Spin inertia, nutational spin waves, and auto-oscillations

Spin inertia establishes ferromagnets, with their advanced materials and spin engineering, as prime candidates for THz-frequency applications. Here, we experimentally investigate propagating nutational spin waves in ferromagnetic thin films, evaluate their dispersion relation, and discuss implications for the underlying mechanisms of spin inertia. Spin-torque-driven dynamics are central to many spin-based technologies, and to ultimately functionalize spin inertia, understanding its interplay with spin torque is essential. We develop a theoretical framework for precessional auto-oscillations in ferromagnets with spin inertia. We introduce the concept of nutational auto-oscillations and discuss their potential for future ultra-high-frequency applications. Finally, we reveal parallels between spin dynamics in ferrimagnets and inertial ferromagnets, which lays the foundation for synergistic knowledge transfer between these research domains. [1] R. Rodriguez et al. Spin inertia and auto-oscillations in ferromagnets. Phys. Rev. Lett. 132, 246701 (2024). [2] M. Cherkasskii et al. Theory of inertial spin dynamics in anisotropic ferromagnets. Phys. Rev. B 106, 054428 (2022).