We investigate analytically the occurrence of magnonic defect states in the exchange regime for the system geometry with the defect linking two semi-infinite superlattices at the same symmetry points. The frequency ranges forbidden and allowed to defect states are determined in the low-frequency region. Non-overlapping frequency ranges allowed to either even or odd defect states are found to occur within each forbidden gap in higher frequencies. Our semi-analytical calculations of the dispersion relation based on the solutions obtained in the matching procedure are supported by the computed transmission spectra.
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