Optimization Of Band Gaps And Properties Of Defect States In Two-Dimensional Magnonic Crystals

Magnonic crystals (MCs) can be regarded as an artificial micro-nano periodic composite material, and its fundamental feature is that band gaps exists in the band structures of spin waves because of the modulation of the periodicity, so as to the spin waves which frequencies locate in the band gaps are forbidden to propagate in the magnonic crystals. The special property distinguishes the magnonic crystals from other general materials, and people can design different band gaps according to their requirements to make the spin wave locate in some certain areas or propagate along some certain directions so that the control for spin wave propagating in the magnonic crystals can be realized. Thus, it has been become a hotspot of current research, and these researches possess potential applications for the design of microwave filters, waveguide, switches, current controlled delay lines, sensors, spin-wave logical device, signal processor and so on.In this paper, the optimization of band gaps and the properties of defect states in two-dimensional (2D) magnonic crystals are mainly investigated, and the detailed contents are listed as follows:Firstly, based on spin-wave dynamics equation, the traditional plane-wave expansion (PWE) method and the improved plane-wave expansion method have been compared in detail by using Bloch theorem and Fourier expansion, and we found the latter is more practicable under the short-wavelength perturbations. So, we change the dynamics equation into the eigen equations of spin waves by using the improved plane-wave expansion method, and then the eigenvalues can be obtained numerically, and the spin-waves dispersions relation of K～Ω are also gained, which are the band structures of spin waves in magnonic crystals.Secondly, spin-wave band structures of two-dimensional magnonic crystals composed of Fe rods squarely arranged in a EuO matrix are theoretically calculated using the improved plane-wave expansion method, and the effects of rotating noncircular scattereres (square, rectangle and hexagon) on band gaps are discussed. The results indicate that it is possible to increase the width of the band gaps or to create new band gaps by rotating the noncircular rods, and the width of the band gaps is the largest under a certain filling fraction by rotating the square rods when the rods squarely arranged in a matrix. Such an approach may open up a new scope for engineering and optimizating band gaps of two-dimensional magnonic crystals.Thirdly, using the improved plane-wave expansion method under supercell approximation, localized properties of defect states in two-dimensional magnonic crystals with single point defects are studied, and the effects of shape (square, circular and rectangular rods) and size of the defect rods on defect states are also discussed when other regular scattereres of magnonic crystals have different shapes, such as square rods and circular rods. The studies show that spin wave is localized around the defect body and forbidden from propagating along other direction in the magnonic crystals. Furthermore, we have found that for the square or circular defect, the influence of the point-defect shape to the properties of the defect modes directly depends,on the magnitude of filling fraction of the point defect body, that is to say, the properties of the defect modes are independent of the shape of the defect for a smaller point defect body, contrarily, they are relevant for a bigger defect filling fraction. However, for the rectangular defect, the defect modes show a dependence on its shape regardless of the defect filling fraction, moreover, the double degenerate defect modes will split into two nondegenerate modes when the ratio of edge widths of the defect reaches a certain value.Finally, based on the study of single point defect, two point defects, multi-point defects and line defects also can be introduced into two-dimensional magnonic crystals, and the properties of the these defect states are investigated, respectively. For the case of coupling between two point defects, the defect modes are split due to the coupling between defect modes, and the splitting degree increases with the decreasing the distance between two defects, and the phase of precession of defect modes’magnetization distributions also varies as the distance. Moreover, the coupling of defect modes is stronger for the defects along (10) direction than the case of the (11) direction. For multi-point defects and line defects, spin waves of certain frequency can propagate along the direction of defects. The magnonic crystals with such properties can be used as the fabricating materials of the directional spin-wave filters or narrow band spin-wave waveguides.The above mentioned numerical results can provide theoretically some values for the applications of magnonic crystals into the fabricating materials of spin-wave devices.