Effects of point defect shapes on defect modes in two-dimensional magnonic crystals

• We introduce three kinds of point defects into two-dimensional magnonic crystals.
• The effects of different-shaped defects on defect modes are studied.
• The modes vary as shape of square or circular defect only for big filling fraction.
• The modes are dependent of the shape of rectangular defect.
• The double degenerate mode will split in a certain condition for rectangular defect.

Based on the plane-wave expansion method, the effects of point defect shapes on defect modes of spin waves in two-dimensional magnonic crystals are numerically investigated. The considered point defect bodies include square defect, circular defect and rectangular defect. For both cases of square defect or circular defect, the defect modes vary obviously as the shape of the defect body only for a bigger defect filling fraction. However, for the case of rectangular defect, the defect modes show a dependence on its shape even if the defect filling fraction is smaller, and the double degeneration of rectangular defect mode will split into two nondegenerate modes when the ratio of edge widths of the rectangular defect reaches a certain value. Besides, whether square defect or rectangular defect, the defect modes change with the orientation of the point defect localizing in the cell only for a bigger defect filling fraction. Such an approach of changing shape of point body may open up a new scope for engineering defect modes and band gaps of spin waves in two-dimensional magnonic crystals.