Magnetoelectric Response of Multiferroic ${\mathrm{BiFeO}}_3$ and Related Materials from First-Principles Calculations

We present a first-principles scheme for computing the magnetoelectric response of multiferroics. We apply our method to ${\mathrm{BiFeO}}_3$ (BFO) and related compounds in which Fe is substituted by other magnetic species. We show that under certain relevant conditions—i.e., in the absence of incommensurate spin modulation, as in BFO thin films and some BFO-based solid solutions—these materials display a large linear magnetoelectric response. Our calculations reveal the atomistic origin of the coupling and allow us to identify the most promising strategies to enhance it.

Figure 1

Panel (a): sketch of the response associated to ${\alpha }_{23}$ of BFO. Only the two Fe atoms in the usual (rhombohedral) cell of BFO are shown. In equilibrium (dashed arrows), the spin of the Fe ions lies on the $xy$ plane; the easy axis is $x$ and a small canting results in a net ${\mathcal{M}}_y^S$. When ${\mathcal{E}}_y$ is applied we obtain an additional canting and a nonzero ${\mathcal{M}}_z$ (solid arrows). Panel (b): cumulative plot for the ${\widehat{\alpha }}_{23}$ coefficient of BFO (see text). Modes dominated by Bi (◆) and Fe (■) displacements are highlighted.