Magnonic spectral gaps and discrete transmission in serial loop structures

In the frame of the long-wavelength Heisenberg model, the magnonic bandgaps and the selective transmission in a serial loop structure, made of loops pasted together with segments of finite length, are investigated theoretically. The loops and the segments are assumed to be one-dimensional ferromagnetic materials. Using a Green function method, we obtained closed-form expressions for the band structure and the transmission coefficients for an arbitrary value of the number N of loops in the serial loop structure. It was found that the gaps originated from the periodicity of the system. The width of these forbidden bands depends on the structural and compositional parameters. We also present analytical and numerical results for the transmission coefficient through a defective geometry where the length of one finite branch has been modified. It was demonstrated that the presence of this defect in the structure can give rise to localized states inside the gaps. We show especially that these localized states are very sensitive to the size of the loops and to the periodicity as well as to the length and the location of the defect branch.