On the Dynamics of KDP Type Ferroelectrics. I : Formulation and Acoustic Anomaly

概要

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KDP type ferroelectrics are investigated on the basis of extended Kobayashi's model in which the proton pseudo-spin system is coupled with the acoustic phonon as well as with the optic phonon in original Kobayashi's model. A perturbational treatment is developed with the aid of the Matsubara Green's functions and a cumulant expansion. Some proper-ties of the phase transition are shown to be inherent the present model independent of e en m approximations : The renormalized velocity V^^~ of the acoustic mode vanishes at the second order transition point T_c while the frequency ω^^〜(0) of the soft ferroelectric mode remains finite at T_c. By assuming the Curie law for the electrical susceptibility (χ(T) =Χ(∞) +C_±/|T-T_c|, the results (V^^〜/V)^2=|T-T_c|/|T-T_e|+ΔT_±) andω^^〜-2(0) ∝(|T-T_c|+ΔT_±)^<1/2> are shown to be obtained. Here ΔT+(ΔT_-) is a constant for T>T_c, (T<T) and ΔT+(ΔT_=C_+/C_-. It is shown that the effect of the relaxation of the soft ferroelectric mode leads to the ultrasonic attenuation α(ω)∝ω^2|T-T_c|^<-3/2>. |T-T_e|+ΔT_±)<-1/2>. These features essentially agree with the simple phenomenological theory and consistent with experiments on KDP and DKDP. Calculations in RPA are performed and results are carefully examined.
理論物理学刊行会の論文
1975-04-25