Core position-dependent gyrotropic and damping contributions to the Thiele equation approach for accurate spin-torque vortex oscillator dynamics

Understanding the nonlinear dynamics of magnetic vortices in spin-torque vortex oscillators (STVOs) is essential for their application in neuromorphic computing. Existing models either rely on the standard Thiele equation approach (TEA), which offer only qualitative predictions, or on micromagnetic simulations (MMS), which are computationally demanding. We present a refined Thiele approach that incorporates the deformation of the vortex profile for the evaluation of the gyrotropic and damping terms. In this manuscript, a more realistic ansatz of the vortex magnetization profile is introduced to extract these effective parameters semi-analytically. A method to extract the gyrotropic and damping terms directly from MMS is also presented. The resulting expressions are benchmarked against state-of-the-art analytical derivations, and reveal a damping anisotropy of the vortex core. This framework captures the essential nonlinearities of STVO dynamics with high fidelity at low computational cost, paving the way for predictive modeling of large-scale neuromorphic circuits based on STVOs.