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 SrTiO3, 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.