Optical orientation of excitons and charged carriers in MAPbI$_3$ perovskite single crystals in the orthorhombic phase

Optical orientation of exciton and carrier spins by circularly polarized light is the basic phenomenon in the spin physics of semiconductors. Here, we investigate spin orientation in MAPbI3 lead halide perovskite crystals at the cryogenic temperature of 1.6 K, where the material has an orthorhombic crystal structure. The recombination and spin dynamics of excitons and carriers are measured by time-resolved photoluminescence after circularly polarized excitation. The optical orientation of excitons reaches 85\%, which persists within their lifetime of 15-80 ps. This high orientation is maintained for excitation laser detunings from the exciton resonance to higher energies by up to 0.3 eV, then decreases and vanishes above 1.5 eV detuning. This indicates that the Dyakonov-Perel spin relaxation mechanism based on inversion symmetry breaking is inactive in MAPbI3 crystals with orthorhombic symmetry. The optical orientation of localized and spatially-separated electrons and holes results in 40\% circular polarization of their emission. Their contributions can be identified from the complex spin beats dynamics in transverse magnetic field. The dynamics analysis gives values of the Land\'e g-factors of 2.83 for electrons and 0.54 for holes. Also, the magnetic-field-induced polarization of excitons and carriers is analyzed in magnetic fields up to 6 T, showing that their spin relaxation times are longer than their lifetimes. Namely, for the excitons, the spin relaxation time exceeds the lifetime by a factor of 6. We model the dynamics of optical orientation degree for cumulative contributions of excitons and carriers and show that the exciton recombination dynamics can control these dynamics. The polarized emission of excitons and localized carriers, produced by their polarization on Zeeman-split levels in magnetic fields, is modeled.