A Computational Method to Estimate Spin-Orbital Interaction Strength in Solid State Systems

Spin–orbit coupling (SOC) drives interesting and non-trivial phenomena in solid-state physics, ranging from topological to magnetic to transport properties. A thorough study of such phenomena often requires effective models where the SOC term is explicitly included. However, the estimation of SOC strength for such models mostly depends on the spectroscopy experiments which can only provide a rough estimate. In this work, we provide a simple yet effective computational approach to estimate the onsite SOC strength using a combination of the ab initio and tight-binding calculations. We demonstrate the wider applicability and high sensitivity of our method by estimating SOC strength of materials with varying SOC strengths and the number of SOC active ions. As examples, we consider strongly correlated, topological, and semiconducting materials. We show that the estimated strengths agree well with the proposed values in the literature lending support to our methodology. This simplistic approach can readily be applied to a wide range of materials.