Magneto-photonic and Magnonic Crystals Based on Ferrite Films – New Types of Magnetic Functional Materials

A new type of photonic crystals entitled “magnonic crystals (MC)” that exhibit forbidden gaps in the microwave spectrum of magnetostatic spin waves (MSW) are reported. The topography of the MCs that consist of two-dimensional (2-D) etched holes periodic structure in yttrium iron garnet films was studied by atomic force and magnetic force magnetometry. The propagation characteristics of spin waves in such 2-D MCs was measured and analyzed. Introduction During the last decade considerable efforts have been made in the sciences and technology for controlling or engineering the optical properties of the materials. For example, a number of artificially arranged materials were engineered to facilitate light propagation in particular direction or in specific regions only. Such materials also enable light to be localized in chosen channels or zones, or even prohibit the propagation of light completely. They are now known as photonic crystals [1]. Generally speaking, the photonic crystal (PC) is a material that possesses periodic index of refraction. A simple example of photonic crystals, also known as one-dimensional (1D) PC is a multilayered periodic structure [2]. In such structures there exist a range of frequencies for which the light (photon) propagation is prohibited. It was also demonstrated that such crystals can be made in two and three dimensions [3]. Such structures can have a complete photonic band gap, meaning that light is prohibited to propagate in any direction inside such a crystal. To realize a PC with a complete photonic band gap, the material must have both high refractive index and proper three dimensional structure. Similar to PC, another class of crystals known as phononic crystals [4] was also reported. These crystals possess the properties of PC but for acoustic waves (phonons) instead of light. There exists, however, still another possibility to control properties of PC by using the magnetic materials for magneto-photonic crystals [5, 6,]. Morover, it is possible to engineer magnetic materials where instead of light (or electromagnetic waves) spin waves (SW) are used as the carriers of information. Drawing an analogy from photonic and phononic crystals they may be called magnonic crystals (because magnons are the quasiparticles of spin waves). Magnetic 1-D periodic layered structures have also been studied for more than a decade since the giant magnetoresistive effect was discovered in the three-layer system containing the magnetic and nonmagnetic layers ([7]). Propagation of spin waves in ferromagnetic films with periodically and weakly varied parameters has been studied extensively [8-10]. On the other hand the spectra of spin waves in multilayered magnetic structures have also been studied for various wave types (dipole and exchange) for magnetic-non-magnetic, all-magnetic, ferroand antiferromagnetic lattices (see [1121] and references therein). In particular, the Green’s function formalism was used for description of spin waves spectra in multilayered structures. Barnas [16] developed the transfer matrix approach for description of spin waves modes in 1 D periodic structures. Gorobetz et al [17, 19] studied spectra in a stack structure with periodically modulated anisotropy. Ferromagnetic resonance and Advances in Science and Technology Vol. 45 (2006) pp 1355-1363 online at http://www.scientific.net © (2006) Trans Tech Publications, Switzerland Online available since 2006/Oct/10 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 130.203.133.34-17/04/08,10:17:38) standing spin waves spectra in a multilayered stack consisting of ultrathin Fe and Ni layers were also studied experimentally [13, 20, 21]. However, the resonance properties of a traveling spin wave in such structure can differ considerably from that of standing spin wave modes. It has been demonstrated that such waves (at the wavelength of submicron) can be excited in inhomogeneous magnetic films at microwave frequencies [22]. Another possibility is to engineer an anisotropic magnetic photonic crystal [23]. A review paper on magnetic photonic crystal containing a detailed list of references was recently published [24]. In this work we treat the problem of spin wave propagation in periodic structures from the point of view different from those previously employed, namely, in the approach used in investigating the properties of photonic and phononic crystals. Therefore, we first review and calculate the spectra of MSW propagation in the 2-D ferromagnetic film periodic structure, and then implement the 2-D MCs and measure its propagation characteristics. Theoretical part The simplest one-dimensional magnonic crystal is a strictly periodic multilayer structure consisting of magnetic layers with different magnetizations, or a similar structure consisting of magnetic and nonmagnetic layers. The realization of such a structure is rather difficult, because the periodicity of the magnetic properties of layers can be violated in the course of the layer growth, which will break the magnonic crystal structure possessing a magnonic bandgap. From the point of view of application, a two-dimensional magnonic crystal formed on the basis of ferromagnetic films seems to be preferable. This crystal represents a ferromagnetic waveguide with two-dimensional magnetization inhomogeneities. The inhomogeneities can be represented by, e.g., implanted elements of another ferromagnet or holes made in the structure. We consider here properties of magnetostatic spin waves (MSW) propagating in a ferromagnetic film with two-dimensional periodically etched surface. Let us consider the upper surface of a ferromagnetic film described by the following equation x=d+ξ(y,z), где ξ(y,z)= dε cos(αQz)(ε1 e+ε1* e), (1) where d is the film thickness, d|ε1| is the amplitude of the surface non-uniformity in Y direction, h|ε| is the amplitude of the surface non-uniformity in Z direction, ε1* is complex conjugate to ε1, Q=2π / Λ and Λ is the structure period in Y direction, ), α=Λ / Λ1, Λ1 is the structure period in Z direction. In order to find the dispersion relation for MSW propagating in a ferromagnetic film with periodically uneven surface one should solve the set of Maxwell’s equations and Landau-Lifshitz equation for magnetization motion along with the boundary conditions for continuity of normal components of magnetic induction and tangential components of magnetic field at the surfaces of the film. The solution for magnetostatic potential and magnetic field, respectively, is found using the coupled wave method which was previously used for investigating of MSW propagation in 1D magnonic crystal (similar to the model of Kronig-Penney motion of electrons in a periodic potential) [24]. As a result of solution of a boundary problem the dispersion relation for a MSW propagating in a film with 2D non-uniformities was obtained as a function of various parameters (periods of the structure, external bias magnetic field H0, etc). Most important thing was found that the dispersion of the wave contains forbidden gaps, where the wave propagation is prohibited. These forbidden gaps form zone structure in dependence of the structure parameters. In Figure 1 we show the dispersion of the wave closely to the resonance frequency defined by the so-called Bragg diffraction condition when the MSW wavenumber is Λ π ≈ k , (2) where Λ is the period of the 2D lattice in the direction of the wave propagation. The following parameters of the film and structure were chosen d = 9 μm, d|ε1| = d|ε| = 1 μm, Λ = 150 μm, H0 = 380 Oe, Ω = 2.868 GHz (Bragg resonance frequency), saturation magnetization 4πM0 = 1750 G and kz = P/4, where P = π/Λ and ky and kz are the wavenumbers of the MSW in the Y and Z directions, 1356 11th International Ceramics Congress