By means of the plane wave method, we study nonuniform, i.e., mode- and k-dependent, effects in the spin-wave spectrum of a two-dimensional bicomponent magnonic crystal. We use the crystal based on a hexagonal lattice squeezed in the direction of the external magnetic field wherein the squeezing applies to the lattice and the shape of inclusions. The squeezing changes both the demagnetizing field and the spatial confinement of the excitation, which may lead to the occurrence of an omnidirectional magnonic band gaps. In particular, we study the role played by propagational effects, which allows us to explain the k-dependent softening of modes. The effects we found enabled us not only to design the width and position of magnonic band gaps, but also to plan their response to a change in the external magnetic field magnitude. This allows the reversible tuning of magnonic band gaps, and it shows that the studied structures are promising candidates for designing magnonic devices that are tunable during operation.
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