Influence of defects on the critical behavior at the 105 K structural phase transition of SrTiO₃: On the origin of the two length scale critical fluctuations

Abstract

The temperature dependence of the sharp and the broad component of the critical scattering above the cubic-to-tetragonal phase transition of SrTiO3 has been studied by means of high-resolution triple-crystal diffractometry using 100-200 keV synchrotron radiation in five samples differing with respect to growth technique and oxygen vacancy concentrations. Emphasis is on changes in the critical behavior, the critical temperature, and the strain fields at the transition from bulk to surface. The sharp component was observed only in surface near regions of highly perfect crystals and is coupled to the occurrence of a long-range strain gradient that was identified by an exponential increase of mosaicity, lattice parameter fluctuations, and Bragg-peak intensity when approaching the surface from the bulk of the sample. Vanishing of the sharp component was observed at the polished/etched surface of a platelet cut off the large perfect crystal after release of strain due to free bending of the platelet. The values of the critical temperature observed in the bulk of the different samples vary between 98.7<~Tc<~105.8 K. In the surface near regions of a highly perfect float-zone grown crystal a variation of Tc of about 0.5 K has been found. Concerning the broad component the critical exponent describing the temperature dependence of the inverse correlation length κb varies between 0.73<~νb<~1.19, the exponent for the susceptibility between 1.49<~χb<~2.9, however, the ratio of the two exponents is almost sample independent and equal to χb/νb=2.1 with a variance of 0.2, in good agreement with the theoretical value of 1.97 obtained by LeGouillou and Zinn-Justin [Phys. Rev. B 21, 3976 (1980)]. The occurrence of the sharp component did not affect significantly the critical exponents for the underlying broad component of the critical scattering. The exponents for the sharp component observed in surface near layers of about 100 μm thickness at the highly perfect float zone and flux grown crystals varied between 0.58<~νs<~1.30, the values for the ratio varied between 3.3<~χs/νs<~4.6. The average value of χs/νs is 3.9 with a variance of 0.5, and is about twice the ratio χb/νb for the broad component as suggested by Harris et al.