Role of Jahn-Teller distortion in the relative stability between the black and yellow phases of transition metal doped CsSnI3 perovskites

Perovskite-based materials $({ABX}_{3})$ show promise for photovoltaic applications; however, commercial use still encounters challenges, specifically $\mathrm{Pb}$ toxicity and structural instabilities of the active phases. A potential lead-free compound is ${\mathrm{CsSnI}}_{3}$; nonetheless, the photoinactive yellow phase is energetically more favorable than the photoactive black phase. An undesired $\text{black}\ensuremath{\rightarrow}\text{yellow}$ phase transition implies structural instabilities, possibly explained by the Goldschmidt tolerance factor of $0.84$. In this study, we employ theoretical calculations to investigate the impact of substitutional bivalent doping in the $B$ sites of ${\mathrm{CsSnI}}_{3}$ with $3d$ transition metals $(TM)$ on tuning the relative energetic stability between the black and yellow phases. Our calculations are based on density functional theory, incorporating on-site Hubbard corrections for the $TM$ $3d$ states. We observe an inversion of the relative stability between the yellow and black phases for dopings with $\mathrm{Co}$, $\mathrm{Cu}$, and $\mathrm{Zn}$. We attribute the interphase relative energy to Jahn-Teller distortions at the doped octahedra, as the black and yellow phases exhibit distinct octahedral interconnections. For instance, the black phase has corner-shared octahedra, resulting in lower elastic costs for accommodating geometric distortions compared to the edge-shared octahedra in the yellow phase. The presented results highlight the influence of symmetry breaks on the stability of perovskite materials and have implications for other perovskite compositions.