Lattice modes in ferroelectric perovskites. III. Soft modes in BaTi $O_{3}$

We report careful right-angle Raman measurements, in the tetragonal phase of BaTi

O_{3}

, of the lowest overdamped "soft"

E (TO)

mode. The measurements are from 22°C to the tetragonal-to-cubic phase transition, which occurs at

T_{c} = 135 °

C. We fit the data to the usual damped-harmonic-oscillator form, and obtain the harmonic frequency

ω_{o}

and the damping constant

γ

. The results are in reasonable agreement with other measurements (which, however, have not gone as high in temperature). Unexpectedly, we find that

ω_{0}

increases up to

T_{c}

, which means that the dielectric constant perpendicular to the ferroelectric axis,

ε_{a}

, decreases right up to

T_{c}

. However, this result agrees with capacitance measurements of

ε_{a}

T = T_{c} - 8 °

C. We also comment on the results of the

A_{1}

modes and reemphasize that all the

A_{1}

and

E

modes disappear abruptly above

T_{c}

and thus obey the appropriate selection rules. There are, however, broad features at about 270 and 520

{cm}^{- 1}

that can be observed above as well as below

T_{c}

. These broad features are not any of the

3 n - 3 = 12

optical modes at the center of the Brillouin zone.

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Lattice modes in ferroelectric perovskites. III. Soft modes in BaTiO3