A Theoretical Study of the FMR Surface Mode Excitation in Metals (Parallel Configuration)

Abstract

Using the analytical FMR theory, the real part of the surface impedance as dependent on the magnetic field and surface anisotropy is calculated for two types of ferromagnetic metals with different exchange-conductivity parameters. The shapes of the obtained two sets of FMR spectra (including the main and surface resonance modes) differ considerably; the discussion of the cause of this effect points to a pronounced influence of the FMR cross-over region.&fit Hilfe der analytischen FMR-Theorie wird der reale Anteil der Oberfliichenimpedanz als Funktion des magnetischen Feldes und der Oberfliichenanisotropie fur zwei Typen von ferromagnetischen Metallen mit verschiedenen Austausch-Leitfahigkeitsparametern berechnet. Die Formen der beiden so bcrechneten Familien dcr FMR-Spektren (eingeschlossen Haupt-und OberfliichenModen) unt.erscheiden sich zicmlich stark; die Diskussion dieses Effekts weist auf einen beachtlichen EinfluB des Gcbiets der FMR-Moden-pberschneidung hin.

On the FMR Theory of Metallic Amorphous Ferromagnets

“…damping term, which in our case of the linear solution is equivalent to the more general Gilbert damping term). This was shown in [15] (by means of numerical calculations) and later by [4,6,8 to 111 (by means of analytical calculations). The problem is governed by the existence (or nonexistence) of the cross-over behaviour in the FMR effect, which leads to a strong mixing of waves of electromagnetic and spin-wave nature inside the sample.…”

“…of crystalline nickel (Q p 0.34, fCR z 6.5 GHz). In the case of pure iron, (8), (8') would be fulfilled only in the far-infrared region of frequencies [6] (Q + 18, fCR 112 GHz). ') In [4], (26), in the square root, the sign of the term i20:C is to be changed to (-i2wiC); in [8].…”

“…damping constant 1, (8), (8') are well fulfilled, especially at higher frequencies. This is the case of many amorphous metglass-type alloys ( e g Fe,,Ni,,B2, [6] for 0 9 0.15, fCR = @,-,/2x % 4.6 GHz, or Fe,,B,, I171 for 52 + 0.25, f 9 12.2 GHz); or also e.g. of crystalline nickel (Q p 0.34, fCR z 6.5 GHz).…”

“…Ql2L2 ' E = G~/ Q is a frequency independent material parameter, the values of the factor F (of the parallel configuration) lie in the interval (0.5 to I), and condition (7b) implies (7a). qCR = qFR + 6q,, is the static magnetic field FMR cross-over point and QCR is the threshold cross-over frequency; at q = qCR and s2 = QcR the two complex energies (or K 2 ) of the electromagnetic wave and the Larmor spin wave are equal [4,6,81. 6qCR weakly decreases with increasing frequency due to the factor F. For illustration, one can rewrite (7a), (7b) in the natural quantities, by using (2) to (5), as Discussing the importance of the ECI influence on the FMR effect one can distinguish between two possible cases:…”

“…It is important to realize that the amorphous alloys generally show (in comparison with crystalline metals, e.g. with iron [6] and cobalt) smaller values of the electrical conductivity, magnetization, and exchange constant. This leads to some specific FMR behaviour of these alloys [6].…”