spin waves from the antidot columns for these frequencies.

Geometry for the calculation of spectra in-between the excitation line and the antidot filter (upper scheme) and magnetization oscillation spectra at various distances from the filter (as shown in the legend at the lower graph). Typical interference patterns observed for frequencies within the gap in the transmission spectra of the same filter (compare to Fig. 5 , spectra for N col = 8) prove the strong reflection of spin waves from the antidot columns for these frequencies.

Upper graph: comparison of the transmission spectrum for the filter with 8 antidot columns to the eigenmode spectrum for the infinite antidot lattice with the same antidot diameters and interdot distances. Images below the graph show the spatial power distributions for the antidot lattice eigenmodes. For most cases, frequencies of eigenmodes which are delocalized in the x-direction ( -modes) correspond to the peaks in the transmission spectrum, frequencies of other eigenmode types (L and )—to the minima in this spectrum. See text for the detailed discussion.

Upper graph: comparison of the transmission spectrum for the filter with 8 antidot columns to the eigenmode spectrum for the infinite antidot lattice with the same antidot diameters and interdot distances. Images below the graph show the spatial power distributions for the antidot lattice eigenmodes. For most cases, frequencies of eigenmodes which are delocalized in the x-direction ( -modes) correspond to the peaks in the transmission spectrum, frequencies of other eigenmode types (L and )—to the minima in this spectrum. See text for the detailed discussion.

Transmitted power spectra P(f) (left column) and transmission ratio T(f) (right column) for various external fields calculated at the same location as in Fig. 5 . Here, N col = 4, ay = ax = 200 nm.

Transmitted power spectra P(f) (left column) and transmission ratio T(f) (right column) for various external fields calculated at the same location as in Fig. 5 . Here, N col = 4, ay = ax = 200 nm.

Transmitted power spectra P(f) for the same systems as in Fig. 7 plotted versus the wave number k. A nearly perfect coincidence of spectra for various fields (as shown in the legend) is clearly seen.

Transmitted power spectra P(f) for the same systems as in Fig. 7 plotted versus the wave number k. A nearly perfect coincidence of spectra for various fields (as shown in the legend) is clearly seen.

Article metrics loading...

Full text loading...

Commenting has been disabled for this content