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P H YSI CAL REVIEW VOLUM E 159, NUMBER 3 15 JULY 1967 First-Ord. er Rarnan Effect Induced by the Static Electric Field in Cubic Perovskite- Tyye Ferroelectrics* V. Dvokkxf I'hysics Department, University of waterloo, 8"ater/oo, Ontario, Canada (Received 16 February 1967) The first-order Raman effect in the paraelectric state of perovskite-type ferroelectrics induced by the field applied on the crystal in the direction of one crystallographic axis is investigated. Attention is paid mainly to the Cochran ferroelectric modes. First, the angular dependence of the Raman scattering eKciency S of these modes is derived when the incident (linearly polarized) and scattered light propagate perpendicularly to each other in the plane perpendicular to the applied Geld, Then, using the quasiharmonic approximation, S for ferroelectric modes is related to electro-optic constants and other measurable quantities. Kith a field of 1 kV/cm applied on the crystal, S equals 10 6— 10 r for BaTi03 in the temperature range 120-150'C. The temperature dependence of this effect is discussed, and it is compared with the first-order Raman e8ect in the tetragonal phase of perovskite crystals. I. INTRODUCTION phonon process which in principle might display experimentally the ferroelectric mode in perovskites. Un- fortunately, since in the paraelectric nonpolar phase of perovskitc crystals all atoms in the unit cell are situ- ated at the centers of symmetry, the first-order Raman process is not allowed in these crystals. However, the centers of symmetry can be lifted by applying to the crystals external forces, as for example mechanical stresses or static electric fields. The main aim of the present paper is to estimate the magnitude of the first- order Raman-scattering CKciency for ferroelectric modes when the static clectnc field is applied to cubic perovskites. 'ANY interesting properties of the paraelectric ~ - state of perovskite-type ferroelectrics are now quite well understood from the point of view of lattice dynamics. (See, for example, Ref. 1. ) The basic idea is that in these crystals there exists a long-wavelength transverse optical vibration (with respect to which the lattice becomes unstable at the Curie-gneiss temperature) with an anomalously low and strongly temperature- dependent frequency. This idea was first experimentally established in Sr Tioa by means of neutron-scattering tcchnlques and far-11lfrared spectroscopy. This type of vibration (ferroelectric mode) with strongly temperature-dependent frequency, which in fact causes the Curie-gneiss behavior of many properties of the material, should exist in all ferroelectrics of the perovskite family. However, direct observation of the temperature dependence of the frequency of the ferroelectric mode in the paraelectric phase meets serious difhculties in perovskites with high Curie-Weiss temperatures (like BaTiOs and several others). The reason is the strong damping of the ferroelectric mode and an unfavorable spectral region of 10 cm '. By means of far-infrared reQec- tivity some measurements have been performed in BaTi03 and a low-temperature-dependent frequency was found. However, the form of this temperature dependence was not established because of experimental uncertainties and different ways of assigning a fre- ucncy to thc fcrroclcctI'1c mode. The 6rst-order Raman effect is another type of one- II. RAMAN-SCATTERING EFFICIENCY FOR FERROELECTRIC MODES Throughout this work. we shall neglect Brillouin scattering and hence we may treat the wave vector of the incident light as electively zero. In this approximation the incident light is scattered in the first-order Raman process by optical modes with the wave vector zero only. The symmetry of cubic perovskites is O~, with five atoms in the unit cell. Three optic modes of Fr„(I'rs) symmetry and one optic mode of Fs (I'ss) symmetry occur in these crystals. 4 ' The modes of Iii„ symmetry are infrared active but none are first-order Raman active. If a sta, tic electric 6eld R is applied to the crystal, parallel to the direction of one of the equivalent crystallographic axes, the s axis say, then the symmetry of the crystal becomes C4„with the four- fold axis lying parallel to the s axis. Asa result. each mode of Fr symmetry splits into one mode of Ar(dr) symmetry and one mode of E(hs) symmetry, while the mode of Fz„symmetry splits into one mode of Br(r4) symmetry and one mode of E symmetry. The modes of Aq and E symmetry are infrared-active and all optic modes be- come first-order Raman active. However, the result of group analysis must be modified to some extent because of the long-range electrostatic forces which are present * Work supported in part by the National Research Council of Canada and in part by the University of Waterloo. f Permanent address: Institute of Physics of the Czechoslovak Academy of Sciences, Prague, Czechoslovakia, ~ B. D. Silverman, in Proceedings of the Internationa/ Meeting on Iierroelectricity, edited by V. Dvor6k, A. Fouskora, and P. Gilogar (Institute of Physics of the Czechoslovak Academy of Sciences, Prague, 1966), Vol. I, p. 3. 2 R. A. Cowley, Phys. Rev. Letters 3, 159 (1962}; A. S. Barker, $r. , and M. Tinkham, Phys. Rev. 125, 1527 (1962). ' J. M. Ballantyne, in I'roceedings of the Internationa/ Meeting on Ferroelectricity, edited by V. Dvorak, A. Fouskora, , and P. Gilogar (Institute of Physics of the Czechoslovak Acade Sciences, Prague& 1966), Vol. I, p. 55 my of 4 B. D. Silverman and Q. F. Koster, Z. Physik 165, 334 (1961. ). ' V. Dvorkk, Phys. Status Solidi 3, 2235 (1963). 159 652

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