measured aIon the b* direction. As one deviates from this direction, the frequency increases rapidly. We observe a similar behavior for the TA phonons pro-.
NEUTRON SCA’lTiWUNG STUDY OF THE
FEIRROELKTRIC PHASE TRANSITION OF SbSI J. P, Pouorrrt and S. M. Sr?Mmo Breokhaven NationalLaboratory,$ Upton,NY 11973,U.S.A.
BellLaborstories, Murray Hill,NJ 07974,U.%A,, (Received25 &IMfpls: accepted fn miscd fom 8 Septmbcr 1978) Abdrrt--Thc paraekWic&rroelectric phase&a&ion of SbSIhasbconstudiedusingneutron5wttork Several low frequencyphononbraochoshave been obmrvcd.In twticuk, it ha5 been ebowothat the [lo01attd[OlOl transverseacousticmode5pokizcd alongthe [OOl]dkctioo withthe samesymmetry8a the 5oft m*, exhibit very aaitotropic
dkpadon
reiatio,n~ in rc~iprocal
Forlargeq values,
apace,
an iinomabm
di8pemioa
ml&on
and
a
very Iargetemparaaucdependence. havebten ob5erwd.AS thw ei?ectsarcshowoto be duoto a couplingwitha soft mode-centi compoocntentity,ThisentitywasobwrvcdaWayfromthe zone center,butat the zone cutter,in contra5twiththe light sc&cringme~u~ments, no wall-defined soft moderesponsecouldbe ob5erwd.
1. INTRODUCIION
Antimony sulfa iodide (SbSI)belongsto the seriesof the
chain structureV-VI-VII ~~~~du~t~ which have been the subject of considerableinterestfor the last severalyearsdue to the numberof remarkable physical propertiesthat they possess. For example,the most studiedcompound,SbSI, exhibitsau unusualcombiuation of stronglycoupledp~onductive, semiconductive and ferroelectricpropertiesand is the strougcst knownpiezoelectriccrystal[l]. Its bandgap has an abnormallylarge tiaras eoefkient and wdii%itsau unusual negative Fw Kcldysh effect when an electric field is applied along the chain ~~. It also shows anomalou3electro-optic and ~t~~h~~ properties; under illumiuationthe chaiu directioncontractsin the ferroelectricphaseand elongatesin the paraelectricone. For these reasons considerable attention has been devoted to this type of structureand to its lattice dynamics. The SbSI familyof crystalspossessesa highly auisotropic structureconsistiugof doubly linkedchains ex~~~o~~~~s,~~~yaw~~~ between adjacentdouble chainsQ,3]. With four SbSI formulaunitsperunit cell (one perchain)this compound uudergoesa weak first order phase transition from a paraelectric (orthorhombic D?,) to a ferroeLctric (orthorhombiiCk) phase at a T, near room temperature.The spontaneouspolar&ion is directedalougthe chain directionand resultsfromthe d&placement along the e axis of the Sb and S ions relativeto the I ions. Underpressure,the first ordernatureof this trsnsition tpernlanalt addrosa:Labor&ire de Physiquedes SoSdcs, wsci6 au CNRS,91405,&uwt Frrace. $RWIU& supportedby thy Divisiou of Basic EaeW $&nces, Dcpprtnent of EIIO~, underContractNO+ W-76-G oz-Oa16.
decreases and a tricritical point at P = 1.4kbar and T = 235K has been reported[41. Until recently, because of the lack of large enough crystals, the lattice dynes studies of this compound were restricted to zone center easements by optical ~~~s[l,~~. Neve~eless, in spite of the great number of normal modes and their relatively low frequencies, the main features of the observed Ramau spectra have been satisfactorily and IK interpreted[l,9,10,133 on the basis of a simplified modelf of liuear atomic chains directedalong the c axis and interactingby isotropic and weak interchain forces. The optical studies were devoted to the damps of the ferroelectric phase transition with evidence that this transitionresults from the softeuingof a zone center modeIT&In particular,in the ferroelectric phase, Kaman spectra have showa a strongly temperature dependent mode whose temperature variation of its frequency accounts roughly for the temperature dependeace of the dielectric constant along the ferroelectric axisl.Tj. FWher analysisof the low frequency part of the Raman spectra has corrected this ideal behavior somewhat by showing that on approachingthe phase trausition, the soft mode crosses one @Ior two11I] other optical modes of the same sync with which it interacts strongly. Finally, closer to T,(IATj% 1OK) Steigmeier et a1.1141 have reported the observation of a central peak, spectrally resolved and interpretedin terms of phonon density flu&uation.Above T, in the centrosymmetric paraelectric phase, only IK ~~ernen~ can give infan on the soft mode behavior and a low frequencycontriiutioncomingfrom the soft mode has been seen[d,10,f2]. The electricallyclampedelastic constants have also been accurately measured by Brillouin scattering at two ~rat~es: one below T,(T, - T = 7 K) and oue
261
J. P. POWGET, S. hf.
268
SHAPRO
above (T - T, = 3 K) [15]. No significantchange in their value between the two phases has been observed. This is a surprisingresult because one expects generally in the ferroelectric phase (non-centrosymmetric) for small q values a coupling vetween the low frequency soft mode and the transverse acoustic (TA) mode of the same symmetry which might soften the C$ and C$ elastic constants. Wowever,measurementscloser to T’ need to be done before a definite conclusion can be drawn. It is only in the last two years that some measurements away from the center of the Brillouin zone have been performed by X-ray diffuse scattering[l6,17] and neutron scattering[l8]. The X-ray diffuse patterns show clearly three difIerent sets of diffuse sheets in both phases. The most intense scattering is perpendicular to the c* axis with integral value of I. Its intensity increases linearly with tem~rature in the ferroelectric phase and shows an approximatelyI’ dependence. It has been concluded that, by analogy with the perovskites, this scattering comes from (h k 0) planar anisotropy of transverse phonon modes polarized along the chain direction. This interpretation was confirmed by the inelastic neutron scattering results of Peirrefeu et al.[18] which show that deep valleys occur along b* in the TA branch polarized along the c direction. This is a mode with the same symmetry as that of the soft mode. No conclusions, however, could be drawn about the soft mode because of the smallnessof their samples. The above quoted experimental results give only a very crude view of the lattice dynamics of SbSI. Optical me~~ements observe a soft mode behavior below T,. No complete study of the dynamics of the phase transition viewed from the paraelectric phase has been done and no further study of the soft mode-centralpeak entity reported by Steigmeir ef al. has been performed. With the availabilityof an exceptionally large crystal we have undertaken a neutron study of some of these questions. Finally, it is interestingto remark that there is another family of compounds like K2Se04 which presents a ferroelectric phase transition between the space groups 04: and C& and with a very close correspondence with SbSI between the position of atoms or group of atoms in the unit cell; however, the binding forces are very different and in K2Se04an incommensuratephase exists that separates the paraelectric phase from the ferroelectric one [ 191. 2. EmERmEwAL
sampIe, grown by the modified flux rne~~[~], was needle-likein shape with the elongation along the c axis of the orthorhombic cell and with a stze of 5 x 5 x 30mm3. First it was glued onto an alumimun sample holder and rno~t~ in an auburn can @led with helium gas and placed in a cryostat where the temperature was controlled to within 20.1 K. The scattering plane chosen was either (k 0 1) or (0 k I). With this last orientation the sample was also placed in a vacuum furnace where the temperature was stabilizedwithin 1K. During this last experiment an overheating at 58OK sub~medone half of the crystal. The mosaic spread was found to be ~0.2” and ~0.3” in The
and K. NASSAU
the (0 k 1) and (h 0 I) plane respectively. Usingthe (0 0 2) Brag8 reflection as a reference, a slight increase of the mosaic spread was observed within a few degrees of the phase transition. This mosaic also exhibited a long tail in the (Okl) plane where most of the measurementswere pe~ormed. The neutron scattering experiments were performed on the triple-axisspectrometers at the Brookhaven highflux beam reactor. The majority of the scans were made in the constant Q mode with fixed incident neutron energy of 13.5and 14.8meV. A pyrolytic graphite filter was used to reduce the higher order neutrons from the mon~hromat~. DitIerent horizontal connations ranging from 20’-KY-tO’-40’to 40’-40’-40’~ were used depending on the resolution and intensity requirements (they are expressed in minutes of angle and the four successive numbers put in the following sequence: in pile, monochromator to sample, sample to analyzer, and analyzer to detector). 3. Ebb
RlSULTS
At the ferroelectric phase transition the structure loses its center of symmetry and the space group changesfrom I?:“, (Pnam) in the para-phase to CZv (Pna2,) in the ferro-phase keeping the same conditions limiting the Bragg reflections. Therefore, no new Bragg reflections will appear below the phase transition.Only the structure factor of some of the allowed Bragg reflections present in both phases change at this transition. The observation of a zone center soft mode is thus complicated by the presence of strong Bragg scattering.Also because of the expected low frequencies, high energy resolution is required with a concomitant decrease in intensity. Scattering in three different Brihouinzones (00 2) , (0 4 2) and (0 13) were studied. The calculated structure factor and the measured intensity of the corresponding Bragg reflection are given in Table 1. No major change of the (00 2) and (04 2) Bragg intensity was found at the phase transition in accordance with the structure factor calculation, but a large change was found for the (0 13) Bragg reflection as already observed by Pierrefeu et al.[f8]. Such ~rn~ra~e variations on heating are shown in Fig. 1. In the ferroelectric phase as the phase transition is approached from below the (0 13) Bragg reflection decreases very strongly in intensity until the paraelectric phase, where, within experimental errors, the intensity is constant. No discontinuityin the intensity is observed. T, of our sample is defined where the intensity begins to change from the constant value. On heating the value T, = 291.520.5 K was found. By the same method a hysteresis of 1 K at the phase transition was found on cooling,confirmingthe tirst order nature of this transition. A similardetention of T, and observation of a hysteresis on the (0 13) Bragg reflection has also been reported by Pierrefeu et al. [18]. Figure 2 presents another dete~ation of T, using the elastic critical scattering observed in the (04 2) zone for q values near the zone center (q parallel to the b* direction in which X-ray diffuse scattering is observed). Figure 2 shows that there is a constant con~bution vistble at low temperature coming from the contamina-
Neutron scatteringstudy of the ferroelectric phasetransition of SbSI
269
Table 1. IPt2cal
'ohs
FNrCIa
Parab
(0 0 2)
26.4
26.9
(0 4 2)
5.5
5.5
(0 1 3)
0.4
1
0
(counts/o.1 mid
IFinel12 arb units=
s 250,000 %
QO
50,000
0.7
T > Tc = 700
3.9
T < Tc see Fig. 1 a.
275 K from Ref. 21 but T 2 289 K in our sample from lattice parameter.
I
b.
300 K from Ref. 22.
C.
Arbitrary units with IFinel12
max
I
I
SbSI G.(O,l.3) AE=i
z
\TC=291.5?.5'
t
I
I 300
T(K)
Fig. I. Temperature variation of the (0 I 3) Bragg intensity. The transition temperature deduced from this measurement is indicated.
= fi2 .-
T,. This method gives T, = 291K in excellent agreement with the previous determination. We have also noticed that the orthorhombic c lattice parameter (along the chain direction) shows an anomalouslylarge decrease (a relative change of 0.4%) on heating just below the phase transition between 287 and 290K. No similareffect was observed for the a or 6 lattice parameter which shows only a small and smooth increase with the temperature without any anomaly in the vicinity of the phase transition. The lattice parameters in the ferroelectric phase at T = 280K are a = 18.507& b = 10.126& c =4.107A and in the paraelectric phase at T = 308K, a = 18.4%A, b = 10.142A and c = 4.091A. The above evidence of critical scattering at the phase transition was the lirst encouraging step toward the observation by neutron scatteringof soft mode behavior in SbSI. For this purpose we performed an approximate calculation of the inelastic structure factor for the soft mode. Omitting the Debye-Waller factor, the inelastic structure factor at the zone center defined by the reciprocal vector G is: Fimi(G)= T (G 9e,Jbdc’m
neutron scatteringlength for the kth atom of the unit cell; IL, and ek being the coordinate and the displacementof atom k respectively. ek is approximated by the static displacementvector of the atomic positions between the para- and ferroelectric phases S&. An additional condition neglected previously[l8] is that the center of mase of the crystal does not move at the phase transition;i.e. & mk8Rk = 0, where mk is the mass of the atom k. The refinementsof structure, quoted in Table 1, indicate that the main change of the atomic positions is along the chain direction. Table 1 gives, for the three Brillouinzones considered, and on an arbitrary scale, the square of the calculated dynamical structure factor. A relatively strong value is found in the (0 13) zone, which already exhibits a large change in the intensity of the elastic Bragg peak in the ferroelectric phase (Fig. 1). In contrast to Pierrefeu et a1.[18]Table 1 shows a very small inelastic structure factor for the soft mode in the with br, the
200
250
300 T(K)
Fii. 2. T_emperature and r) variationsof the elastic scatteringin the (0 4 2) zone. The transition temperature deduced from this measurementis indicated.
by the tails of the Bragg peak. But as the (04 2) does not change with the temperature (see Table l), this does not atkct our determination of
tion
Bragg intensity
(1)
270
J. P. POUOET,
S. hi. SHAP~O and
(00 2) zone. But since the (00 2) Bragg reflection is extremely strong, this zone is useful for the measurements of the transverse acoustic phonon branch (TA) polarized along the chain direction, a mode with the same symmetry as that of the soft mode. Pinally, it is useful to note that we have not only restricted our measurements in the (00 2) and (0 13) Brillouinzones but measuredin the neighboringBrillouin zones (10 2), (0 f 2) and (0 0 3) because there is a certain continuity of the behavior of the phonon branch between neighboringzones along the a* and b* directions (see, e.g. the results of Pierrefeu et a/.[181showingthe strong anisotropy along the b* direction for the TA mode in the (0 0 2) zone and for its continuation is terms of the TO mode in the (0 12) zone). This leads to the convenient use of an extended scheme of two ne~bo~g zones for the plot of the phonon dispersion relations. Such doubhg of the Brillouinzones along a* and b* is related to the already quoted physical idea to describe the compoundby a simplifiedstructure with only one doubly linked chain per unit cell (in this procedure the a and b parameters are divided by two). In this extended zone scheme the continuity of behavior of the phonon branch produces a continuity of the atomic movement in the sense of a passage from an “in phase” movement to an “out of phase” movementbetween the two doubly linked neighboringchains belongingto the real unit cell. Symmetry any indicate also that the passage from one zone to the next one (i.e. from one type of movement to the other one), through the zone boundary must be continuous along a* (glideplane along the direction) and discontinuous(i.e. with a gap of energy) along b*. (a) Aco~~ic modes The TA modes proper perpendicularto the chain direction but polarized parallel to it (e//[OOll)were measured about the (00 2) Bragg peak. The measurements were extended beyond the zone boundary into the next Brillouin zone where the TA modes become TO modes co~es~n~ to an out of phase motion of neck chains. The movements were made along the (5 0 0] and [On OJdirections and the results shown in Figs. 3 and 4 respectively. The surprisingfeatures is the large temperature dependence for the larger q values. ‘Ihis produces for Qar0.20 in the ferroelectric phase an apparent kink in the TA branch which becomes more pronounced as the phase position is approached from below. In the paraeiectric phase an anomalous 9 behavior in the TA branch is also observed for q 2 0.15. Figure 4 shows that it begins to be partially removed only at several hundred degrees above the phase transition. This anomalous q behavior, also observed in the (042)~~~~~~~~~~~~~. Figures 3 and 4 show that the TA mode does not change drasticallyfor q values less than 0.15.On heating from the ferroelectric phase only a slightdecrease of the sound velocity is observed. At 285K and 2MK the elastic constants Cu and G$ deduced from the slope of these TA modes are (within our experimental errors) in perfect agreement with the accurate measurements of Sandercock[lfl u&g Brillouinscattering[231.
K. NASSAU I I SbSI
3.5
I
I
I
,
/
I
/ I
‘5 g 2.5
0 80°K ‘250°K * 275’ * 285” * 280” 0 300” a 325”
0.5 (002) 0
01
02
ZONE 0.3
04
(102) 05
06
07
1 , K K K i K --Tc ; K
ZONE 08
09
IO
ICOOl
Fig. 3. Temperature dependent dispersion curves for ii 001 transverse acoustic and transverse optical (41 [O 0 I]) phonons in SbSI.
(002) 0
0 I
0.2
ZONE 0.3
0.4
1 05
I 06
/ 0.7
/ 08
, 09
IO
[01701 Fig. 4. Temperature dependent dispersion curves for [O 1 O] longitudinal acoustic, transverse acoustic and transverse optical @[OO 11) phonons in SbSI. The corresponding sound velocity, calculated from Czs and Cu elastic constants[lS] are also indicated.
Figure 4 shows at 300K in the paraelectric phase a curious hatched region for O.lSb*I q ~+.0,2Ob*.In this region, it has not been possible to define clearly the phonon frequency. This behavior is ovserved for T 2!QK to above 325K. It is illustrated in Fig. 5 by three selected scans performed with a very good resolution. The line width in Fig. 5(a),SE = 0.25meV, represents the instrumental resolution for this type of scan. For q = O.lOb* and q =O.U)b* below and above the hatched region, a well-defined one phonon response is clearly observed. In the hatched region, for q = O.lSb* in this figure, we get only a broad response in energy with no single one phonon peak clearly defined. A big decrease by a factor of 4 of the intensity and consequently the dynamical structure factor of this TA mode is observed when the hatched region is crossed from the low 4 region to the high q one, indicating a change in the nature of the phonon mode. However, from the scan presented in Pii. 5(b), it is ditIicult to describe this hatched region; is there an interchwe between two one
Neutronscatteringstudy of the ferroelectricphase transitionof SbSl
271
300 .g t p
toll:
20-20-20-40
200
3 & 100
Ex*
14.7msV
co& 40-40-40-40 (b)
.c 9
300
:, c
T .T, 0 295
K
l 534
K
5 8
200
I
0
1 0
I
0.5 NEUTRON
I I.0 ENERGY
LOSS
1.0 ENERGY
I I .5
0.5
2.0
tmrV)
Fig. 5. Neutron energy loss profile obtaioed from (a): q = 0.10, (b) q = 0.15 ad (c): q = 020 (see Fig. 6(a) for their location), in the paraelectrk phaseof SbSI at 295 K, with an incidentenergy of 13.5meV amIa 20?-1W-104@co%matioo.The verticalbarsin (a) show the instrumentalresolution.
phonon responses or one heavily damped phonon response? ‘Ibis TA mode is clearly interactiug with something,but we have heen unsuccessful in determining with what it is interacting. On heating in the paraelectric phase, Fe. 4 shows that the phonon branch becomes less anomalous. For q = 0.2b*, at 406K, and above, it becomes possible to define a one phonon response with a welldellned maximum over the entire Brillouinzone. In the ferroelectric phase, the dispersion relations drawn in Figs. 3 and 4 do not exhibit the same anomalous q dcgmdenti, but there is a rapid change of slope around q - 0.2 for temperatures near the phase transition. For this q rc@on, and these Ernst we have also observed an unusualshape for the phouon respon=. Fi 6 shows the anomalousresponse for q = 0.2b* at temperatures near T, in the paraelectric (Fig. 6a) and the ferroelectric phases (I@. 6b). This 6gure also demonstrates how the anomalous response of this TA mode disappears as IT- ?“I increases. For T 4 7” (Fig. 6a) at T = 265K, the phonon response already is quite normal and for T*E (Fig. 6b) the response again appears normal. This implies that the interaction can be ‘Yumedofi” by moviug in temperature further from T, This interaction is strongly localixed in the directkns perpendicularto the chain directions. If the proIuq@on direfztiondeviates even slightly from the b* dire&ion+a normal one phonon response is obtained. FQure 7(a) showsthedisparioa~e~T==Kforp~~~ ~~b.~f~a~~~-
1.5
2.0
2.5
(msV)
Fig. 6. Comparisonbetween phonon pro&s obtained for r) = 0.2; (a) in the fcrroelectricphaseat 265 and 288K and (b) in the pnraelectricphase at 295 and 534K.
ing an angle of 150with the b* direction. Figure 7(b) shows the spectral profiles for the two directions. It is clear that the photon response becomes normal when q deviates from the b* directions and the dispersion changesquite drastically. An additioual evidence for the strong anisotropy is obtained in measuring the dispersion curves along several symmetry dhections. Pierrefeu ct al. [ 18j showed tbat a deep valley existed in the phonon dispersioncurve measured aIon the b* direction. As one deviates from this direction, the frequency increases rapidly. We observe a similar behavior for the TA phonons propagatingalong the u+ direction with polarizationalong c. Fgure 8 shows the dispersion curve in the para and ferroelectric phases and reveals the rapid increase in frequency in going along the 10.50g] direction. This anisotropy was also seen in the X-ray scattering experiments which revealed strong diffuse streaks perpendicular to the c* direction[lQ 171. This anisotropy is expected for a quasi-onedimensionalsystem. The lower frequency for the TA modes polar&d parallel to the c* direction impliesthat the chains are weakly coupled and can slide easily relative to one another. (b) Lowfrequexcy nwa%Sin rk (0 13) zone Let us recall that we have aheady found in the (04 2) xone @ii. 2) some evidence of critical scattering at the ferroelectric phase &an&ion. However, the inelastic structure factor calculationreported in Table 1 indicates that the (0 13) zone is the most favorable place to observe, the soft mode. However, measurementsin this zone present several ditkulties. A first dlkulty comes fromthepreseueeofanaIlowedBraggreik&oninboth p~w~h~~~q~0~~~~.
J. P. I
‘“’ SbSI
I
I
S. M. SHAPIRO and K. NMAU
POUGKT,
I
T,0.2.5 and which seems to merge into it for 7)= 0.25. (iii) another low frequency response appearing around 3 meV for n = 0.20 and whose frequency seems to decrease as n decreases. A zone center constant Q scan is shown in Fig. 10(a) on a more extended energy scale. Although it has been taken at 295K, it exhibits the same features that are observed at 300 K: the (0 13) elastic Bragg reflection then a long tail of cross section with a level of twice the background out to 5 meV. No sharp phonon response is
Neutron scattering study of the ferrockctric
k SbSl 1 = 300.K
400
;
300
* 5 2
200
0’ ”
100
0
I
2
3
NEUTRON ENERGY GAIN(meV)
Fii. 9. Low energy neutron gein pro6ks for ditTercnt q values in 13) zone of para&cui~SbSIat 300K. The shaded area.,
the (0
drawn for r) = 0.5, gives the baclrground.
50
.E m 2
I-
BACKGROUND 0
I
I
I
200
f g 150
-
100
-
50
I
I
(b)
I
l
ij.(O.O.6.3)
0
~=co.o6.3.om
0
SbSI
n3
slightly different constant Q = (0,1,3.05) scan probing the longkhnal polakation. Now a clear one phonon response is observed at 5 meV and the backgroundlevel is reached at lower energy. A comparisonbetween these two scans in Fii. 10(a)gives the fourth feature observed in this zone. (iv) A one phonon response at 5meV (observed clearly in both phases by Raman scattering and in the present study in the ferroelectric phase). Additionally,a very broad response in energy is observed which might be the “continuation”of the third feature observed near the xone center, in Fig. 9. The presence of these four responses within a 5 meV energy range leads to very complicatedspectra. In order to obtain a better understandingof these experimental results we shall examine with more detail all these features and their temperaturedependences. First, let us consider the central peak. Its existence is clearly demonstratedin Fig. 9 where the signalis above the backgroundlevel even near the zone boundary. The energy width is resolution limited at SE = 0.8meV. No higher resolution scans have been perforiucd in order to detect au eventual intrinsic contribution to the energy width.As I) is decreasedthe low frequency mode feature (iii) becomes overdamped and merges into the central component. This prevents the determination of the central peak alone in this region. We can, however, study the behavior of the central peak-ove&mped mode response for n = 0.2b+ as a function of temperature. This response is shown in Rig. 11(a).The intensity clearly diverges as T-, T, while the line width remains resolution limited. Integrating this over energy and plotting its reciprocal times the temperaturewe obtain a linear response as shownin Fu. 11(b). This is precisely what is expected for a soft phonon response. In a neutron scatter& experiment, the observed intensity in the high temperature limit is (2) where A(@)is the spectral correlationfunction whichfor phonons has the form of a damped harmonic oscillator[24].If we integrate this over energy we obtain
t
01
phase transition of
I I
I
I
I
I
I
I
2
3
4
5
6
7
NEUTRON
ENERGY
GAIN
(msV)
Fig. 10. Comparison between the neutron energy gain pro6ks obtained at 29JK in the paraekctric phase of SbSI for (a) Q=(013)andQ=(013.tMjconstrmt&saad(b)tbe~i, Q = (0 0.8 3). and tbc special “IS” OF, Q = (0 0.8 3.022). constant scans. The vertical bars show the instrumcnt8l resoluth.
where u,’ is the frequency of the response of the system 2=aBq2+Aq2. @=I
(4)
For a classicalsoft mode (SM) behavior, m2 a (T - T,) which explainsthe v dependene in Rig. 11(b). lheseresultsalsofollowtheq2dependenceobtained observedbutthelongtailofcrosssectionnpesentaa from eqns (3) and (4) for q = 0.2b* and O.lSb+. Extnieeffect.@nasimilarscanperformedatBS5K,where pie. ll(b)is the (013) elastic rekctkm has a 30 times bigger in- trapoM&toq=O,thedashedcurveof tensity, the background level is reached for energim obtahmdwhich in§s the temperature axis very near greater than 2meV.) lhe same tIgure also shows a TC. JKSVdQ.No.4-B
J. P.
POUGET,
hf. SHAPRO and K. Nnss~u
S.
10(
\
0 T*306U T=534K
l
50
c L
0.7
;;
(bf bbS1
i
I
q*oz qso.15
0.5
q=o[extra~latio~)
‘2
it)
(ms’v’) I
Q=(O,i-q,31
0.6
.r.
lr
-I 0 NEUTRON ENERGY
-2
e t
0 too
2
I
8
;
5;
50
9 Ji
0.4
..?
0.3
;r: 0.2
0
0. I
0
,/
0
200
I 300
I 400
I
500
7 IK>
Fig. I I. (a) Central ~amponent profiles for several tem~ratures for * = 0.2 in the paraeiectric phase of SbSf. The backgrolmd level is also indicated. (b) T/X(q)plot vs temperature of the area I(q) below the central proflcs presented in (a) for q = 0.20 and 9 = 0.15. The points corresponding to q = 0 correspond to an ~xtrapo~a~n of the behavior of if@ ~suming a qv2law. The transition temperature deduced from Figs. 1 and 2 measurements is indicated.
I NEUTRON
I
2
3 ENERGY
4 LOSS
5
6
fmev)
Fig. 12. Neutron energy loss profiles at 308 and 535 K in the p~el~t~c phase of SbSI for (a) q = O.iOaad (b) 7 = 0.15.
energy excitation presu~~y moves to higher energies because of the strong anisotropy. A broad peak centered around 3.5meV remains and this is the contirmationof the optic mode observed in Fig. IO(a). For smaller n, no well-definedpeak is observed, but wingsextendingout to -4.0 meV are observed which are only slightly temperature dependent in the paraeIectric phase. The real nature of the scattering is evidenced by the disappearance of feature (iii) on moving q slightly away from the pure transverse direction (Fig. 10). In the dispersioncurve presented in Fig. 13,the results low
These features suggestthat this may indeed be the soft mode which is overdamped at q = 0 in the pamelect& phase. But at a finite q value (q >0.2b*), the soft mode might, in principle, correspond to either response (i) or response (ii) shown in Fig. 9. On heating, the central component (response i) decreases in intensity but never becomes underdampedeven at the zone boundary. The response (ii) which is overdampedat q 3 O.Zb*becomes underdog for targer q values and ap~~en~y has a soft mode-Ekebehavior. But this response decreases in intensity on heating and is no longer observable for T > 400K. Also, it disappears when q deviates from a pure transverse [O101d~ection. However, feature (iii) observed at small q values also is suggestiveof soft mode behavior. Figure 12shows the spectra for smah q in the [Ov 3f direction at two different temperatures. There appears a mode whose i , j , , i e , i , i cl. I 0 0.1 0.2 0.3 5.4 0.5 0.6 0.7 0.8 0.9 i.0 frequency is weakly tem~rat~ dependent near low iwa 2.0meV and a shoulder near 4.0meV. The behavior of this mode at larger v is comphcated Fig. 13. (0 IO] temperatore dependent dispersion curves of the by the mixingwith the higherenergy mode designatedas thre+ low energy branches observed in the (0 13) and (003) feature (iv) and shown in Fig. IO(b).At &rite Q, Fig. zones. The behavior below 1 meV and the centraJ component are not indicated. The dotted cum8 represeot the exudation 10(b),for the pure transverse direction a sharp peak at described in the text toward the position of the soft mode 3,OmeV is observed in addition to a long tail. If q obser& in Raman (R) and infrared(IR)studies at 288and 300K respectively. deviates slightly from the pure transverse direction, the
Neutronscattering studyoftbc fmoelectric
phasetrsnsitionof SbSI
27s
Ruponaa (hi, a very low frequency mode observable as an underdampedexcitation only for T)>0.256+, diw appears rapidly in intcmity as T, - T increases. ‘Ihis tCmpenrturedepeDdsacsiSObserVOd.Tbemain~~ branch is ooIy visiik for T >275 K. It has a frequency observed arc the optic braacb (called AZ)at -5.OmeV verys~totheTAmodeshowninF~.4ende~~i~ audauotherbmuch,A,,withastroqs&persiorrttearthe a strong tempenture dependence as seen in F@. 13. zoueceuter.lhishasaweaktemperatmedep&eXe characteristic of soft mode behavior. If we use eqn (4) &sponses (iiii and (iv) are the A, and AS branches measuredin the paraelectricphase for small u. for its q dependence we obtain ti-l.OmeV at q=O Attemptstolocatethesoftmodeasmeasuredinthe which is close to the value observed in the IB measureBaman scattering are shown in Pi. 14 for T = 285 and ments [lo, 121.‘I&e two branches cross at r) -OZb* and the A, branch extends above the AZbranch. Another 288K. For the zone center scan Fq. 14(a)we observe a feature observed which also has soft mode-likebehavior peak around 5 meV which is temperature dependent but is the overdamped mode for q -0.2bL which becomes does not soften. Iiowever, there is additionalscattering between this peak and AE=O which increases in inunderdampedfor larger q values. tensity as T, is approched. At T = 288K, this seems to (2) Furudecrlic phase. In the (0 13) zone below T, be a peak distinguishablefrom the A1mode. As we get the spectra are still complicated by the observation of away from the zone center a very broad response is four responses all with frequencies less than 5.OmeV. observed as in Fe. 14(b).Finally, for u = 0.2b+, the A2 For measurementsalong [Ou 31a central peak is obser- branch has decreased in energy due to its negative disved which shows a weak temperature dependence, in persion and we have difficultymeasuringany additional that it increases slightly as T, is approached.This was low frequency response. Several constant E scans were not studied in detail since in this transverse scan, there performed which did reveal a peak and these scans are could be a sign&ant contributionto the elastic scatter- inch&d in Fu. 13 with horizontal error bars. If we ing from the mosaic spread of the crystal. We observed extrapolate this A9 branch to q = 0, using eqn (4) we that the crystal mosaic spreaddid changereversibly near obtainanenergyof~=2.2meVatq=OforT=288K the transition temperature. Well below TC,the mosaic which is in good agreement with the Baman measurewidth as measmed about (0 0 2) is 0.36”.Just below T, at ments of the soft mode [7,8,10,11]. From Fig. 13, we T = 288”the mosaic width increases to 0.72”.Above T,, see as in the paraelectricphase that the A, and A2branch the mosaic spread againbecomes narrower.This process seem to cross each other near r) = O%b*. was reversii and is not well understood, but could certainly mask the central peak. Fiie 2 shows that a strong temperature dependent AE =0 scat&ring is Aa shown above, no clearcut experimentalpicture has present as measuredin another Brillouinzone. emerged to descrii the inelastic neutron scattering study of the phase transitioa in 8bSI. In this section, we will speculate on the origin of some of the couplings I I I I , SbSI observed. 0 T*285 K Our measurementsin the (h 0 1)and (0 k I) planes show . T=288K . 1 that the dispersionis highlyanisotropicwith deep valleys along the [O101 direction (Fii. 7a) and [NO] direction (Fig. 8), both directionsperpendicularto the chain directions. This is expected if we have a quasi-onedimensional structure, but it is important to note that large anisotropy has also been observed in other compounds which do not possess any apparent chain-likestructure, i.e. the cubic perovskite-typecompoundsKTaCh[25,X] and KNbChP7l. All temperature dependence is conlined to directions exactly perpendicularto the chain direction. A study of the acoustic modes shows a strong variation of frequency vs temperature below T,, but less of a temperature dependence above T, (Figs. 3 and 4). This temperature behavior is also seen in the AE = 0 scatterineobservedinthe(O42)uMeandshowninFig.2.This behaviorbecomes clearer when it is realized that the TA mode propa@ing ptrpadicular to c+. and polarized 1 I I I I 0 2 3 4 5 6 7 alonpc*hstheJamesymmetry(A,)astbeJoftmode.It NEUTRON ENERGY GAIN (meV1 is therefore reasom& to consider that this strong 4. 14. Cd between the neutronentray aain pro&s temperatllredepondenceoftheTAr_uodeisaresultof oMniacd~28Jmd21WKiatbcfenoekctricphueofSbSIfor (a) r)= 0, (b) r)= 0.10aad (c) ()= 0.2o.For r)= 0 the dubed the coupling between it and the soft optic mode. This curvesrepresentsthe lowfrcqee~~ypait of the dataobtainedst coupKngcouIdexistoverawiderangeofqvalues.Asoft 265Kwitl1thebrkgroundlevel. mode TA coupling has been observed in several struc-
ofourobservatiarsaresummarM.Ihepoiutsat3WK represent data taken from 2!H to 325K where no
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216
J. P. POUIXT,S. M. SH~RO and K. NASSAU
tural phase transitions such as KTa03 [25] and BaTi@ 1281. In KTaOp, Axe et ai.[25] have shown that in a centrosymmetric crystal (the case for SbSI above T,), the soft mode-TA coupling vanishes as q+O in such a way as to leave the acoustic velocity unaffected. They also observed a large temperature dependence of the acoustic mode frequency out to the zone boundary. Similarfeatures are observed in SbSI as shownin Figs. 3 and 4. Additionally, the Brillouin scattering measurements of the elastic constants show them to be unaffected by the transition[l5]. The main ditference between KTaOs and SbSI is that in the former the spectral response of the TA phonon is always quite normal, whereas in SbSI, as shown in Figs. 5 and 6, the spectral response is complicated. This could be due to the fact that in SbSI, the frequency d#erence between the soft mode and the TA mode is smallerthan in KTaOs and the interaction much stronger. Unfortunately, we have not clearly observed the soft optic mode in the range of q values where the couplingis strongest. The fact that the acoustic modes in the ferroelectric phase show such large anomalies away from q = 0 is ditlicult to understand. This, and the similarities with K&O,[19] led us to speculate that maybe an incommensuratephase existed. A search for superlatticepeaks at AE = 0 about where the minimaexist in the acoustic branches yielded no evidence of any incommensurabilities. If the modes were uncoupled we would not expect to see the soft mode in the (00 2) zone because of the weak inelastic structure factor (Table 1). However, because of the interaction, intensity may be “borrowed” from the strong TA mode in the region where they interact. In a similarway, we expect the TA mode to be observablein the (0 13) Brillouinzone where the SM shouldbe strong and the acoustic mode quite weak since the elastic structure factor is small (Table 1). The very low frequency mode observable in the (0 13) for q r0.256* could be the TA mode. The fact that its frequency is slightlylower than the TA mode measured in the (00 2) zone might be explainedby interference effects between the two modes. This is similarto what was observed in BaTiG where the zone dependemce of the response of the TA mode arises due to a TA-soft mode coupling[28]. Two additionalfacts are also in favor of a mixingfor q ~0.2 between the TA mode and the SM: (a) The TA mode becomes less anomalouson heating in the paraelectric phase indicating a decrease of the interaction, which is consistent with an increase in the SM frequency as T - T, increases. (b) The anomalous behavior of the TA mode is confined only to the directions perpendicular to the c direction (Fig. 8a). On slightchangesfrom this direction, the response in normal. This same behavior was observed in KTaOJ[26]. Additionally,the low frequency feature observed in the (0 13) zone for q r0.256* (feature (ii) described above) disappears when the TA mode becomes less anomalous. This supports a strong interaction between the TA and the SM
Let us now return to the curious shape of the TA branch observed in the (00 2) Brillouinzone. Even with an interaction witb the soft optic mode it is difficultto understand why the TA mode has such a large width only around q - 0.2b*. This may be explained by the recent microscopic calculation of Huberman and Martin1291concerningthe couplingbetween the acoustic phonons and a central component.They find that close to T,, the acoustic mode becomes overdamped for a range of wave vectors but remains well defined for q -+O and for larger q. In our measurements and the Brillouin scattering[lS] well defined TA modes are observed for q = 0 and for the larger q’s. Let us now consider the central peak in SbSI. Recent light scattering measurements by Steigmeier et a1.[14] report on a divergingcentral component,distinct from a soft mode. In our measurements for q = 0 we cannot state that there is a central peak since the very intense Bragg scattering would mask any other scattering at q = 0. Our data for T < T, at q = 0 (Fig. 14a)shows that there is scatteringextendingout to -4.0 meV existing as wings,but it does not narrow, nor does it diverge strongly as T - T,. For larger q’s there also is scattering at AE = 0 but exhibits little temperature dependence. There still remains the problem that we have not been able to identify unambiguouslythe soft mode. The strong coupling between the several excitations over a limited energy range makes it difficultto untangle the features. The light scatteringmeasurementsrevealed evidence of a complicatedphase transition. The original Raman study showeda singlesoft mode[7j but later studiesindicateda couplingof two modes[8]. A third set of measurements indicated that as many as three modes mightbe coupled at q = 0 [ll]. (On the basis of the present results some of the features seen in the light scattering are most likely second order Ramanprocesses.) An explanationof the ditferences between Ramanand neutron experimentsmay lie in the combinedeffects of a very anisotropic dispersion surface and the relatively poor momentum resolution of a neutron spectrometer[30].When the spectrometer is set for q = 0 it is probing a finite region in q space due to its limited momentum resolution. The energy surfaces may be changing rapidly within the resolution volume and the resultingspectrumwillbe smearedout givingrise to long tails as observed in Figs. 10 and 14.Additionalevidence for this comes from the large splitting of the LO (13.8meV)-TO(1.1meV) q = 0 modes as determined by IR measurements[6,lo]. For the q =0 neutron measurementsof Figs. 10 and 14, the &rite size of the resolution may be probing both the TO and LO oscillations. We now discuss the symmetry of the observed modes and compare it to the results of the optical measurements. The higher frequency branch around BE 5.0meV (Fig. 13), designated as AZ, corresponds to atomic motions parallel to the chain direction since this branch is observed most stronglyin the (00 3) and (0 13) Brilkmin zones. An optic mode of frequency 37cm-’ (4.6meV) with this polarization was observed in both phases of the Ramanscatteringspectra and labeled Ts at
Neutronscatteringstudy of the ferroclectricphase transitionof SbSI
q = 0. (In the following, we shall use the symmetry notations of the paraelectric phase.) At the zone boundary, this branchchangessymmetryto Aa,whichis of the same representationas the soft mode branch which may explainthe large ~rn~ra~ dependenceof this branch. At the (00 3) zone center the symmetry becomes rs which should have been seen in the Raman studies except that the frequency may be so low (25cm-‘) that it was maskedby ghost lines of the spectrum. The branch As, which may be the soft mode, is only clearly seen for O.lOb*
