An empirical approach to measuring interface energies in mixed-phase bismuth ferrite

In complex oxide heteroepitaxy, strain engineering is a powerful tool to obtain phases in thin films that may be otherwise unstable in bulk. A successful example of this approach is mixed phase bismuth ferrite (BiFeO3) epitaxial thin films. The coexistence of a tetragonal-like (T-like) matrix and rhombohedral-like (R-like) striations provides an enhanced electromechanical response, along with other attractive functional behaviors. In this paper, we compare the energetics associated with two thickness dependent strain relaxation mechanisms in this system: domain walls arising from monoclinic distortion in the T-like phase, and the interphase boundary between the host T-like matrix and tilted R-like phases. Combining x-ray diffraction measurements with scanning probe microscopy, we extract quantitative values using an empirical energy balance approach. The domain wall and phase boundary energies are found to be 113 $\pm$ 21 and 426 $\pm$ 23 mJ.m$^{-2}$, respectively. These numerical estimates will help us realize designer phase boundaries in multiferroics, which possess colossal responses to external stimuli, attractive for a diverse range of functional applications.