Influence of defects on the critical behaviour at the \boldmath{105} K structural phase transition of SrTiO$_3$: I. The broad component

The critical fluctuations in SrTiO$_3$ near its $105 K$ structural phase transition were studied with triple axis diffractometry using high energy ($\ge 100 keV$) synchrotron radiation in different SrTiO$_3$ crystals with different oxygen vacancy concentrations. Due to the presence of oxygen vacancies the critical behaviour is changed compared to defect-free systems. In our experiments a smearing out of the squared order parameter and a crossover of the critical exponents $\nu$ and $\gamma$ above the phase transition temperature is observed, with the crossover temperature strongly depending on the concentration of the defects. To understand the experimental findings, e.g. the unusual values for the critical exponents found near the critical temperature, the Ginzburg-Landau-Wilson functional for structural phase transitions in disordered systems was analyzed using renormalization group theory and the replica trick. Considering the effects of defects which locally increase the transition temperature leads to a qualitative understanding of the observed behaviour. The crossover behaviour of the critical exponents can be modeled and a quantitative analysis of the observed experimental data is presented.