Surface impedance of SSWR in thin metallic films for parallel configuration

Abstract

SSWR (standing spin-wave resonance) spectra for parallel configuration were calculated analytically for the case of metallic thin films, including surface anisotropy (of equal value at both surfaces); Landau-Lifshits damping, and electrical conductivity effects. The analytical formulae for the surface impedance and for the microwave magnetic fields propagating in the film arc derived, symmetrical and antisymmetrical cases of spin-wave mode excitation are treated following Wolf's method.Die analytischen Formeln fur die Oberfliicheninipedanz und magnetische Hochfrequerizfeldcr fur SSWR (Spinwellenresonanz) in tliiririen nietallischen Schichten (fur den Fall der paralleleri Konfipiration) wertleri angegeben, sowie elektrische Leitfiihigkeit, Landau-Lifshitz-Dampfung, und Oberflachenanisotropie (gleich groO auf beideii Seiten der Schicht). Fur die Uritersiicliurig der gleichphasigen und gegenphasigen Anregung von SWR wird die Methotle von Wolf arigeweridet .

Spin-wave resonance in high-conductivity films: The Fe-Co alloy system

“…The resulting secular equation for the wave numbers is biquadratic for the NC and bicubic for the PC. 5 After applying appropriate boundary conditions 2,14 for h ជ and m ជ , finally ͑following rather long algebra͒, the tangential components (e t and h t ) of e ជ and h ជ are determined and, hence, the normalized surface impedance 2 Zϭͱ2A 2…”

“…Re(Z s,a ) stands for the real part of the surface impedance ͑symmetric and antisymmetric contributions, respectively͒ which is calculated from the CT. 5 This is not done here as the precise value of the experimental parameter a/b is difficult to adjust. The second feature concerns the higher-order modes.…”

“…The latter complicate the theory considerably, and, e.g., the quite complex case of the external field parallel to the film plane ͓parallel configuration ͑PC͔͒ was only recently treated in detail with introducing formulae for the surface impedance Z. 5 Generally, much work was devoted to the understanding of SSWR spectra but, remarkably, despite the precision achievable by the method, the potential was not fully exploited for the extraction of information on various magnetic materials, and most of the work was done only on certain systems, mainly on Permalloy ͑Fe 20 Ni 80 ).…”