Strain-tuned properties of hybrid improper ferroelectric superlattices through first-principles calculations and machine learning

We have performed first-principles density functional theory (DFT) calculations and machine learning (ML) to investigate the effect of biaxial strain on ferroelectric and magnetic properties of hybrid improper ferroelectric (LaFeO₃)₁ /(LnFeO₃)₁ superlattices (SL) where Ln= La-Lu and Y. In Pnma symmetry trilinear coupling between three phonon modes described as F ~ α Q_T Q_R Q_P (where α is the coupling coefficient and Q_T, Q_R and Q_P are tilt, rotation of BO₆ octahedra and polar distortion, respectively), establishes the polar space group and non-cancelation of the layered polarization give rise to net polarization. Here, we have discovered a recipe to calculate coupling coefficients between the participating modes and discussed the effect of strain on the coupling constants. We report that strain can enhance the polarization considerably and can change the easy magnetization axis. Finally, using ML, we have predicted the change in polarization upon strain. Our prediction of change in polarization by ML is in excellent agreement with the DFT calculations (Ref. Monirul et. al., Phys. Rev. B 101, 054101(2020)).