Microwave spectral analysis by means of nonresonant parametric recovery of spin-wave signals in a thin magnetic film

Abstract

We report on the storage and non-resonant parametric recovery of microwave signals carried by a dipolar surface spin-wave pulse in a thin ferrimagnetic film. The information about the intensity of the spectral components of the signal within a narrow frequency band is saved due to the excitation of a dipolar-exchange standing spin-wave mode across the film thickness and is afterwards restored by means of parametric amplification of this mode. The intensity of the restored signal measured for varying shifts between the signal carrier frequency and half of the pumping frequency, which is equal to the frequency of the standing mode, reveals information about the entire frequency spectrum of the input microwave signal.

Microscopic spin-wave theory for yttrium-iron garnet films

“…2 with Fig. 3 we conclude that for the samples used in experiments [1,2,3,4,5,8,9,10,11] the minimum of the dispersion is exactly in this range so that better analytical approximations are needed for a more accurate description of the magnon dispersion in the vicinity of the minimum.…”

“…3 is more accurate in the experimentally interesting regime of wave-vectors close to k min . Although rough estimates of the interactions vertices can be found in the literature [30], more accurate microscopic calculations which properly take into account the momentum-dependence of the vertices are needed in order to gain a better understanding of the role of spin-wave interactions in the experiments [1,2,3,4,5,8,9,10,11]. For example, it would be interesting to know the intrinsic damping of the lowest magnon mode for wave-vectors close to k min due to magnon-magnon interactions.…”

“…In order to proceed we have to keep in mind that a stripe with thickness d and width w is obviously not translationally invariant, so that we cannot simply use a full Fourier transform to diagonalize the Hamiltonian. Because in the experimentally studied samples [1,2,3,4,5,8,9,10,11] the width w of the stripe is much larger than the thickness d, we can assume that w is practically infinite, so that our system can be considered to have discrete translational invariance in the y-and z-directions. We may then partially diagonalizeĤ 2 in Eq.…”

“…[26,27]) and 20 magnetic ions in the primitive cell. Fortunately, on the energy scales relevant to experiments [1,2,3,4,5,8,9,10,11] only the lowest magnon band is important, so that we can describe the physical properties of YIG at room temperature in terms of an effective spin S quantum Heisenberg ferromagnet on a cubic lattice with lattice spacing [27] a = 12.376Å .…”

“…The existence of such a dispersion minimum has been predicted by Kalinikos and Slavin [6,7] within a phenomenological approach based on the Landau-Lifshitz equation. Unfortunately, such a phenomenological approach does not provide a microscopic understanding of correlation effects, which might be important to explain some aspects of experiments probing the non-equilibrium behaviour of the magnon gas in YIG [1,2,3,4,5,8,9,10,11]. This has motivated us to study this problem within the framework of the usual 1/S-expansion for ordered quantum spin systems, which is based on the bosonization of an effective microscopic Heisenberg model using either the HolsteinPrimakoff [12] or the Dyson-Maleev transformation [13,14], and the subsequent classification of the interaction processes in powers of the small parameter 1/S.…”