Spin waves (SWs) in magnetically ordered media inherently exhibit rich nonlinear dynamics, giving rise to integer harmonic generation under driven conditions. Understanding and controlling these nonlinear harmonics is essential for both fundamental spin-wave physics and practical applications based on nonlinear wave responses. Here we present a theoretical analysis of nonlinear harmonic generation in exchange-dominated propagating SWs based on the Landau-Lifshitz-Gilbert equation. We examine two configurations, one with the bias field aligned perfectly along the anisotropy easy axis and the other with the field tilted by a small angle. Under the steady-state plane-wave assumption, we derive quantitative relations for the first-, second-, and third-order harmonics in both transverse and longitudinal spin-wave components. Our analysis reveals that elliptical precession induces odd-order harmonics in the transverse components, whereas tilting the precession axis leads to the appearance of even-order harmonics. Numerical simulations of spin-wave propagation in a thin magnetic film are performed to confirm the accuracy and validity range of the derived integer-harmonic relations. These results deepen the understanding of nonlinear dynamics in exchange-dominated SWs and offer theoretical insights for spin-wave-based nonlinear signal processing and computing.

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• Neuromorphic computing
• Spin waves
• Nonlinear waves
• Chaos & nonlinear dynamics
• Landau-Lifschitz-Gilbert equation