Emergent Orbital Dynamics in Strongly Spin-Orbit Coupled Systems

Abstract: The interplay between spin and orbital degrees of freedom gives rise to a variety of emergent phases in correlated 4d and 5d transition-metal systems. Strong spin-orbit coupling (SOC) significantly alters Jahn-Teller (JT) physics, often suppressing static distortions or promoting dynamic fluctuations, thereby reducing or even quenching orbital polarization. While intersite hybridization is a fundamental aspect of crystalline solids, its role in shaping the dynamics of spin-orbit-entangled states has received comparatively little attention. Here, we show that electronic hopping can locally restore orbital polarization when the ground state is perturbed, even in the absence of static orbital order. Using a Matsubara lattice formalism, we analyze how local orbital perturbations propagate through correlated, spin-orbit-entangled systems. When intersite hopping is included, such perturbations induce short-range orbital polarization with a characteristic orthogonal response at nearest-neighbor sites. Although the energy scale of these hybridization-driven orbital reconstructions likely makes their detection challenging, they may still influence low-energy spectral features and interact with other excitations. These results underscore the importance of including orbital dynamics in the interpretation of spectroscopic data and provide a framework for understanding dynamical responses in spin-orbit-entangled materials.