In this paper, the plane wave method is extended to include the diffuse interface in the calculation of the dispersion of spin waves in two-dimension magnonic crystals. The diffuse interfaces with linear and sinusoidal profiles of variation in the spontaneous magnetization and exchange constant are considered and the effects of the thicknesses and profiles of diffuse interfaces on the magnonic band gaps are investigated. The results show that the thicknesses and profiles of diffuse interfaces are clearly seen to play a significant role in determining the size and position of the magnonic band gaps in the both square and triangular lattices in the exchange interaction regime. The smooth (linear or sinusoidal) interface does not lead to disappearance of the band gaps, instead it may lead to larger band gaps than those in the model with sharp (infinitely thin) diffuse interface under certain conditions.
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