Theoretical progress on the temperature dependence of magnetic moments in strong spin-orbit-coupled systems

Transition-metal compounds with strong spin-orbit coupling (SOC) have attracted significant attention due to their potential for hosting exotic magnetic states such as frustrated magnetism, as well as their promising optoelectronic applications in hybrid halides. In these systems, the pronounced SOC effects often lead to magnetic behaviors that can not be adequately described by the standard Curie-Weiss law. In this review, based on our recent investigations, we summarize progress on the temperature evolution of magnetic susceptibilities and magnetic moments in SOC-driven systems. We first outline the general background. Using perovskite compounds as representative examples, we then systematically introduce the microscopic origin of the temperature dependence of magnetic susceptibilities for d¹-d⁵ electronic configurations. We further discuss the evolution of magnetic moments and susceptibilities in systems based on magnetic clusters, such as dimers or trimers, and introduce modified Curie-Weiss fitting approaches that account for the temperature dependence of magnetic moments. Finally, we summarize current research trends and offer an outlook on potential future developments in this field.