Curvature-induced spin-wave dynamics in Ni₃₀Co₇₀magnetic nanotubes: angular ferromagnetic resonance, multi-mode...

Curvilinear magnetism offers a powerful route to engineer spin-wave phenomena beyond the limitations of planar architectures. In Curvilinear systems, geometry itself acts as an active control parameter. Magnetic nanotubes (MNTs) represent an archetypal three-dimensional (3D) platform. In MNTs, curvature induces emergent anisotropies, symmetry breaking, and nonreciprocal spin-wave transport without relying on interfacial Dzyaloshinskii-Moriya interactions. In this manuscript, we investigate spin-wave dynamics in thick-walled Ni₃₀Co₇₀MNTs using broadband, angular-dependent ferromagnetic resonance spectroscopy. We observe pronounced splitting and excitation of spin-wave modes that are absent in thin shells and planar films. The angular evolution of the spectra exhibits a maximum mode splitting nearφH=600. These modes arise from a competition between short-range exchange and curvature-enhanced dipolar interactions. Comparison of the measured resonance field separations with theoretical nanotube spin-wave spectra yields effective spin-wave wave-vectors (ksw) in the range of∼0.25-0.52 nm^-1. These values are in excellent agreement with existing theoretical predictions and BLS measurements on nanotubes. Our results provide ensemble-level experimental evidence of curvature-induced lifting of multi-mode excitation, and spectral asymmetry in MNTs. Furthermore, the present work advances both the fundamental understanding of spin-wave physics in 3D shells and the realization of reconfigurable, low-loss magnonic circuitry based on curvilinear nanomagnets.