Mapping gradient-driven morphological phase transition at the conductive domain walls of strained multiferroic films

The coupling between antiferrodistortion (AFD) and ferroelectric (FE) polarization, universal for all tilted perovskite multiferroics, is known to strongly correlate with domain wall functionalities in the materials. The intrinsic mechanisms of domain wall phenomena, especially AFD-FE coupling-induced phenomena at the domain walls, have continued to intrigue the scientific and technological communities because of the need to develop future nanoscale electronic devices. Over the past years, theoretical studies have often shown controversial results, owing to the fact that they are neither sufficiently nor directly corroborated with experimental evidence. In this work, the AFD-FE coupling at uncharged 180° and 71° domain walls in $\mathrm{BiFe}{\mathrm{O}}_3$ films is investigated by means of aberration-corrected scanning transmission electron microscopy with high-resolution scanning transmission electron microscopy and rationalized by phenomenological Landau-Ginzburg-Devonshire (LGD) theory. We reveal a peculiar morphology at the AFD-FE walls, including kinks, meandering, and trianglelike regions with opposite oxygen displacements and curvature near the interface. The LGD theory confirms that the tilt gradient energy induces these unusual morphologies and the features would change delicately with different kinds of domain walls. Moreover, the 180° AFD-FE walls are proved to be conductive with an unexpected reduction of the Fe-O-Fe bond angle, which is distinct from theoretical predictions. By exploring AFD-FE coupling at the domain walls, and its induced functionalities, we provide exciting evidence into the links between structural distortions and its electronic properties, which provide great benefit for fundamental understanding of domain wall functionalities as well as functional manipulations for novel nanodevices.

Figure 1

Crystal structures showing the AFD-FE walls in BFO film. (a) Atomic structure of bulk BFO crystal showing the oxygen octahedral rotation (black curved arrows). (b), (c) Atomic structure models for 180° (b) and 71° (c) AFD-FE walls projected along ${\left[001\right]}_{\mathrm{pc}}$ and ${\left[110\right]}_{\mathrm{pc}}$ directions.

Figure 2

An 18-nm BFO film grown on PSO ${\left(001\right)}_{\mathrm{O}}$ substrate (180° domain wall). (a) Cross-sectional HAADF image of BFO/PSO interface project along the ${\left[110\right]}_{\mathrm{pc}}$ direction. Two 180° domain walls are marked. The insets are enlarged images of each domain. The blue and yellow solid circles denote the position of $\mathrm{B}{\mathrm{i}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ columns. The yellow arrows denote the polarization direction in each domain. (b), (c) are $\mathrm{F}{\mathrm{e}}^{3+}$ displacements mapping of the red and blue rectangles in (a), respectively. The kinked domain walls are marked by red arrows. (d) ABF image of the same area as panel (a). The red and blue trianglelike regions are marked to demonstrate the AFD walls. The blue insets are superposition of the atomic schematics with enlarged images of each domain. Images (e), (f) are oxygen displacement components along ${\left[\overline{1}10\right]}_{\mathrm{pc}}$ and ${\left[001\right]}_{\mathrm{pc}}$, respectively. The trianglelike regions and AFD wall meandering are marked by white dotted areas.

Figure 3

Conductive AFM and corresponding $B$-O-$B$ bond analyses for 18-nm BFO film grown on PSO ${\left(001\right)}_{\mathrm{O}}$ substrate with 180° domain walls. (a), (b) Vertical PFM (a) and corresponding conductive AFM (b) images for 180° domain walls. (c) TEM bright-field image for BFO film. (d), (e) $B$-O-$B$ bond angle (d) and $B$-O bond length (e) distributions corresponding to the 180° domain walls in Fig. 2.

Figure 4

A 7-nm BFO film grown on PSO ${\left(001\right)}_{\mathrm{O}}$ substrate (71° domain wall). (a) HAADF image of BFO/PSO interface. The 71° domain wall is marked. The insets are enlarged images of each domain. The blue and yellow solid circles denote the position of $\mathrm{B}{\mathrm{i}}^{3+}$ and $\mathrm{F}{\mathrm{e}}^{3+}$ columns. The blue arrows denote the polarization direction in each domain. (b) $\mathrm{F}{\mathrm{e}}^{3+}$ displacements mapping of the red rectangle in panel (a). (c) ABF image of the 71° domain wall. The 71° AFD wall is marked. The blue insets are superpositions of the schematics with enlarged images of each domain. (d) Oxygen displacement components along the ${\left[\overline{1}10\right]}_{\mathrm{pc}}$ direction. The AFD wall broadenings are marked by white dotted areas. The white arrows denote the curvature near the interfaces.

Figure 5

Considered system for modeling. Considered system, consisting of thin BFO film, placed between electrically conducting top and bottom electrodes, and PSO substrate. The {111} cut with domain stripes is shown.

Figure 6

{101} oriented 180° DWs in 18-nm BFO film on $\mathrm{PrSc}{\mathrm{O}}_3$ substrate, relaxing from initial straight DWs at $t=0$ to the intermediate state $t=13{\tau }_{\mathrm{K}}$, and than to the final state $t>25{\tau }_{\mathrm{K}}$. Distribution of the AFD order parameter ${\mathrm{\Phi }}_i$ (a)–(c) and polarization $P_i$ (d)–(f) components in the cross section of a thin BFO film with {101} oriented 180° DWs. Film thickness is 18 nm, room temperature. Tilted coordinate system is used for $x_1$.

Figure 7

{101} oriented 180° DWs in 18-nm BFO film on $\mathrm{PrSc}{\mathrm{O}}_3$ substrate, after a very long relaxation time. Distribution of the AFD order parameter ${\mathrm{\Phi }}_i$ (a)–(c) and polarization $P_i$ (d)–(f) components in the $\left\{x_1{x}_2\right\}$ cross section of a thin BFO film with {101} oriented 180° DWs. Film thickness is 18 nm, room temperature. Tilted coordinate system is used for $x_1$.

Figure 8

{110} oriented 71° DWs in BFO film on $\mathrm{PrSc}{\mathrm{O}}_3$ substrate (fully relaxed). Distribution of different components of the AFD order parameter ${\mathrm{\Phi }}_i$ (a)–(c) and polarization $P_i$ (d)–(f) in the $\left\{x_1{x}_2\right\}$ cross section of 7-nm BFO film with {110} oriented 71° DWs, room temperature.

Figure 9

Normalized static conductivity across {101} oriented 180° DWs in 18-nm BFO film on PSO substrate. Parameters are listed in Table 1; the trace of deformation potential tensor is ${\mathrm{\Xi }}_{ii}^C=20\mathrm{eV}$. Color bar is CAFM contrast in relative units.