在這篇研究中，我們回顧了不同形狀、直徑、厚度的Py圓點陣列對鐵磁共振(ferromagnetic resonance, FMR)造成的影響。並且為了提高磁性薄膜的磁性能，對不同的墊材進行研究。

在這項實驗中，我們使用了電子束微影技術分別製作薄膜和直徑為5 μm，邊對邊間距為5 μm，厚度為30 nm的鎳鐵合金圓點陣列。並且透過電子束蒸鍍儀系統在室溫條件下成長樣品。我們選擇了共平面波導(Coplanar waveguide, CPW)的樣品結構，利用向量網路分析儀(vector network analyzer, VNA)輸入微波信號，在外加磁場的作用下，測量了鐵磁共振(ferromagnetic resonance, FMR)現象。

In this study, we examined the influence of Py (Permalloy) dot arrays with different shapes, diameters, and thicknesses on ferromagnetic resonance (FMR). Additionally, we investigated different underlayers in order to enhance the magnetic properties of thin films.
In this experiment, electron beam lithography was used to fabricate thin films and permalloy dot arrays with a diameter of 5 μm, a spacing of 5 μm, and a thickness of 30 nm. These arrays were grown using an electron beam evaporation system at room temperature. We selected a sample structure based on a coplanar waveguide (CPW) and employed a vector network analyzer (VNA) to introduce microwave signals. Under the influence of an externally applied magnetic field, we measured the phenomenon of ferromagnetic resonance (FMR).

1. Ashcroft, N.W., et al., Solid State Physics: Revised Edition. 2016: CENGAGE Learning Asia.
2. Bertotti, G., Hysteresis in magnetism: for physicists, materials scientists, and engineers. 1998: Gulf Professional Publishing.
3. Zhou, S., Y. Wang, and Y. Liu, Modelling of Magnetic Stray Fields in Multilayer Magnetic Films with In-Plane or Perpendicular Anisotropy. Magnetochemistry, 2022. 8(11): p. 159.
4. Buschow, K., et al., Magnetostrictive materials. Physics of Magnetism and Magnetic Materials, 2003: p. 171-175.
5. Griffiths, D.J., Introduction to Electrodynamics. 2014: Pearson Education.
6. Liu, C., et al., Long-distance propagation of short-wavelength spin waves. Nature communications, 2018. 9(1): p. 1-8.
7. Ji, L., et al., Isotropic Ferromagnetic Resonances Induced by Suppressed Anisotropy in Soft Magnetic Microstructures. Engineered Science, 2022. 19: p. 136-143.
8. Ding, J., et al., Higher order vortex gyrotropic modes in circular ferromagnetic nanodots. Scientific reports, 2014. 4(1): p. 1-6.
9. Shimon, G., A. Adeyeye, and C. Ross, Comparative study of the ferromagnetic resonance behavior of coupled rectangular and circular Ni 80 Fe 20 rings. Physical Review B, 2014. 89(2): p. 024302.
10. Bhat, V., et al., FMR study of permalloy films patterned into square lattices of diamond antidots. IEEE transactions on magnetics, 2013. 49(3): p. 1029-1032.
11. Wu, M., Nonlinear spin waves in magnetic film feedback rings. Solid State Physics, 2010. 62: p. 163-224.
12. Vogt, K., et al., Realization of a spin-wave multiplexer. Nature communications, 2014. 5(1): p. 1-5.
13. Mahato, B., et al., Tunable configurational anisotropy in collective magnetization dynamics of Ni80Fe20 nanodot arrays with varying dot shapes. Journal of Applied Physics, 2015. 117(21): p. 213909.
14. Kakazei, G., et al., Spin-wave spectra of perpendicularly magnetized circular submicron dot arrays. Applied Physics Letters, 2004. 85(3): p. 443-445.
15. Bunyaev, S., et al., Splitting of standing spin-wave modes in circular submicron ferromagnetic dot under axial symmetry violation. Scientific Reports, 2015. 5(1): p. 1-7.
16. Klein, O., et al., Ferromagnetic resonance force spectroscopy of individual submicron-size samples. Physical Review B, 2008. 78(14): p. 144410.
17. Kharlan, J., et al., Merging of spin-wave modes in obliquely magnetized circular nanodots. Physical Review B, 2022. 105(1): p. 014407.
18. Lupo, P., D. Kumar, and A. Adeyeye, Size dependence of spin-wave modes in Ni80Fe20 nanodisks. AIP Advances, 2015. 5(7): p. 077179.
19. Zhou, X., et al., Axially and radially quantized spin waves in thick permalloy nanodots. Physical Review B, 2015. 92(5): p. 054401.
20. Dobrovolskiy, O.V., et al., Spin-wave spectroscopy of individual ferromagnetic nanodisks. Nanoscale, 2020. 12(41): p. 21207-21217.
21. Finkel, A.C., N. Reeves-McLaren, and N. Morley, Influence of soft magnetic underlayers on the magnetic properties of Co90Fe10 films. Journal of magnetism and magnetic materials, 2014. 357: p. 87-92.
22. Cakmaktepe, S., M.I. Coskun, and A. Yildiz, Underlayer effect on structural and magnetic properties of Co90Fe10 thin films. Lithuanian Journal of Physics, 2013. 53(2).
23. Jung, H., W. Doyle, and S. Matsunuma, Influence of underlayers on the soft properties of high magnetization FeCo films. Journal of applied physics, 2003. 93(10): p. 6462-6464.
24. Liu, X. and A. Morisako, Magnetic properties of FeCo films prepared by co-sputtering and hydrogenous gas reactive sputtering. IEEE Transactions on Magnetics, 2008. 44(11): p. 3910-3912.
25. Wang, X., et al., Preparation of soft magnetic FeCo-based films for writers. Journal of Applied Physics, 2009. 105(7): p. 07B714.
26. Jung, H., et al., Soft anisotropic high magnetization Cu/FeCo films. Applied physics letters, 2002. 81(13): p. 2415-2417.
27. Sun, N. and S. Wang, Soft magnetism of Fe–Co–N thin films with a Permalloy underlayer. Journal of applied physics, 2002. 92(3): p. 1477-1482.
28. Huo, Y., et al., Multiple low-energy excitation states in FeNi disks observed by broadband ferromagnetic resonance measurement. Physical Review B, 2016. 94(18): p. 184421.