Ferroelectric phase transition and crystal asymmetry monitoring of SrTiO₃ using quasi TE _m,1,1 and quasi TM _m,1,1 modes

Dielectric spectroscopy of a SrTiO 3 single crystal over a broad range of microwave frequency using quasi T E m, 1, 1 and quasi T M m, 1, 1 modes reveals crystal asymmetry from typical measurement of Q-factor, transmission, or frequency characteristics in continuous cooling down to a few Kelvin. The properties of the modes due to the crystal asymmetry are validated by implementing a quasiharmonic phonon approximation. The observed ferroelectric phase transition temperature is around 51 K, and quantum-mechanical stabilization of the paraelectric phase arises below 5 K with very high permittivity. Also, an antiferrodistortive transition was indicated at 105 K. Landau's theory of correlation length supports the observation of an extra-loss term so the transition may be identified near the Q-factor maxima or transmission maxima depending on the other loss terms present in the cavity. Thus, the ferroelectric phase transition with respect to temperature is identified when its extra-loss term causes a discontinuity or deviation in the derivative of the temperature characteristic near the minimum of total cavity loss (maximum Q-factor or maximum transmission temperature characteristic). This temperature is confirmed by transmission amplitude variation of quasi T E 2, 1, 1 under 200 V dc electric field showing the existence of the soft-mode. These measurements support a typical polarization model and explicit temperature dependency of the soft-mode incorporating an imaginary frequency.