  The hybrid organic inorganic perovskites (HOIPs) have attracted much
attention for their potential applications as novel optoelectronic devices.
Remarkably, the Rashba band splitting, together with specific spin orientations
in k space (i.e., spin texture), has been found to be relevant for the
optoelectronic performances. In this work, by using first principles
calculations and symmetry analyses, we study the electric polarization,
magnetism, and spin texture properties of the antiferromagnetic (AFM) HOIP
ferroelectric TMCM_MnCl3 (TMCM = (CH3)3NCH2Cl, trimethylchloromethyl ammonium).
This recently synthesized compound is a prototype of order disorder and
displacement-type ferroelectric with a large piezoelectric response, high
ferroelectric transition temperature, and excellent photoluminescence
properties [You et al., Science 357, 306 (2017)]. The most interesting result
is that the inversion symmetry breaking coupled to the spin orbit coupling
gives rise to a Rashba-like band splitting and a related robust persistent spin
texture (PST) and/or typical spiral spin texture, which can be manipulated by
tuning the ferroelectric or, surprisingly, also by the AFM magnetic order
parameter. The tunability of spin texture upon switching of AFM order parameter
is largely unexplored and our findings not only provide a platform to
understand the physics of AFM spin texture but also support the AFM HOIP
ferroelectrics as a promising class of optoelectronic materials.
