First-principles investigation of the structural phases and enhanced response properties of the BiFeO$_3$-LaFeO$_3$ multiferroic solid solution

We present a first-principles study of the Bi1-xLaxFeO3 (BLFO) solid solution formed by multiferroic BiFeO3 (BFO) and the paraelectric antiferromagnet LaFeO3 (LFO). We discuss the structural transformations that BLFO undergoes as a function of La content and the connection of our results with the existing crystallographic studies. We find that, in a wide range of intermediate compositions, BLFO presents competitive phases that are essentially degenerate in energy. Further, our results suggest that, within this unusual morphotropic region, an electric field might be used to induce various types of paraelectric-to-ferroelectric transitions in the compound. We also discuss BLFO's response properties and show that they can be significantly enhanced by partial substitution of Bi/La atoms in the pure BFO and LFO materials. We analyze the atomistic mechanisms responsible for such improved properties and show that the effects can be captured by simple phenomenological models that treat explicitly the composition x in a Landau-like potential.