Influence of anisotropic strain on the dielectric and ferroelectric properties of ${\text{SrTiO}}_3$ thin films on ${\text{DyScO}}_3$ substrates

The in-plane dielectric and ferroelectric properties of coherent anisotropically strained ${\text{SrTiO}}_3$ thin films grown on orthorhombic (101) ${\text{DyScO}}_3$ substrates were examined as a function of the angle between the applied electric field and the principal directions of the substrate. The dielectric permittivity revealed two distinct maxima as a function of temperature along the ${\left[100\right]}_p$ and ${\left[010\right]}_p$ ${\text{SrTiO}}_3$ pseudocubic directions. These data, in conjunction with optical second-harmonic generation, show that the switchable ferroelectric polarization develops first predominantly along the in-plane axis with the larger tensile strain before developing a polarization component along the perpendicular direction with smaller strain as well, leading to domain twinning at the lower temperature. Finally, weak signatures in the dielectric and second-harmonic generation response were detected at the ${\text{SrTiO}}_3$ tilt transition close to 165 K. These studies indicate that anisotropic biaxial strain can lead to new ferroelectric domain reorientation transitions that are not observed in isotropically strained films.

Figure 1

(Color online) In-plane dielectric permittivity at 5 kHz of a $250\text{Å}$ thick ${\text{SrTiO}}_3$ thin film measured as a function of temperature for several in-plane angles showing two distinct peaks ($T_1$ and $T_2$) sampled as a function of angle. $0°$ is aligned with the longer ${\left[010\right]}_p$ ${\text{SrTiO}}_3$ axis (parallel to [010] ${\text{DyScO}}_3$), and $90°$ is aligned along the shorter ${\left[100\right]}_p$ ${\text{SrTiO}}_3$ (parallel to $\left[10\overline{1}\right]$ ${\text{DyScO}}_3$).

Figure 2

(Color online) Switchable polarization as a function of temperature for the two principal in-plane directions of the $250\text{Å}$ thick ${\text{SrTiO}}_3$ film on (101) ${\text{DyScO}}_3$.

Figure 3

(Color online) Switchable polarization measured as a function of in-plane angle from the longer (more strained) axis at 70 K for a $250\text{Å}$ thick ${\text{SrTiO}}_3$ film. The experimental data (◼) is shown with the solid line and the models are shown with dashed lines.

Figure 4

(Color online) In-plane dielectric constant of a $250\text{Å}$ thick film measured on zero-field heating and cooling for (a) along the longer in-plane direction and (b) along the shorter in-plane direction showing signatures of three peaks in both principal directions.

Figure 5

(Color online) (a) In-plane dielectric constant and (b) loss tangent for the $500\text{Å}$ thick film measured along the shorter in-plane axis on heating after cooling the films without dc bias (ZF: zero field) represented by dashed lines and under 3 kV/cm dc bias (FC: field cooled) represented by solid lines. All the frequencies collapse after field cooling, indicating a more normal ferroelectric state.

Figure 6

(Color online) (a) In-plane dielectric constant and (b) loss tangent data measured along the longer axis on heating for a $500\text{Å}$ thick film cooled without dc bias (ZF: zero field) shown as dashes and under 3 kV/cm dc bias (FC: field cooled) represented by solid lines. There is much less frequency dispersion in the measurement after field cooling, indicating a more normal ferroelectric transition.

Figure 7

(Color online) The schematic on the top depicts the second-harmonic generation (SHG) setup where light of frequency $\omega$ and linear polarization, at an angle $\theta$ with respect to the $x$ axis, is converted to light of frequency $2\omega$, after interacting with the sample. By varying the angle $\theta$, and fixing an analyzer along the $x$, $y$, $x^{\prime }$, and $y^{\prime }$ directions SHG intensity polar plots, i.e., $I_x^{2\omega }$, $I_y^{2\omega }$, $I_{x^{\prime }}^{2\omega }$, and $I_{y^{\prime }}^{2\omega }$ are obtained. Figures 7a, 7b, 7c, 7d, 7e, 7f show SHG polar plots at 175 K. These compare the theoretical models, represented by the thin solid red lines to the experimental data, represented by open circles. In particular, the comparison is the following: (a) model I fit, $I_x^{2\omega }$, (b) model I fit, $I_y^{2\omega }$ (c) model II, case I fit, $I_x^{2\omega }$, (d) model II, case I fit, $I_y^{2\omega }$, (e) model II, case II fit, $I_{x^{\prime }}^{2\omega }$, and (f) model II, case II fit, $I_{y^{\prime }}^{2\omega }$. The thick solid red lines in Figs. 7c, 7d, 7e, 7f represent intensities which must be reciprocal in order for the fitting models to be valid. Clearly, this is true only for Figs. 7c, 7d, based on model II, case I.

Figure 8

(Color online) Temperature dependence of the nonlinear coefficient $\left|d_{31}^{\prime }/d_{33}\right|$. Shown here are the quantities that correspond to left- and right-hand sides of Eq. (8) (black solid lines) and Eq. (9) (red dashed lines). For all measured temperatures, Eq. (8) is valid since the left- and the right-hand side quantities are equal (black squares and stars), whereas clearly Eq. (9) is not valid. Since, Eq. (8) is satisfied, we can conclude that the in-plane polarization is along the ${⟨100⟩}_p$ and not the ${⟨110⟩}_p$ directions.

Figure 9

Shown here is the temperature dependence of (a) second-harmonic intensity with a fixed analyzer along the $y$ direction and $\theta =0°$, i.e., $I_y^{2\omega }\left(0°\right)$ and (b) the absolute ratio of the net polarization along the $y$ axis to the net polarization along the $x$ axis, $\left|P_y^{\text{net}}/P_x^{\text{net}}\right|$ Both (a) and (b) are in good agreement with the electrical measurements of the polarization in Fig. 2. Figure 9c shows the temperature dependence of the nonlinear coefficient ratio $\left|d_{15}^{\prime }/d_{33}\right|$ and Fig. 9d shows the offset angle $\left(\phi \right)$ from the polar plot fitting as a function of temperature. Both show an anomaly at 175 K that can be most likely attributed to the AFD transition.

Figure 10

(Color online) Representative domain structures from phase-field simulations following each of the three transitions for (a) ${\alpha }_{12}=5.5\times {10}^{-12}{\text{cm}}^6\text{dyn}/{\text{esu}}^4$ and (b) ${\alpha }_{12}=1.7\times {10}^{-12}{\text{cm}}^6\text{dyn}/{\text{esu}}^4$. Different colors are used to identify the four kinds of domain variants for both (100) and (110) polar states and the directions of the vectors $p$ and $q$ are shown by the arrows.