Mechanism of the Anomalous Dependence between Spin-Orbit Coupling and Dimensionality in Lead Halide Perovskites

The spin-orbit coupling (SOC) effect of lead (Pb) atoms is a consequential attribute of the unique optoelectronic and defect properties of lead halide perovskites (LHPs). It has been found that the SOC effect varies significantly as the structural dimensionality changes with an anomalous dependence; i.e., while the SOC strength monotonically decreases as structural dimensionality decreases from three-dimensional (3D) to two-dimensional (2D) and then to one-dimensional (1D), the zero-dimensional (0D) SOC strength is greater than the 1D SOC strength. The underlying mechanism of such a SOC dimensionality dependence anomaly remains elusive. In this work, we show that Pb 6p energy splitting increases from 3D to 2D and to 1D LHPs due to the increased degree of distortion, leading to a reduced SOC strength. However, the degree of distortion decreases for the 1D to 0D transformation, resulting in reverse SOC enhancement. The mechanism described in this work can be employed to regulate the SOC effect in the design of perovskite materials.