Correlation between surface rumpling and structural phase transformation in SrTiO${}_3$

We present x-ray reflectivity , x-ray diffraction, and atomic force microscopy measurements of single-crystal SrTiO${}_3$ taken as a function of temperature. We found a rumpling transformation of the SrTiO${}_3$ surface after cooling the sample below ∼105 K. The rumpling transformation is correlated with the cubic-to-tetragonal phase transformation that occurs at the same temperature. The rumpling transformation is reversible.

Figure 1

(a) X-ray scattering geometry using position-sensitive detector. (b) Scattering geometry in reciprocal space.

Figure 2

(a)–(d) Reciprocal space map ($Q_x$-$Q_z$ map) of x-ray reflectivity at different temperatures on cooling of the SrTiO${}_3$ crystal. Dash-dash line (white) along $Q_x$ $=$ 0 in (c) shows the specular reflectivity, whereas the dash-dash lines (black) show the reflected intensity from large waviness roughness, which is giving broadening at the specular ridge. (e) Temperature-dependent diffuse XRR at $Q_z$ $=$ 0.1138 Å${}^{-1}$ and (f) specular XRR. Diffuse XRR in (e) are shifted by a factor of ∼2.5 for clear visibility. Inset of (f) shows the electron scattering length density (SLD) depth profile, which gave best fit to specular XRR data measured on cooling sample from 290 to 77 K.

Figure 3

(a) Temperature-dependent variation of full width at half maxima (FWHM) of specular x-ray reflection at an angle of incidence 0.8°. Temperature-dependent variation of FWHM of (004) reflection of SrTiO${}_3$ by x-ray diffraction in (b) radial and (c) rocking scan .

Figure 4

AFM measurements (1 × 1 μm${}^2$) at different temperatures of (a) 300, (b) 210, (c) 100, and (d) 61 K from SrTiO${}_3$ surface. The AFM measurements were performed in the following order: 300, 61, 100, and 210 K. (e)–(h) show the height information along a line marked in (a)–(d), respectively. The AFM images (a)–(d) are represented using derivative enhanced images. However, the line profiles (e)–(h) are taken from raw AFM data.

Figure 5

Representation of surface modification inferred from x-ray scattering measurements (a) below and (b) above 105 K. (c) Variation of roughness with temperature measured using XRR and AFM . (d) Histograms showing the fluctuation of surface height after removal of a systematic trend (discussed in text).