Dipole Order in Halide Perovskites: Polarization and Rashba Band Splittings

ABX₃ (A = organic cation; B = Sn, Pb; and X = halogen) organohalide perovskites have recently attracted much attention for their photovoltaic applications. Such hybrid compounds are derived from the replacement of the inorganic monovalent metal element by an organic cation, for example, methylammonium ion (MA = CH₃NH₃⁺) and formamidinium ion (FA= ⁺HC(NH₂)₂). In particular, since the organic cations are polar, it is interesting to investigate their possible long-range ordering and the corresponding Rashba spin-split bands. In this work, by using density functional theory calculations, we estimate the ferroelectric polarization corresponding to a complete ordering of dipole moments for the optimized structures of 12 perovskite halides, with A = MA, FA; B = Pb, Sn; X = Cl, Br, I. The adiabatic path and functional mode analysis have been discussed for all cases. The calculated values of the polarization may be as high as a conventional inorganic ferroelectric compound, such as BaTiO₃. The concomitant inversion symmetry breaking, coupled to the sizable spin-orbit coupling of Pb and Sn, results in a fairly large Rashba spin-splitting effect for both valence and conduction bands. We highlight a rather anisotropic dispersion of spin-orbit split bands which gives rise to different Rashba parameters in different directions perpendicular to the polar axis in k-space. Furthermore, we found a weak and positive correlation between the magnitude of polarization and relevant spin-split band parameters. Since the mechanism for enhanced carrier lifetime in 3D Rashba materials is connected to the reduced recombination rate due to the spin-forbidden transition, our study could aid in the understanding of the fundamental physics of organometal halide perovskites and the optimization and design of materials for better performance.