RESUMEN
Recent experimental confirmation of spin inertia in ferromagnets positions this well-developed material class as a prime candidate for THz frequency applications. Spin-torque driven critical spin dynamics, such as auto-oscillations, play the central role in many spin-based technologies. Yet, the pressing question on spin inertia's effect on spin-torque driven dynamics in ferromagnets has remained unexplored. Here, we develop the theoretical framework of precessional auto-oscillations for ferromagnets with spin inertia. We discover and introduce the concept of nutational auto-oscillations and demonstrate that they can become pivotal for future ultrahigh frequency technologies. We conclude by revealing parallels between spin dynamics in ferrimagnets and inertial ferromagnets and derive an isomorphism that establishes a foundation for synergistic knowledge transfer between these research fields.