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This is the final version of the article. Available from the American Institute of Physics via the DOI in this record.Within the framework of the solid state theory, an expression for the spectrum of spin waves propagating in a thin magnetic nanowire curled into a helix (spiral) is obtained. Its modification under the effect of a periodic modulation of the helical pitch is analyzed. In particular, it is shown that the periodic modulation of the helix pitch leads to the appearance of band gaps in the spectrum of spin waves. The influence of the modulation depth of the helical pitch on a size of the first gap is considered. © 2013 American Institute of Physics.This work was supported in part by the project NoWaPhen (FP7 GA 247556)

An effect of the curvature induced anisotropy on the spectrum of spin waves in a curved magnetic nanowire