An Analytical Theory of FMR in Bulk Metals (Parallel Configuration). II. Penetration Depths

Abstract

The general formulae for the penetration depths of the three waves, which are excited in a bulk ferromagnetic metal in the ferromagnetic resonance (FMR) region, are evaluated for parallel configuration and compared with the antiresonance skin-depth expression. The concept of the FMR "effective skin-depth'' is introduced.Die allgemeinen Formeln fur die Eindringtiefe der drei Wellen, welche in massiven ferromagnetischen Metallen im Bereich der ferromagnetischen Resonanz (FMR) angeregt werden, werden fur den Fall der parallelen Konfiguration ausgewertet und verglichen mit dem Ausdruck der Antiresonanz-Skindicke. Das Konzept der ,,Effektiven Skindicke" fur FMR wird eingefuhrt.

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

“…the quantity measured in the experiment) will be investigated as dependent on the static magnetic field intensity and for different values of the surface anisotropy constant K , and a t frequencies sufficient for the observation of the surface mode. The use of the analytical FMR theory [3,4,9,15,17,18] is appropriate in this case, because only K, values corresponding t o 6 up to 0.5 (see below and e.g, [9]) are considered.…”

On the FMR Theory of Metallic Amorphous Ferromagnets

“…The treatment and discussion of DRs in a simpler form (case 11, (9), (ll), (12)) brings a more detailed physical insight into the problem of the energy interchange (and damping) between waves in FMR (it will be applied for the evaluation of the surface impedance, i.e. the quantity measured in the experiment, in Section3).…”

“…Each pair of waves (described by the square of the propagation constants K i , n = 1, 2, 3) is composed of two waves with f K,, propagating in two opposite directions. In this paper, where bulk metals are investigated (and the approximation of the infinite half-space is used) only the waves with positive K , values (strongly damped [9]) are propagating from the irradiated air-metal boundary inside the sample.…”

“…The complex propagation constants K,, n = 1, 2, 3 are (see (6)) proportional to the complex wave vectors k, = k; + ig'" of the waves. We introduce here the relations for the penetration depth 6, [9] and for the wavelength 1, of the (mainly excited) electromagnetic wave (in the case of FMR of amorphous alloys) as where K', and K';" are expressed in (14a), (14b). In the FMR point, for y = yFR (neglecting C of order of unity, in comparison with ( U L ) -2 of order of lo5 to lo6) we get…”

An Analytical Theory of FMR in Bulk Metals (Parallel Configuration). IV. Exchange Dominated Surface Modes

“…the measurable quantity in the FMR experiment, were calculated as dependent on the static magnetic field intensity (and frequency), neglecting the direct ALSW contribution in (111, 6 t o 9) (the indirect influence of ALSW K, on Z is still present in both Larmor h,1,3, see (111,4,5)). Let us note that for the AR region [23] and for the main FMR mode the neglection of the anti-Larmor spin-wave (sometimes called surface spin wave [20]) direct contribution t o 2 is a very good approximation (of the order of magnitude or better, compared with the numerical, exact solution, e.g. [5]).…”