The Critical Role of Itinerant Contributions to Orbital Angular Momentum Relaxation and Dynamics

Orbital angular momentum (OAM) is a promising degree of freedom for low-dissipation transport and magnetization control, yet its relaxation mechanisms remain controversial, with atomcentered approximations (ACA) predicting much shorter OAM diffusion lengths than experiments. We address this discrepancy using first-principles Lindbladian density-matrix dynamics, capturing electron-phonon scattering and itinerant OAM contributions, together with a first-principles parameterized tight-binding approach that separates the ACA and itinerant components. In MoS2,a strong-spin-orbit-coupling (SOC) system, orbital relaxation is multi-timescale, with fast intervalley redistribution followed by slower decay coupled to the spin. In weak-SOC silicene, spin and orbital dynamics decouple; an electric field tunes spin relaxation while leaving orbital lifetimes unchanged. In both materials, ACA orbital lifetimes are at least one order of magnitude shorter than itinerant ones, due to ultrafast precession driven by crystal-field splitting, absent from the itinerant component. These results demonstrate that going beyond atom-centered models is essential for describing orbital relaxation and diffusion.