Toward ultra-fast spintronics with ferromagnets: spin inertia, nutational spin waves, and auto-oscillations

The coupling of spins to other degrees of freedom, such as electrons and the lattice, effectively enhances the inertia of spin motion. A striking consequence of spin inertia is the emergence of an ultra-high-frequency nutational mode, coexisting with the conventional GHz-frequency precessional dynamics [1,2]. Recent experimental confirmation of this phenomenon has established 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 [1] and discuss their potential for future ultra-high-frequency applications. Finally, we reveal parallels between spin dynamics in ferrimagnets and inertial ferromagnets, deriving an isomorphism that lays the foundation for synergistic knowledge transfer between these research domains.

[1] R. Rodriguez, M. Cherkasskii, Rundong Jiang, R. Mondal, A. Etesamirad, A. Tossounian, B.A. Ivanov, I. Barsukov. Spin inertia and auto-oscillations in ferromagnets. Phys. Rev. Lett. 132, 246701 (2024)

[2] M. Cherkasskii, I. Barsukov, R. Mondal, M. Farle, A. Semisalova. Theory of inertial spin dynamics in anisotropic ferromagnets. Phys. Rev. B 106, 054428 (2022)