Orientation-resolved domain mapping in tetragonal ${\mathbf{SrTiO}}_3$ using polarized Raman spectroscopy

We present microscopically resolved, polarized spectroscopy of Raman scattering collected from tetragonal ${\mathrm{SrTiO}}_3$. The anisotropic response of first-order Raman peaks within a single tetragonal domain has been measured. From these data, we assign symmetries to the phonons seen in the first-order Raman spectrum which is normally complicated by uncontrolled domain structure. Using a translation stage, we map the local domain orientation of a $3\text{−}\mu {\mathrm{m}}^3$ crystal volume near the laser focus and compare it to wide-field polarized images. This technique can be performed with readily available instruments and is relevant to the study of a wide range of related materials, interfaces, and devices.

Figure 1

(a) Two-dimensional representations of the cubic and tetragonal crystal structures formed by ${\mathrm{SrTiO}}_3$. In the tetragonal phase, octahedra which rotate clockwise (counterclockwise) in the basal plane are shown as light pink (dark blue) squares. The black dashed lines in each crystal structure outline the unit cell. Two planes of oxygen octahedra are shown in the tetragonal structure, representing the doubling of the unit cell along the tetragonal principal axis. (b) Three possible orientations of the tetragonal principal $c$ axis along the quasicubic crystal axes $X,Y$, and $Z$ are possible. (c) Schematic drawing of the experimental geometry on a tetragonal STO sample with twinned $X$- and $Y$-oriented domains. Excitation laser light (light green arrow) is focused into the crystal and Raman-scattered light (red arrow) is collected. The polarizations of the excitation and Raman-scattered light are kept parallel and rotated within the $X\text{−}Y$ plane of the crystal. Octahedral rotations are exaggerated for clarity.

Figure 2

Schematic of the polarized Raman microscope setup. Component labels are explained in the text.

Figure 3

(a) A typical Raman spectrum collected from an approximately $3\text{−}\mu {\mathrm{m}}^3$ volume of a tetragonal ${\mathrm{SrTiO}}_3$ sample. As described in the text, the sample temperature at the laser focus is inferred from the spectrum to be between 50 and 60 K. The volume probed was approximately $100\mu \mathrm{m}$ below the surface. This spectrum was collected at polarization angle $\theta \approx {120}^{\circ }$, indicated by the white dashed line in (b). This angle was chosen for this plot because all of the relevant first-order Raman peaks are visible. (b) Polarization dependence of the Raman spectrum in (a) showing anisotropic strengths of first-order peaks. Comparison of these anisotropic responses with the three possibilities shown in Table 1 indicates that the tetragonal principal axis is along the $X$ axis. The second $E_{\mathrm{g}}$ peak appearing to the left of 0 is the anti-Stokes shift complement of the peak appearing just to its right. (c) Measured polarization variation of the four peaks labeled in (a) and fits to anisotropic scattering intensities $I_{\mathrm{i},\mathrm{X}}\left(\theta \right)$ given in Table 1. (d) Zoomed-in view of the highlighted region in (c) showing that that a nonzero signal is measured from the $A_{1\mathrm{g}}$ peak (blue circles) at $\theta ={90}^{\circ }$. (e)–(h) Normalized polar plots of the same data shown in (c) for comparison with Table 1. The legend at the bottom right applied to subplots (c)–(h).

Figure 4

(a) Tetragonal ${\mathrm{SrTiO}}_3$ viewed in a wide-field microscope image. Polarization-dependent Raman spectra were collected approximately $100\mu \mathrm{m}$ below the surface at the three labeled points. (b) Polarization dependence of first-order Raman peaks at points P0, P1, and P2 indicated in (a). The analysis and data processing used to produce these plots are identical to that used for Figs. 3–3. Comparison of the data with the anisotropic Raman intensities calculated in Table 1 indicates that lighter areas in the wide-field image (P0 and P1) are $X$-oriented tetragonal domains while darker areas (P2) are $Y$-oriented tetragonal domains. Spectral temperature signatures (described in the text) suggest the sample temperature at the laser focus was between 45 and 55 K.

Figure 5

(a) Wide-field, polarized microscope image of tetragonal ${\mathrm{SrTiO}}_3$ showing dense twinning of $X$- and $Y$-oriented tetragonal domains with walls running at approximately ${45}^{\circ }$ with respect to the in-plane quasicubic axes. A scanning-confocal measurement of the Raman signal for excitation light polarized along the $X$ axis $(0^{\circ }$ in polar plots) was performed at a depth near $100\mu \mathrm{m}$ in the approximately parallelogram-shaped region outlined in black. The dashed blue line running diagonally through the parallelogram indicates the line cut of wide-field image intensity plotted in (c). (b) Relative strength of the $A_{1\mathrm{g}}$ Raman peak measured at points spaced by $\sim 1\mu \mathrm{m}$ in the region outlined in (a). Stripes of varied intensity are seen in a similar pattern to that observed from this region in the wide-field image. Light and dark regions are interpreted to be $X$- and $Y$-oriented tetragonal domains, respectively. The red line indicates a line cut in the of the mapped intensity plotted in (c). (d) Polar plots of $A_{1\mathrm{g}}$ strength measured at the points indicated with matching symbols in (b). As in Fig. 4, spectral temperature signatures (described in the text) suggest the sample temperature at the laser focus was between 45 and 55 K.