Phase transitions and precursor phenomena in doped quantum paraelectrics

Impurity-induced phase transitions in quantum paraelectrics like SrTiO3:Ca2 + (SCT) are treated within the framework of a heterogeneous transverse Isin g model. It is capable of describing both off-and on-center impurity system s in a realistic way. Owing to the local meanfield approach, however, the c alculation fails to show the highly non-classic critical behavior observed in experiments. In addition, all fluctuation phenomena above the critical t emperature are completely averaged out. In this precursor range fluctuating polar nanodomains are encountered, which give rise e.g. to relaxer-type po lydispersive response, quasi first-order Raman scattering, bilinear couplin g between transverse acoustic and polar soft-modes, and hyper-Rayleigh scat tering which scales as omega(TOI)(-4). A novel SHG peak observed in SCT (x = 0.014) at T approximate to 40 K is attributed to hyper-Raman scattering a t the difference mode of accidentally degenerate E-u and E-g soft-modes.