Ab initio phase diagram of BaTiO$_3$ under epitaxial strain revisited

TL;DR

This study revisits the phase diagram of BaTiO$_3$ under biaxial strain using first principles, revealing complex domain structures and phase sequences that depend on strain conditions and lattice anisotropy.

Contribution

It provides a detailed analysis of BaTiO$_3$'s phase behavior under various strain conditions, including non-uniform strain, using an effective Hamiltonian approach.

Findings

Identification of multi-domain structures under tensile strain.

Recovery of bulk-like phase sequences locally in strained systems.

Extension of results to anisotropic in-plane strain conditions.

Abstract

We revisit the phase diagram of BaTiO$_3$ under biaxial strain using a first principles-based effective Hamiltonian approach. We show that, in addition to the tetragonal ($c$), quasi-rhombohedral ($r$), and quasi-orthorhombic ($aa$) ferroelectric phases, that have been discussed previously, there are temperature and strain regions, in particular under tensile strain, where the system decomposes into multi-domain structures. In such cases, the strained system, at least on a local level, recovers the same phase sequence as the unclamped bulk material. Furthermore, we extend these results from the case of "uniform" biaxial strain to the situation where the two in-plane lattice constants are strained differently and show that similar considerations apply in this case.