Microscopic Origin of the Giant Ferroelectric Polarization in Tetragonal-like ${\mathrm{BiFeO}}_3$

We report direct experimental evidence for a room-temperature, $\sim 130\mu \mathrm{C}/{\mathrm{cm}}^2$ ferroelectric polarization from the tetragonal-like ${\mathrm{BiFeO}}_3$ phase. The physical origin of this remarkable enhancement of ferroelectric polarization has been investigated by a combination of x-ray absorption spectroscopy, scanning transmission electron microscopy, and first principles calculations. A large strain-induced Fe-ion displacement relative to the oxygen octahedra, combined with the contribution of Bi $6s$ lone pair electrons, is the mechanism driving the large ferroelectric polarization in this tetragonal-like phase.

Figure 1

Local probe-based ferroelectric switching in $T$-phase BFO. (a) the out-of-plane PFM images after a positive ($+3\mathrm{V}$) and negative ($-3\mathrm{V}$) probe bias switching of the $T$-phase BFO; the relative dark and bright contrasts indicate the polarization states point upward and downward. (b) the piezoresponse phase curves of the pure $T$-phase (15 nm on LAO), mixed-phase ($\sim 160\mathrm{nm}$ on LAO), and $R$-phase BFO ($\sim 15\mathrm{nm}$ on ${\mathrm{SrTiO}}_3$ and $\sim 250\mathrm{nm}$ on LAO).

Figure 2

Macroscopic ferroelectric measurement of BFO films with different volume fractions of the $T$ phase. (a) an AFM image of a mixed-phase film with a $T$-phase concentration of $\sim 70\%$, where the flat area indicates the pure $T$ phase and the stripelike area is the mixture of $T$ and $R$ phases. (b) room-temperature P-E loops of pure $R$-phase capacitor (circles) and mixed-phase capacitor (squares) with a $T$-phase concentration of $\sim 70\%$; a strong enhancement of ferroelectric polarization contributed by the $T$ phase in mixed-phase BFO has been observed. (c) pulsed measurement of the switched polarization of the $R$ (squares) and mixed phases with the volume fraction of the $T$ phase of $\sim 70\%$ (right-side-up triangles) and $\sim 90\%$ (sideways triangles). (d) switched polarization on the $R$ and mixed phases as a function of the volume fraction of the $R$-phase BFO. A ferroelectric polarization of $\sim 150\mu \mathrm{C}/{\mathrm{cm}}^2$ can be extrapolated in a pure $T$-phase capacitor according to this trend.

Figure 3

Experimental and simulated x-ray absorption spectra showing the electronic structure of the $T$-phase BFO. (a) a linear polarized x ray shining on the $T$-phase BFO with $E$ parallel and perpendicular to the $c$ axis; (b) the experimental spectra; (c) the simulated spectra with $\Delta e_g=-\Delta t_{2g}=0.35\mathrm{eV}$; (d) $\Delta Z_{\mathrm{Fe}}=0.53\AA$ without applied electric field; (e) $\Delta Z_{\mathrm{Fe}}=0.71\AA$ and $\Delta Z_{\mathrm{Bi}}=1\AA$ with electric field, where the $\Delta Z$ denotes the movement of Fe away from the center (the cartoon is the cluster used in the simulation); and (f) the $\Delta e_g$ (line with uppermost circle) and $\Delta t_{2g}$ (line with lowermost circle) as functions of the $\Delta Z$, where the $\Delta Z$ denotes the movement of Fe and Bi away from the oxygen center. The optimal values of $\Delta e_g$ and $\Delta t_{2g}$ are given by the lower and upper dots.

Figure 4

First principles calculations and high-resolution STEM analysis of the $T$-phase BFO. (a) ferroelectric displacements of the Bi and Fe ions and the O octahedron in the $R$ and $T$ phases, obtained from first principles calculations. The displacements along the pseudocubic [111] direction are shown for the $R$ phase, whereas, for the $T$ phase, the displacements along the pseudocubic [001] direction are shown. The insert shows the crystal structures of the $R$- and $T$-phase BFO. (b) the high-resolution STEM image, giving a direct observation of the relative atomic displacement of Bi and Fe, which is consistent with the result from first principles calculations. 500 unit cells from different samples and locations have been analyzed in order to extract the average value of the atomic displacement shown in the magnified image.