Tailoring the electron and hole Land\'e factors in lead halide perovskite nanocrystals by quantum confinement and halide exchange

The tunability of the optical properties of lead halide perovskite nanocrystals makes them highly appealing for applications. Both, halide anion exchange and quantum confinement pave the way for tailoring their band gap energy. For spintronics applications, the Land\'e g-factors of electrons and hole are of great importance. By means of the empirical tight-binding and $\textbf{k}\cdot\textbf{p}$ methods, we calculate them for nanocrystals of the class of all-inorganic lead halide perovskites CsPb$X_3$ ($X = \text{I},\,\text{Br},\,\text{Cl}$). The hole g-factor as function of the band gap follows the universal dependence found for bulk perovskites, while for the electrons a considerable modification is predicted. Based on the $\textbf{k}\cdot\textbf{p}$ analysis we conclude that this difference arises from the interaction of the bottom conduction band with the spin-orbit split electron states. The model predictions are confirmed by experimental data for the electron and hole g-factors in CsPbI3 nanocrystals placed in a glass matrix, measured by time-resolved Faraday ellipticity in a magnetic field at cryogenic temperatures.