Nonreciprocal inertial spin-wave dynamics in twisted magnetic nanostrips

Abstract

We develop a theoretical framework for inertial spin-wave dynamics in three-dimensional twisted soft-magnetic nanostrips, where curvature and torsion couple with magnetic inertia to generate terahertz (THz) magnetic oscillations. The resulting spin-wave spectra exhibit pronounced nonreciprocity due to effective symmetry breaking arising from geometric chirality and inertial effects. We show that this behavior is governed by a curvature-induced geometric (Berry) phase, which we analytically capture through compact expressions for dispersion relations and spectral linewidths in both nutational (THz) and precessional (GHz) regimes. Topological variations, including Möbius and helical geometries, impose distinct wavenumber quantization rules, elucidating the role of topology in spin-wave transport. These results position twisted magnetic strips as a viable platform for curvilinear THz magnonics and nonreciprocal spintronic applications.

Figures (5)

• Figure 1: Sketch of a curved ultrathin strip. $(\bm e_1, \bm e_2, \bm e_3)$ is the local reference frame induced by the parametric representation $\bm r_S(u,v)$ as function of the curvilinear coordinates $(u,v)$.
• Figure 2: Helical spin wave rectified along the curvilinear abscissa $u$ of the strip axis.
• Figure 3: Examples of twisted nanostrips: (a) Möbius; (b) Helix. The color code represents spin wave oscillation amplitude at each location ranging from zero (blue) to maximum (red).
• Figure 4: Dispersion relations for Möbius strips with $n=-1$ (blue), $n=-2$ (green), $n=-3$ (red). Solid lines rely on eq.\ref{['eq:dispersion relation nutation']} (resp. eq.\ref{['eq:dispersion relation precession']}) in left (resp. right) panels, symbols refer to wavenumber quantization \ref{['eq:Moebius quantization']}.
• Figure 5: Comparison between group velocities of spin waves for Möbius strips with $n=-1$ (blue), $n=-2$ (green), $n=-3$ (red). Solid lines refer to $v_g(k)=\gamma M_s\partial \omega/\partial k$, dashed black lines correspond to the ultimete speed limit $v_g(k\rightarrow\pm\infty)=\pm\frac{\ell_\mathrm{ex}}{t_\mathrm{in}}$, symbols refer to wavenumber quantization \ref{['eq:Moebius quantization']}. Dashed purple line refers to $v_g(k)$ with $n=-3$, $\xi=0$ (no inertia). The insets magnify the regions around $k=0$.