In the early 60s, the soft-mode concept was proposed to describe the mechanism of the ferroelectric structural phase transitions . This concept is based on the assumption that the crystal gets unstable against a particular normal vibration of the lattice (phonon). Then, already in the high temperature phase, among others, there exists a certain unstable phonon (the "soft mode") whose frequency is going down as the temperature is approaching the TC (the phonon "softens") becoming zero at TC ;  meaning thereby that the correspondent vibration (or the atomic positions) become "frozen" at this temperature and produce a structure of another symmetry with a finite dipole moment.

Since the soft modes in ferroelectrics lead to electrical polarization, they are optically active and can be detected by means of optical spectroscopy in the spectra of dielectric permittivity (real and imaginary parts).

Spectroscopic studies of the soft modes provides with a very powerful tool for investigating the ferroelectric transitions.

 The behavior of the parameters of the soft mode is governed by three  laws:

[A]  static dielectric permittivity produced by the soft mode obeys the Curie-Weiss law

 ε(0) ~ (T - TC)^ -1

[B] the eigenfrequency omega(t) of the soft mode follows the Cochran behavior, 

ω(t) ~ (T - T0)^1/2

where T0 is the soft mode condensation temperature.

[C]the static dielectric constant and the soft mode frequency are connected via the Lyddane-Sachs-Teller[LST] relation: 

εinf/ε0(T)= ω  t^2(T)/ω  L^2

where εinf is the high frequency dielectric constant and ωL is the longitudinal frequency of the corresponding vibration.

Normally the phonons which are getting soft have frequencies below 100 - 200          cm^-1 well above the transition temperature. When softening WHILE APPROACHING  the TC, these modes go to lower frequencies, finally leaving the range where the conventional infrared spectrometers  can operate and enter the submillimeter-millimeter wavelength domain.

Further to what Sehgal said, these soft phonon modes can also be detected at or near room temperature, i.e. below the Transition Temperature by Raman Spectra. Theoretically, thich could also be done by Multiple-Time-Scale-Analysis (PRB, 2010, Vol84) on a governing equation guiding polarization vs. electric field vectors. However, it is not known whether anybody even attempted to match the MTSA frequency with those found in Raman or IR expt.   

thank you very much sir for your useful discussions prof.Manohar Sehgal and prof. A. K. Bandyopadhyay

Thanks a lot to: Hai-Yao Deng

Below transition temperature, say at room temperature, is it then possible to find out soft phonons at different modes from the dispersion relation, as done experimentally by Raman or ISRS.....

The soft phonon concept in ferroelectrics and many different examples of soft modes which frequency near Tc drops below the limits of optical spectroscopies are discussed  in the book by J. Grigas "Microwave Dielectric Spectroscppy of Ferroelectrics and Related Materials (Gordon and Breach Publishers, USA).

Soft mode at the vicinity of transition temperature shows dielectric crystal behaviour a an incipient ferroelectric crystal. Whispering Gallery mode q-factor reveals double potential well loss below transition temperature

The complete phonon softening can be detected by inelastic neutron scattering. The question is that while there exists incomplete phonon softening or localized phonon softening, how could we detect it? I am considering whether the intrinsic phonon softening theory is established.

 Q-factor of WG modes in the crystal quantifies the inherent dissipation of mode energy, and reveals different metastable states . The transition in to ferroelectric phase can be observed in terms of Q-factor saturation ∂Q/∂T=0 based on Ginzburg-Landau theory with characteristic spontenious polarization P_s=0.