Spin-wave band gaps created by rotating square rods in triangular lattice magnonic crystals

Recently, magnonic crystals which are the magnetic counterparts of photonic crystals or phononic crystals are becoming a hot area of research. In this paper, band structure of two-dimensional magnotic crystal composed of square rods triangularly arranged are calculated by using the plane-wave expansion method. Spin-wave band structures of two-dimensional magnonic crystal composed of Fe triangularly arranged Fe in an EuO matrix. The results show that when the filling ratio f=0.4, only two absolute band gaps can be found in the case of θ=0°. The first gap appears between the first band and the second band, the second gap between the sixth band and the seventh band. However, the number of band gaps can be improved by rotating the square rods through θ=25°, there are eight absolute band gaps that can be found. The first gap appears between the first band and the second band, the fifth gap between the sixth band and the seventh band. The new band gaps can be found, the second gap appears between the third band and the fourth band, the third gap between the fourth band and the fifth band, the fourth gap between the fifth band and the sixth band, the sixth gap between the seventh band and the eighth band, the seventh gap between the eighth band and the ninth band, the eighth gap between the ninth band and the tenth band. These results show that it is possible to create spin-wave gaps by rotating square rods in a two-dimensional magnotic crystal. The numerical results of the normalized gap width ΔΩ/Ωg of the first gap between the first band and the second band always changes with filling fraction f and rotational angles θ. When f=0.6 we calculated the first normalized gap width ΔΩ/Ωg. when f=0.6 and θ=0°, the first gap width ΔΩ=0.812(μ0ω/g) and the normalized gap width ΔΩ/Ωg=0.9187. The results show that from the first normalized gap widths the largest one can be found when f=0.6 and θ=5°, the first gap width ΔΩ=0.937(μ0ω/g) and the normalized gap width ΔΩ/Ωg=0.9591. The results show that the numerical, rotating square rods can make the low frequency band gap widen in the triangular lattice of two-dimensional magnonic crystal.