Curvature-Induced Magnon Frequency Combs

Abstract

Generating magnon frequency combs (MFCs) with tunable spacing via a single-frequency driving is crucial for practical applications but it typically relies on complex spin textures like skyrmions or vortices. Here, we theoretically and numerically demonstrate MFC generation in geometrically curved ferromagnetic thin films using single-frequency microwave excitation, without topological spin textures. We first show that the curvature transforms the planar ferromagnetic resonance into a localized, redshifted magnon bound state, which, under non-resonant driving, activates sequential three-magnon scattering processes assisted by the curvature-driven effective anisotropy and Dzyaloshinskii-Moriya interaction. It finally produces equally spaced, robust frequency combs with spacing exactly set by the bound mode frequency. Moreover, we find that the curvature gradient at the hybrid interface mimics an analog event horizon, with the bound state's redshift resembling gravitational effects in black hole physics. Micromagnetic simulations confirm these curvature-driven nonlinear phenomenon, unveiling a novel geometric strategy for controlling magnon interactions and advancing compact magnonic devices.

Figures (4)

• Figure 1: (a) Rotationally symmetric surface generated by revolving the curve in (b) about the $z$-axis. Black arrows depict the local orthonormal basis $(\mathbf{e}_s, \mathbf{e}_\chi, \mathbf{e}_n)$ of the curvilinear coordinate system. (b) Profile of the smooth curve $z(r)$ in the $r$-$z$ plane, with the central section ($r_1\leqslant r \leqslant r_1+r_2$) defined by a half-period cosine function of amplitude $R$. Arrows indicate the tangential and normal unit vectors at a point on the curve. The dashed cyan line represents the arc length $s$ measured from $r=0$.
• Figure 2: (a) Radial distribution of the ground-state polar angle $\Theta$ for various surface heights $R$. (b) Minimum polar angle $\Theta_{\min}$ versus $R$, with symbols from numerical calculations and red curve from analytical formula.
• Figure 3: (a) Spatial distribution of the effective potential $U_{\text{eff}}$ for various surface heights. (b) Profile of bound magnon states for different $R$. (c) Frequency of the curvature-induced magnon bound state versus the surface height, with symbols from numerical simulation and curve from analytical formula (\ref{['eq:Bound']}). (d) Magnon spectrum for $R = 45$ nm under a sinc-function field $h_0 \text{sinc}(\omega_c t)\hat{x}$ over the curved region ($r\leqslant r_1+r_2$) with cutoff frequency $\omega_c / 2\pi = 10$ GHz and amplitude $\mu_0 h_0 = 10$ mT. Inset: distribution of $\vartheta$ and $\phi$ in the $r$-$\chi$ plane for the bounded magnon mode at $0.65\ \text{GHz}$.
• Figure 4: (a) System response versus driving amplitude $\mu_0 h$ for fixed $R = 45$ nm; color indicates excitation amplitude. (b) Enlarged view near 10 GHz from (a). Inset: frequency of the magnon bound state as a function of the drive-field amplitude. (c) Driving-, sum- and difference-frequency peaks amplitudes versus driving field strength; inflection points indicate a 140 mT threshold, with dots from micromagnetic simulations, and curves from solutions of Eq. \ref{['eq:Numerical']}. (d) Threshold field versus surface height $R$: Blue points from simulations, red line from analytical fitting.