Geometry-controlled spin-wave spectra and mode filtering in helicoidal permalloy nanowires

We investigate the role of helicoidal geometry in shaping the static and dynamic magnetic properties of three-dimensional permalloy nanowires using micromagnetic simulations. By systematically varying the number of turns (Formula presented) (Formula presented) and the relative thickness parameter (Formula presented) (Formula presented), we analyze the interplay between geometry, energetic stability, and spin-wave (SW) excitations. In the static regime, the total energy increases with (Formula presented) (Formula presented) due to enhanced long-range magnetostatic interactions induced by curvature, whereas increasing (Formula presented) (Formula presented) reduces the energy through a more homogeneous magnetization profile and weaker demagnetizing fields, leading to a robust equilibrium configuration governed by the helicoidal geometry. In the dynamic regime, discrete SW modes emerge, dominated by a collective excitation with strong intensity and weak dependence on (Formula presented) (Formula presented), while a systematic redshift of the resonance frequency is observed with increasing (Formula presented) (Formula presented), driven by modifications of the effective internal magnetic field. Importantly, we demonstrate that helicoidal geometry acts as an intrinsic spectral filter, selectively suppressing higher-order modes in hollow structures. These findings establish helicoidal nanowires as versatile platforms for controlling both the spectral and spatial characteristics of SW excitations, opening new opportunities for three-dimensional magnonic and spintronic applications.