^{1}

^{1}

^{1}

^{1}

Spin waves in 2D periodic magnetic nanocomposites are studied by means of the plane wave method. The effect of the ellipticity and in-plane rotation of the scattering centers on the band structure is investigated, to indicate new possibilities of fine tuning of spin-wave filter passbands.

Magnetic composites with a structure modulated periodically on the nanoscale are the subject of a very intensive research activity, and the interest in their properties is increasing [

The most frequently mentioned of the numerous potential applications of MCs include microwave resonators, magnonic waveguides, spin-wave emitters, and filters [

In this study we examine the possibilities of modeling the spin-wave spectrum of 2D MCs that could be used for fine tuning of spin-wave filter passbands [

Figure

(a) Schematic view of the 2D MC under consideration, section in the plane of periodicity. (b) High-symmetry line over the 2D Brillouin zone for ellipses arranged in a square lattice.

We shall consider in-plane propagation of spin waves, that is, their propagation in the plane of periodicity, in 2D MCs as described above. Thus, the wave vectors to be considered are limited to the Brillouin zone of the 2D lattice. Figure

Our theoretical approach is based on a set of equations including the linearized Landau-Lifshitz equation and Maxwell’s magnetostatic equations [

Figure

Ten lowest bands in the spin-wave spectrum of a 2D Co/Fe composite with lattice constant (a) 50 nm and (b) 100 nm, calculated along the high-symmetry line in the 2D Brillouin zone (cf. Figure

Figure

(a), (c) Three lowest magnonic gaps (shaded) versus rod ellipticity

Also for rods rotated by 45° (Figure

In a Co/Fe composite with a filling fraction of 0.5 and rods unrotated in the plane of periodicity (the major semiaxis following the

The same as in Figure

A completely different behavior of the spin-wave spectrum is seen for the same filling fraction (

In the 2D magnetic composites considered in this paper, with Co rods embedded in an Fe matrix, the increase in importance of the magnetostatic interactions results in the formation of band gaps in the spin-wave spectrum. These magnonic gaps are destroyed as the exchange interactions begin to play a dominant role. On the other hand, the increase in importance of the exchange interactions not only results in a widening of the bands, but also, consequently, causes the possible gaps to move towards higher frequencies. In contrast, when the magnetostatic interactions gain in importance at the cost of the exchange interactions, the frequency range in which magnonic gaps will occur lowers substantially. This finding is consistent with the results obtained for 2D composites with an EuO matrix [

The use of rods in the shape of elliptic cylinders as scattering centers in 2D magnetic composites implies the introduction of two addition structural parameters: the cross-sectional ellipticity of the rods and the angle of their rotation in the plane perpendicular to the rod axis (the plane of spin-wave propagation). In contrast to the lattice constant, a change of which will strongly modify the spin-wave spectrum, these new parameters allow fine tuning of the width and position of the bands and gaps. For specific in-plane rotation angles, changing the rod ellipticity will modify the position of a band without changing its width or cause two adjacent bands to shrink substantially without affecting the width of the gap between them. Thus, an appropriate use of rods of elliptical cross section offers additional possibilities in the design of spin-wave filters with precisely adjusted passband.

Those results were presented at 18th International Conference on Composite Materials, Jeju Island, Korea. The research leading to these results has received funding from the European Community’s Seventh Framework Programme (FP7/2007-2013) under Grant Agreement no. 228673 for MAGNONICS project.