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The magnetization dynamics of nanoelements with tapered ends have been studied by micromagnetic simulations. Several spin-wave modes and their evolutions with the sharpness of the element ends are characterized. The edge mode localized in the two ends of the element can be effectively tuned by the element shape. Its frequency increases rapidly with the tapered parameter h and its localized area gradually expands toward the element center, and it finally merges into the fundamental mode at a critical tapered parameter h0. For nanoelements with h > h0, the edge mode is completely suppressed. The standing spin-wave modes mainly in the internal area of the element are less affected by the element shape. The shifts of their frequencies are small and they display different tendencies. The evolution of the spin-wave modes with the element shape is explained by considering the change of the internal field.

We present a new type of magnonic crystal consisting of a series of periodically distributed magnetic domain walls in a uniform strip. When spin waves propagate in such a structure, allowed and forbidden bands are formed due to translation symmetry and scattering of the spin waves at the domain wall boundaries caused by the dynamic stray field in the domain wall region. The control of the bandgap position in frequency and its width by the period of magnonic crystal and the domain wall width is investigated. It is found that the bandgap position decreases monotonously with the increase of the period or domain wall width, while the bandgap width displays an oscillated behavior. The origin of the oscillation of the bandgap width is discussed. This work may provide a new way of designing reconfigurable magnonic devices.