Figure 1

Physical properties of (001) BFO films as a function of tensile misfit strain. Panel (a) shows the polarization in $\mu \mathrm{C}/{\mathrm{cm}}^2$, while panel (b) displays the AFD vector in radians. Panels (c) and (d) represent the monoclinic angle and epitaxial stress, respectively. Panel (e) shows the magnitude of the antiferromagnetic vector, while panel (g) displays the magnetization (for the most stable direction of the antiferromagnetic vector, i.e., $[1\overline{1}0]$). These magnetic moments are expressed in Bohr magneton per Fe atom. Panel (f) displays the $x$, $y$, and $z$ components of the order parameter quantifying the Bi antiphase displacements.Reuse & Permissions

Figure 2

Left panel: schematic view of the AFD vector $\Omega$, AFM vector $\mathbf{L}$ and magnetization $\mathbf{M}$ in the two phases found in the present work: (a) $Cc$ phase; (b) $Ima2$ phase. In panel (a), the solid and dashed arrows are related to two different tensile strain region (low strain in the dashed case, higher strain in the solid case). Right Panel: top view ([001] axis perpendicular to the picture) of these two phases. (c) $Cc$ monoclinic phase (tensile strain smaller than $\approx 8\%$), with the oxygen octahedra tilting around [001], as well as, the ferroelectric distortions (in-plane component of the polarization, i.e., along the pseudocubic [110] direction) being clearly visible. (d) $Ima2$ orthorhombic phase (tensile strain larger than $\approx 8\%$), with the strong ferroelectric distortions being clearly visible, as well as the Bi antiphase displacements (that also exist in the $Cc$ phase). The yellow and green arrows feature these Bi motions in two consecutive planes perpendicular to the out-of-plane direction.Reuse & Permissions