Structural Distortions and Ferroelectricity in Antiperovskite Oxides with Tetrel Elements

TL;DR

The paper addresses crystal-structure trends in antiperovskite oxides X$_3$TtO with tetrel A and alkaline earth B, using first-principles calculations to extend tolerance-factor concepts to antiperovskites and to assess ferroelectricity via cation ordering and heterostructuring. It demonstrates that octahedral rotations are governed by the tolerance factor, with ground states often orthorhombic and no intermediate $a^0a^0c^-$ phase, explained through a Landau free-energy framework. The work further shows that hybrid improper ferroelectricity can arise in double antiperovskites under layered A-site order or strain, suggesting practical routes to polar states in these materials, though many DAPs are metallic or have small gaps. A detailed covalent bonding analysis using COHP reveals substantial A–X and X–X mixing, highlighting electronic structures that differ markedly from oxide perovskites and potentially affecting coupling to topology and superconductivity in AP systems.

Abstract

Antiperovskites share the same structure as perovskites, but allow completely different chemistries and nominal charge states of anions to be stabilized. This gives rise to many interesting phenomena, including septet superconductivity and topological crystalline insulating phases in these systems. Despite this, the work on the crystal structural trends in these compounds are more limited compared to perovskites. In this study, we consider the family of antiperovskite oxides with tetrel elements (Si, Ge, Sn, Pb) and alkaline earth metals (Ca, Sr, Ba), and perform a detailed study of their crystal structures using first principles density functional theory. We show how tolerance factor arguments can be constructed to predict their structure in a way parallel to the perovskites, and furthermore, how heterostructuring (or cation-order) can be used to induce ferroelectricity in these systems which may provide an experimental knob to modify electronic structure. We conclude by a discussion of the electronic structure of antiperovskites, and show that they display interesting trends not observed in regular perovskites, including significant antibonding interactions between face-center ions, which might need to be taken into account building effective electronic models of these compounds.

Figures (17)

• Figure 1: The crystal structures of cubic (a) perovskite, BaSnO$_3$, and (b) AP, Ba$_3$SnO.
• Figure 2: Octahedral rotations in perovskites: (a) $a^+b^0b^0$ and (b) $a^-a^-c^+$ rotation patterns.
• Figure 3: Phase diagram of octahedral rotations. The colored areas represent $Pbnm$, $Ibmm$ or $Pm\bar{3}m$ phases, predicted by experimental results and DFT calculations. The phase transition temperatures are denoted by black triangles. Below them are the details of DFT calculations: The energies of tilted structures are given relative to energies of cubic phase $Pm\bar{3}m$. The experimental data are reproduced from nuss2015tilting.
• Figure 4: The phonon dispersion relations (left) and total phonon density of states (right) for cubic (a) Ba$_3$GeO, (b) Ba$_3$PbO, (c) Sr$_3$SnO. Unstable modes at high symmetry points M and R, which are discussed in the text, are denoted by red circles.
• Figure 5: (a)-(c) the atom-resolved phonon band structures for germanium APs; The oxygen band predicted by the model in (d) is overlaid; The green and blue dots label the polar mode and the breathing mode, respectively. (d) Simplified model for oxygen vibration sampled on a cubic lattice. $C_1$ represents the force constant between two adjacent oxygen atoms, and $C_0$ represents the restoring force constant in order to avoid linearity near the $\Gamma$ point. (e) Schematic for polar modes in proper ferroelectric perovskites. (f) Schematic for the breathing mode.