Depth dependence of the structural phase transition of SrTiO${}_3$ studied with $\beta$-NMR and grazing incidence x-ray diffraction

We present an investigation of the near-surface tetragonal phase transition in SrTiO${}_3$, using the complementary techniques of beta-detected nuclear magnetic resonance and grazing-incidence X-ray diffraction. The results show a clear depth dependence of the phase transition on scales of a few microns. The measurements support a model in which there are tetragonal domains forming in the sample at temperatures much higher than the bulk phase transition temperature. Moreover, we find that these domains tend to form at higher temperatures preferentially near the free surface of the crystal. The details of the tetragonal domain formation and their depth/lateral dependencies are discussed.

Figure 1

Illustration of the propagation of tetragonal domains from the surface of STO (left). The light and dark shaded areas represent tetragonal and cubic domains, respectively. (a) and (b) show scenario I and II, respectively.

Figure 2

The normalized initial polarization of ${}^8\mathrm{Li}$ as a function of temperature. The empty and filled squares are measurements on a polished STO sample and at implantation energy of 28 and 2 keV, respectively. The triangles are measurements on the etched sample at 28 keV. The inset shows the implantation profiles.

Figure 3

The ($\frac{1}{2}$ $\frac{3}{2}$ $\frac{1}{2}$) X-ray Bragg peak of the tetragonal structure measured at (a) T $=$ 105 K and (b) 170 K at the critical grazing incident angle for total external reflection of $0.{15}^{°}$.

Figure 4

The ($\frac{1}{2}$ $\frac{3}{2}$ $\frac{1}{2}$) X-ray Bragg peak of the tetragonal structure measured at (a) T $=$ 120 K, (b) 130 K and (c) 140 K at different grazing incident angles, corresponding to the quoted mean depth. The lines are the fits described in the text.

Figure 5

The values of the width of the TDS and Bragg component as a function of temperature from fits to Eq. (1). The solid lines are guide to the eye.

Figure 6

(a) $A_{\mathrm{Bragg}}/A_{\mathrm{TDS}}$ as a function of incident angle or mean depth. The values for $T=120$ K were divided by a factor 15 to enable plotting all three temperatures on the same figure clearly. The dashed lines are a guide to the eye. (b) The calculated mean depth as a function of X-ray incident angle for STO with X-rays of energy 16 keV.[30, 31]