Using the Landau-Ginzburg-Devonshire approach, we predict the intrinsic instability of the ferroelectric-ferroelastic domain walls in the multiferroic $\mathrm{BiFe}{\mathrm{O}}_3$ emerging from the interplay between the gradient terms of the antiferrodistortive and ferroelectric order parameters at the walls. These instabilities are the interface analog of the structural instabilities in the vicinity of phase coexistence in the bulk, and so they do not stem from incomplete polarization screening in thin films or its spatial confinement, electrostrictive or flexoelectric coupling. The effect of $\mathrm{BiFe}{\mathrm{O}}_3$ material parameters on the ${71}^{\circ }$, ${109}^{\circ }$, and ${180}^{\circ }$ walls is explored, and it is shown that the meandering instability appears at ${109}^{\circ }$ and ${180}^{\circ }$ walls for small gradient energies, and the walls become straight and broaden for higher gradients. In contrast to the ${180}^{\circ }$ and ${109}^{\circ }$ domain walls, uncharged ${71}^{\circ }$ walls are always straight, and their width increases with increasing the tilt gradient coefficient. The wall instability and associated intrinsic meandering provide insight into the behavior of morphotropic and relaxor materials, wall pinning, and mechanisms of interactions between order parameter fields and local microstructure.

• Received 16 October 2018
• Revised 31 December 2018

DOI:https://doi.org/10.1103/PhysRevB.99.014112