Rules and mechanisms governing octahedral tilts in perovskites under pressure

The rotation of octahedra (octahedral tilting) is common in ABO(3) perovskites and relevant to many physical phenomena, ranging from electronic and magnetic properties, metal-insulator transitions to improper ferroelectricity. Hydrostatic pressure is an efficient way to tune and control octahedral tiltings. However, the pressure behavior of such tiltings can dramatically differ from one material to another, with the origins of such differences remaining controversial. In this paper, we discover several new mechanisms and formulate a set of simple rules that allow us to understand how pressure affects oxygen octahedral tiltings via the use and analysis of first-principles results for a variety of compounds. Besides the known A-O interactions, we reveal that the interactions between specific B ions and oxygen ions contribute to the tilting instability. We explain the previously reported trend that the derivative of the oxygen octahedral tilting with respect to pressure (dR/dP) usually decreases with both the tolerance factor and the ionization state of the A ion by illustrating the key role of A-O interactions and their change under pressure. Furthermore, three new mechanisms/rules are discovered, namely that (i) the octahedral rotations in ABO(3) perovskites with empty low-lying d states on the B site are greatly enhanced by pressure, in order to lower the electronic kinetic energy; (ii) dR/dP is enhanced when the system possesses weak tilt instabilities, and (iii) for the most common phase exhibited by perovskites-the orthorhombic Pbnm state-the in-phase and antiphase octahedral rotations are not automatically both suppressed or both enhanced by the application of pressure because of a trilinear coupling between these two rotation types and an antipolar mode involving the A ions. We further predict that the polarization associated with the so-called hybrid improper ferroelectricity could be manipulated by hydrostatic pressure by indirectly controlling the amplitude of octahedral rotations.