Soft mode behavior in transition metal doped SrTiO$_3$ thin films on MgO substrates

The ferroelectric soft mode in polycrystalline pristine SrTiO$_3$ and weakly doped SrTiO$_3$:M (M = 2 at % Fe, Ni, Mn, Co) thin films on (001) MgO substrates has been studied using time-domain terahertz spectroscopy. Spectra of real and imaginary parts of film permittivity were determined in the frequency range of 5–100 cm$^{-1}$ at temperatures between 5 and 300 K. Central frequency and dielectric contribution of the ferroelectric soft mode show Barrett-like temperature dependencies similar to crystalline SrTiO$_3$. Large negative values of Curie temperature and enhanced positive values of Barrett quantum temperatures are discovered indicating that doped SrTiO$_3$ thin films are farther from ferroelectric phase transition than SrTiO$_3$ crystals.