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We calculate the spin-wave spectra of two-dimensional composite materials consisting of periodic square arrays of parallel cylinders made of a ferromagnetic material embedded in a ferromagnetic background. Each material is described by its spontaneous magnetization M S and exchange constant A. An external static magnetic field is applied along the direction of the cylinders and both ferromagnetic materials are assumed to be magnetized parallel to this magnetic field. We consider the spin-waves propagation in the plane perpendicular to the cylinders. We reveal the existence of gaps in the magnon band structure of composite systems such as the periodic array of Fe cylinders in an EuO matrix. We investigate the existence of these gaps in relation to the physical parameters of the materials involved. We also study the influence of the lattice parameter ͑i.e., the square array periodicity͒ and the effect of the filling fraction of the cylinders on the magnon band structure. ͓S0163-1829͑96͒09626-9͔

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Yablonovitch's papers reported experimental evidence for the existence of an absolute frequency gap in the spectrum of electromagnetic waves propagating in a periodic dielectric structure (a photonic crystal). The possibility of the existence of complete energy gaps in the spectra of other excitations propagating in periodic macrostructures -by analogy to photonic crystals -was considered in a number of studies. In this work we investigated the magnon spectrum of a two-dimensional periodic composite consisting of infinitely long cylindrical ferromagnetic rods periodically embedded in a homogeneous medium with magnetic properties differing from those of the cylinders. We show that the magnonic spectrum of this composite structure exhibits frequency regions forbidden for magnon propagation, and those energy gaps are found to be sensitive to the exchange contrast between the constituent materials as well as to the contrast of their magnetizations; both the magnetization and the exchange contrasts become gap-creating factors. The widths of the respective gaps obtained in the magnonic spectra are studied as functions of different parameters characterizing the magnetic structure under investigation.

It had been shown recently that the calculated mαgnonic spectra of two-dimensional periodic ferromagnetic composites can present frequency ranges forbidden for the propagation of magnon excitations throughout the composite. However, those forbidden energy gaps were found to be highly sensitive to the exchange contrast between the component ferromagnetic materials but were very weakly sensitive to the contrast in spontaneous magnetizations of the two materials. Accordingly, in this paper we introduce a r.ew mathematical definition of the exchange field acting in inhomogeneous medium. With this new definition the present theory gives magnonic spectra reasonably sensitive to magnetization contrast, as they should be from the physical viewpoint; moreover, the magnetization contrast now becomes a gap-creating factor as well.PACS numbers: 75.50.GgWe consider a periodic structure composed of infinitely long cylinders made of a ferromagnetic material Α embedded in a ferromagnetic matrix B. The cylinders are assumed parallel to the x3-axis of Cartesian coordinates leading to the existence of a two-dimensional periodic square lattice in the (e 1 , x 2 )-plane (Fig. 1a). The composite is acted on in the x 3 -direction by a static magnetic field H0 ; the magnetization of the two materials Α and B are parallel to H0 . The lattice constant is denoted by α; the filling fraction f is defined as the ratio of the area of the cross-section of a cylinder and that of the two-dimensional elementary cell. The ferromagnetic materials A and B are characterized by two quantities: their spontaneous magnetizations MsA and MSB , and their exchange constants ΑΑ and ΑΒ, both dependent on the position vector x = (x 1 , x2) lying in the plane perpendicular to the axis of the cylinders (whereas all these four quantities are homogeneous in the g3-direction: