Orbital Hall conductivity and relaxation in thin films with variable disorder

Electric-field-induced orbital angular momentum has emerged as a fundamental electronic degree of freedom in solid-state devices. It complements the spintronic functionalities used to sense and manipulate magnetic states. However, how orbital angular momentum evolves and relaxes in conductors with various degrees of structural and thermal order remain poorly understood. Here we demonstrate that the orbital Hall effect and orbital relaxation are robust and quantifiable in strongly disordered Mn thin films up to single-crystalline α-Mn. Using orbital Hanle magnetoresistance as a probe, we find that the orbital Hall conductivity scales linearly with electrical conductivity in the hopping-dominated regime from amorphous to polycrystalline films. This reveals a scaling behaviour analogous to the anomalous and spin Hall effects in bad metals. The orbital relaxation time, of the order of picoseconds, decreases with increasing crystalline order. Temperature-dependent measurements identify distinct relaxation channels. We observe in disordered films a crossover from on-site orbital dephasing to interorbital hopping with increasing temperature. In single-crystalline α-Mn, orbital relaxation is dominated by Elliott-Yafet-type scattering. Our findings establish orbital angular momentum as a structurally resilient degree of freedom and elucidate its relaxation dynamics across crystalline and disordered systems, thus enabling orbital control in different classes of materials.