Hysteretic Excitation in Non-collinear Antiferromagnetic Spin-Torque Oscillators: A Terminal Velocity Motion Perspective

Abstract: We present a theoretical framework for non-collinear antiferromagnetic spin torque oscillators (NC-AFM STO) by unifying spin dynamics under the Poisson Bracket formalism. Shifting from traditional torque-based descriptions to an operational symmetry perspective, we develop two complementary viewpoints: a vector perspective identifying infinite degenerate Rigid Body Precession (RBP) states where exchange energy depends solely on the total magnetic momentum, and a particle perspective decomposing dynamics into Center-of-Mass (CM) translation and Relative Motion (RM) oscillation. Using time-dependent rotational and translational transformation techniques, we analytically resolve the rapid (~10 ps) transient evolution into a stable RBP state driven by SOT and damping. We demonstrate that the out-of-plane anisotropy (OPA) lifts the exchange degeneracy, triggering a long-term (~1 ns) oscillatory decay toward a steady state characterized by uniform spin z-components and a 120-degree inter-spin locking angle. This state is accurately governed by our Terminal Velocity Motion (TVM) model [arXiv:2305.14013], where exchange coupling transforms into kinetic energy with a light effective mass. The model precisely predicts SOT-driven transients, hysteretic excitation, and the dynamic phase diagram. Finally, we account for the sub-critical current regime mismatch by identifying a 'Rigid-Body Breaking' effect: a surge in effective friction caused by the self-resonance of RM variables induced by CM translation, mediated by the in-plane anisotropy (IPA).