# First-principles based Landau-Devonshire potential for BiFeO$_3$

## TL;DR

This paper introduces a first-principles computational method to accurately derive the Landau-Devonshire potential for BiFeO$_3$, focusing on the energy surface near the ground state to better understand its phase transitions.

## Contribution

It develops a novel approach using eigenvector-based configuration space to determine the Landau-Devonshire potential from first principles, improving the analysis of structural phase transitions.

## Key findings

- Successfully applied to BiFeO$_3$ to compute energy contributions
- Probes energy surface near the ground state more effectively
- Provides detailed insights into strain, polarization, and tilt degrees of freedom

## Abstract

The work describes a first-principles-based computational strategy for studying structural phase transitions, and in particular, for determination of the so-called Landau-Devonshire potential - the classical zero-temperature limit of the Gibbs energy, expanded in terms of order parameters. It exploits the configuration space attached to the eigenvectors of the modes frozen in the ground state, rather than the space spanned by the unstable modes of the high-symmetry phase, as done usually. This allows us to carefully probe the part of the energy surface in the vicinity of the ground state, which is most relevant for the properties of the ordered phase. We apply this procedure to BiFeO$_3$ and perform ab-initio calculations in order to determine potential energy contributions associated with strain, polarization and oxygen octahedra tilt degrees of freedom, compatible with its two-formula unit cell periodic boundary conditions.