Controlling the direction of the magnetization by an electric field in multiferroics that are both ferroelectric and strongly ferromagnetic will open the door to the design of the next generation of spintronics and memory devices. Using first-principles simulations, we report that the discovery that the ${\mathrm{PbTiO}}_3/\mathrm{LaTi}{\mathrm{O}}_3$ ($\mathrm{PTO}/\mathrm{LTO}$) superlattice possesses such highly desired control, as evidenced by the electric-field-induced rotation of 90° and even a possible full reversal of its magnetization in some cases. Moreover, such systems also exhibit Jahn-Teller distortions, as well as orbital orderings, that are switchable by the electric field, therefore making $\mathrm{PTO}/\mathrm{LTO}$ of importance for the tuning of electronic properties too. The origin for such striking electric-field controls of magnetization, Jahn-Teller deformations, and orbital orderings resides in the existence of three different types of energetic coupling: one coupling polarization with antiphase and in-phase oxygen octahedral tiltings, a second one coupling polarization with antiphase oxygen octahedra tilting and Jahn-Teller distortions, and finally a biquadratic coupling between antiphase oxygen octahedral tilting and magnetization.

A novel strategy of band structure engineering of van der Waals heterostructure is proposed using a ferroelectric (FE) clamped sandwich structure from first principles. The validity of the strategy is demonstrated in the sandwich structure of ${\mathrm{In}}_2{\mathrm{Se}}_3$/bilayer-${\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$ (${\mathrm{In}}_2{\mathrm{Se}}_3/\mathrm{bi}-{\mathrm{CrI}}_3/{\mathrm{In}}_2{\mathrm{Se}}_3$) made by ferroelectric ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers and semiconducting bilayer (SB) ${\mathrm{CrI}}_3$. Four states with different band structures in the FE/SB/FE sandwich structure are obtained by switching the FE polarization in the top and bottom ${\mathrm{In}}_2{\mathrm{Se}}_3$ layers. Two of the states possess spin-splitting semiconducting band structures with opposite spin channel in conduction bands which are generated from a spin-degenerated band structure of the ${\mathrm{CrI}}_3$ bilayer, resulting in an electric field controllable and nonvolatile four states spin-field effect transistor. The strategy of using FE layers to engineer band structures and generate spin-splitting semiconducting band structure in van der Waals heterostructure opens a new route in two-dimensional electronics and spintronics.

High-melting-point oxides of chemical formula $AB{\mathrm{O}}_3$ with $A=\mathrm{Ca}$, Sr, Ba and $B=\mathrm{Zr}$, Hf are investigated as a function of hydrostatic pressure up to 200 GPa by combining first-principles calculations with a particle swarm optimization method. Ca- and Sr-based systems: (1) first undergo a reconstructive phase transition from a perovskite state to a novel structure that belongs to the post-post-perovskite family and (2) then experience an isostructural transition to a second, also new post-post-perovskite state at higher pressures, via the sudden formation of a specific out-of-plane $B\text{−}\mathrm{O}$ bond. In contrast, the studied Ba compounds evolve from a perovskite phase to a third novel post-post-perovskite structure via another reconstructive phase transition. The original characteristics of these three different post-post-perovskite states are emphasized. Unusual electronic properties, including significant piezochromic effects and an insulator-metal transition, are also reported and explained.

Two monoclinic C2/m phases and an insulator–metal transition were discovered in CsPbI₃ at high pressure. Furthermore, the largest piezochromic effect in the perovskites occurs in the non-Pv-Pnma phase of CsPbI₃ below 10 GPa.