Strain-Induced Polarization Rotation in Epitaxial (001) ${\mathrm{BiFeO}}_3$ Thin Films

Direct measurement of the remanent polarization of high quality (001)-oriented epitaxial ${\mathrm{BiFeO}}_3$ thin films shows a strong strain dependence, even larger than conventional (001)-oriented ${\mathrm{PbTiO}}_3$ films. Thermodynamic analysis reveals that a strain-induced polarization rotation mechanism is responsible for the large change in the out-of-plane polarization of (001) ${\mathrm{BiFeO}}_3$ with biaxial strain while the spontaneous polarization itself remains almost constant.

Figure 1

(a) Typical bright-field TEM image of a ${\mathrm{BiFeO}}_3/\mathrm{SrRu}{\mathrm{O}}_3/\mathrm{SrTi}{\mathrm{O}}_3$ heterostructure grown on a 4°-miscut (001) Si substrate showing 71° ferroelectric domains along the $[101{]}_p$ direction. A high resolution TEM image of ${\mathrm{BiFeO}}_3$ at a 71° ferroelectric domain wall in the ${\mathrm{BiFeO}}_3$ film and an electron diffraction pattern from the indicated ${\mathrm{BiFeO}}_3$ region are shown. (b) HRXRD $\theta -2\theta$ scans of 400-nm-thick ${\mathrm{BiFeO}}_3$ films before and after lift-off, ● and ▪ correspond to diffraction peaks from Pt top electrodes and the Au plate, respectively. The insets show an expanded view around the ${002}_p$ ${\mathrm{BiFeO}}_3$ peaks with the vertical line for the $2\theta$ value of bulk ${002}_p$ ${\mathrm{BiFeO}}_3$.

Figure 2

(a) Reciprocal-space maps of the 400-nm-thick as-grown film on a Si substrate. Reciprocal-space images of the ${113}_p$ reflection show two peaks (domains) marked with a dotted line. After rotating the film azimuthally by 180°, the peak splitting along the $[00L{]}_p$ direction was unchanged. This is because the as-grown film has monoclinic symmetry, in which the ${113}_p$ reflection has twofold symmetry with two different $d$-spacings shown in the schematic drawing of the $\{113{\}}_p$ planes in the unit cell. (b) Reciprocal-space maps of the strain-free ${\mathrm{BiFeO}}_3$ membrane. After rotating the film azimuthally by 180°, the image shows different peak splitting along the $[00L{]}_p$ direction. This is because the membrane has rhombohedral symmetry, in which the ${113}_p$ reflection does not have twofold symmetry and there are three different $d$-spacings as shown in the schematic drawing of the $\{113{\}}_p$ planes in the unit cell.

Figure 3

Polarization-electric field ($P\mathrm{\text{−}}E$) hysteresis loops of a 400-nm-thick as-grown ${\mathrm{BiFeO}}_3$ film grown on Si and a strain-free ${\mathrm{BiFeO}}_3$ membrane. Both loops were obtained from the same capacitor before and after lift-off. The $P\mathrm{\text{−}}E$ hysteresis loop of a 400-nm-thick ${\mathrm{BiFeO}}_3$ film grown on a ${\mathrm{SrTiO}}_3$ substrate is shown for comparison. The membrane exhibits a significantly reduced coercive field. The discontinuity at zero electric field (negative polarization axis) for ${\mathrm{BiFeO}}_3$ membranes and ${\mathrm{BiFeO}}_3$ on Si is due to a strong built-in bias in the films.

Figure 4

(a) Remanent polarization as a function of the in-plane strain of $(001{)}_p$ ${\mathrm{BiFeO}}_3$ films grown on ${\mathrm{SrTiO}}_3$ and Si substrates and strain-free $(001{)}_p$ ${\mathrm{BiFeO}}_3$ membranes. The experimental data are very consistent with the $P_3$ values obtained from thermodynamic calculations, (b) The spontaneous polarization directions of the rhombohedral ($R$) and monoclinic ($M_A$ and $M_B$) phases of ${\mathrm{BiFeO}}_3$. The monoclinic $M_A$ and $M_B$ phases occur for biaxial compressive and tensile strains, respectively. In-plane strains induce the rotation of the spontaneous polarization in the $(110{)}_p$ plane. For $M_A$ and $M_B$ phases, the rotation of $P_s$ is much more pronounced than the simple rotation of $P_s$ by the change in the $c/a$ ratio (denoted by $C$ and $T$).