Table Of ContentPolarized Raman study of the phonon dynamics in Pb(Mg1/3Nb2/3)O3 crystal
∗
Oleksiy Svitelskiy and Jean Toulouse
Department of Physics, Lehigh University, Bethlehem, PA 18015, USA
Z.-G.Ye
3 Department of Chemistry, Simon Fraser University, Burnaby, BC, V5A 1S6, Canada
0
0 Pb(Mg1/3Nb2/3)O3 is one of the simplest representatives of the class of lead relaxors and often
2 servesasamodelsystemformorecomplicatedcompounds. Inthispaperweanalysebothpolarized
and depolarized Raman scattering spectra, measured in the temperature range between 1000 and
n
100K,bymultiplepeakdecomposition. Basing onthisanalysis, wepresentthepictureoftransfor-
a
mations in the crystal and the nature of the spectral lines. According to our model, the formation
J
oftheFm3m symmetry in thechemically ordered regions as well astheappearance andfreezing of
5
thepolarnanoregionsaretheconsequencesofthesamephenomenon: ionoff-centereddisplacements
2
andtheirreorientationalthermalmotion. Theloweringtemperatureprogressivelylimitsthismotion
fromeighttofour,twoandonlyonesite. RamanscatteringexistsduetothepresenceoftheFm3m
]
i andpolarclusters. Itisaproductofthemultiphononinteractionprocess,mediatedbythepresence
c
of thedynamic and static disorder.
s
-
l
mtr I. INTRODUCTION theformofPb[B21+/2B51+/3]1/2[B5+]1/2O39,10. Thishypoth-
esis avoids assumption of the considerable space charges
. and calls for other reasons to explain relaxor behavior,
t Pb(Mg Nb )O (PMN)is oneofthe earliestmem-
a 1/3 2/3 3 including the random fields due to the disorder-induced
m bers of the growing family of lead ferroelectric relaxors,
localanisotropy11,effectsrelatedtodifferentionicradii12
which, due to its applicationpotential,has been attract-
- or both13.
d ing attention of researchers for many years. However,
n despite significant efforts, many properties of lead com- The presence of areas with special order causes crys-
o poundsarestillunclearandtheverynatureoftherelaxor talline structure to change in an intricate way. At the
c
behavior has yet to be understood. The difficulties stem high temperature limit, the crystal has a uniform primi-
[
from the high complexity of these materials with a high tive cubic (Pm3m) structure. Lowering the temperature
1 degree of compositional, chemical and structural disor- leads to distinguishability betweenMg2+ andNb5+ sites
v der. andtoformationintheorderedregionsofafacecentered
1
Pb(Mg Nb )O has a perovskite structure with, (Fm3m) superstructure. The temperature of the Fm3m
0 1/3 2/3 3
5 on average, a cubic Pm3m symmetry, with Mg2+ and clusters formation has yet to be determined. Husson’s
1 Nb5+ ions interchanging on B sites. Measurements of data suggests they presence at T∼850 K14. Our data
0 the dielectric constant show that the crystal does not (seebelow)raisethe upperlimittoatemperaturehigher
3 undergo a sharp transition to a ferroelectric phase. In- than 1000 K.
0
/ stead, the dielectric constantexhibits a broad maximum Cooling the sample leads to the nucleation of polar
at at Tmax ∼ 270 K1. Below Td ∼ 620 K, it deviates nanoregions (PNR’s) characterized by the local distor-
m fromCurie-Weiss law3 and, at T.350K, exhibits strong tions. Thesedistortionsare responsibleforthe deviation
dispersion2. The structure of PMN is not homogeneous. of the dielectric constant from Curie-Weiss law at T 3.
- d
d IfMgandNboccupationratiowereuniformlyandideally Their presence also causes a non-linearity in the tem-
n equal1:2throughoutthecrystal,itwouldhavearhombo- perature dependence of the optical refraction index15.
o hedralsymmetryR3m. But,anetworkofsuperstructure Size of the PNR’s is equal to 30-80 ˚A depending on
c clusters with face centeredcubic symmetry (Fm3m), de- temperature16. The appearance of polar distortions is
:
v stroys the picture. The size of these clusters is of the a consequence of the ion off-centering that is a com-
Xi order of 2-3 nm; the distance between the centers of the mon property of many perovskites. By structural sim-
neighboring clusters is near 2.5 nm4,5. ilarity, one could expect that the mechanism of the po-
r
a Themostwidelyacceptedhypothesis,so-called“space- lar regions formation in PMN is analogous to the one in
charge model”, associates these Fm3m clusters with an- KTa1−xNbxO3 (KTN)17. However, unlike KTN where
tiferroelectrically ordered6 areas where Mg:Nb occupa- Nb5+ is the only off-centered positive ion, PMN repre-
tion ratio is equal to 1:1, i.e. with local composition sents a more difficult case. Here, not only both ions
Pb(Mg Nb )O 7,8. Such 1:1 clusters carry an exces- of B-type, Mg2+ and Nb5+, are shifted by ∼0.1-0.2 ˚A,
1/2 1/2 3
sive negative charge, which is compensated by the posi- but also Pb2+, ion of A-type, is off-centered by ∼0.25-
tivelychargedhostmatrix. Networkofthesechargesacts 0.35˚A18,19,20,21,22. TheB-ionstendtoshiftalonga(111)
as a source of random fields and may prevent the occur- direction, thus having eight equivalent positions. The
renceofthe“normal”phasetransition. Alternatively,the shifts of the Pb2+-ions exhibit a spherically symmetric
Fm3m clusters might be explained by the local order in distribution22. It is often assumed11,12,13,14 that Nb5+,
2
TABLE I: Interpretations of Raman scattering spectrum from PMN offered by various research groups. Note, many of the
entries in thetable mutually excludeeach other.
Research 45 cm−1 130 cm−1 260 cm−1 420 cm−1 500-600 780 cm−1
Group cm−1
Husson14 Pb-Ostretching modes O-B-O Mg-O-Mg Nb-O...Nb Nb-O...Mg
(1990) bending stretching stretching stretching
Dimza41 Coexistence of tetragonal
(1992) and rhombohedral phases
Krainik26 (1993) TO1
Idink40 All spectrum is dueto one phonon processes, originates
(1994) from rhombohedral symmetry clusters and consists of 9 modes
Marssi27,28,29,30 TO1 TO2 TO3 TO4 TO2+TO4 or LO4 (1996)
(1996-98) Nb-O-Mgor LO4 (1998)
Jiang32 (1999) Dueto positional disorder of lead Dueto Fm3m clusters and vibration of oxygen octahedra
All spectrum originates from Fm3m clusters, similarly to thecase of PbSc1/2Ta1/2O3
VV-E ??
g
Lushnikov33,34 VH-2T2g A1g
Siny35,36,37,38,39 or Disorder-induced scattering from silent modes Breathing mode
(1999) VV and one VH and second-order scattering of oxigen
havefractal
character
another VH-T2g
Dujovne31 (2002) TA+disorder
due to its position in the cell and small radius, acts as the one side of the problem. Another side is the as-
the main ferroelectric agent. signment of particular lines. The question of the soft
At high temperature, the off-centered ions are free to ferroelectric mode (TO1) and the strong Raman line at
reorient among all allowed off-centered positions. Cool- ∼45 cm−1, which is close to where the TO1 is expected
ing down and the growing role of the electric interac- to be found, has been like a stumbling block for inves-
tions causes the appearance of correlated regions con- tigators. Interpretations of the PMN Raman spectrum
sisting of several neighboring cells. Each such region is offeredbyvariousresearchgroupsaresummarizedinTa-
characterized by a giant electric dipole moment and a ble I. This table reflects the variety of mutually exclud-
local distortion from the cubic symmetry. The PNR’s ing opinions ranging from those that explain the light
are capable of reorientational motion as whole units. In scattering by disorder in general (groups of Husson14,
KTN, the development of these regions leads, at some Krainik26,Marssi27,28,29,30,Dujovne31)tothosethatcon-
critical temperature, to a phase transition. However, in nectittothepresenceofsomeparticulartypeofdisorder,
PMN, the polar regions develop under constraints im- the one that can lead to the appearance of clusters with
posed by the local anisotropy. As a result, no ferroelec- symmetry allowing first-order scattering, like face cen-
tric phase transition,but a glasslikefreezingof the polar tered cubic (Jiang32, Lushnikov33,34, Siny35,36,37,38,39),
regions is observed11. A bias electric field of magnitude rhombohedral(Idink40)ortetragonal(Dimza41). Theas-
∼1.8 kV/cm, applied in the (111) direction, is sufficient signement of particular lines is even more contradictory.
to compensate for the influence of the frustrating effects Recently made first-principle calculations42 can confirm
andtoinduce, atT ∼210K,atransitionto the rhom- only few of them. We believe, the arguments might be
do
bohedral R3m ferroelectric phase23. resolved by taking into account the possibility of coexis-
tence of different mechanisms, each playing a role in the
Raman spectra of PMN have been measured and re-
ported by several research groups14,24. But, the high scattering processes.
complexity of the processes caused difficulties in their Recently published low branches of phonon dispersion
interpretation, especially due to possible coexistence of curves43,44,45,46, measured by neutron scattering, must
clusters with Pm3m, Fm3m and R3m symmetry. It has be helpful for the phonon assignment of some of the Ra-
been shown that the major spectral lines are of first- man lines. According to these data, the strong 45 cm−1
order character25. In cubic crystals first-order Raman line has an energy close to the energy of the zone cen-
scattering is prohibited by symmetry. Explanation of ter (ZC) TO or the zone boundary (ZB) TA phonon.
1
the appearance of first-order scattering in principle is Lowering the temperature, TO zone center phonon ex-
1
3
hibits softening, at T∼T K, due to the drastic increase
d
of damping, it disappears. The overdamping continues
downtoT ∼210K43. Italsocausessignificant,almost B
do
sixfold,broadeningofthe TAphononbranch47. Itseems
13
reasonable to expect that the Raman line at 45 cm−1 A
is also affected by the described phenomenon. However, 12 D
none of the known Raman reports show any significant C E
T (K)
effects that could be attributed to this overdamping. 11
The formation of the lower-symmetry clusters in 1000
10
the host crystal is accompanied by relaxational and
reorientational dynamics. This dynamics should be s) 9
reflected in the light scattering spectrum either di- nit
rectly or through interaction with the phonon modes. b. u 8 800
Theoretical considerations48 show that internal relax- r
(a 7 700
ational motion leads to the appearance of the cen- y 650
tral peak (CP) in the Raman spectrum. Interac- nsit 6 600
tions of this motion with phonons can cause soften- e
t
ooiKnnf(gCfrsNeoeef)vdxeot-rhKmaelC,mllt41iyk8−.epxe)a4sl9Tk,5aoh0lf,ei5-s1he,ca5r2lypidsrcteeao-dclmisycpatinowouinidtnsehds(h.Kianv(tCeeRrNnbe)aecxele-nnKtdBlteyerg,s1rt−eweexdes, Reduced in 345 C1 C2 D1D2 F E1 E2 455500
have analyzed53 the reorientational motion in ferroelec-
tricKTa1−xNbxO3 crystals. Inthispaperwediscussthe 2 325
role of the relaxational and reorientational dynamics in
the scattering processes from PMN crystal. 1 210
In the paper presented we offer a complex analysis 110
0
of temperature dependencies of polarized (VV) and de-
polarized (VH) Raman spectra from a single crystalline 0 200 400 600 800 1000
PMN sample. This analysis is based on multiple peak Wavenumber (cm-1)
decomposition. An attempt to apply similar kind of
analysis has earlier been made by Siny et al.54. But,
it was restricted to the low frequency VV spectra in a
limited temperature range (with maximum temperature
FIG. 1: Examples of Raman scattering spectra measured at
∼620 K), concentrating on the central peak (CP) only.
various temperatures without polarization analysis and cor-
To obtain the complete picture, we consider the temper-
rected by thepopulation factor.
ature evolutionof the whole Raman scatteringspectrum
(upto1000cm−1)inthe100-1000Ktemperaturerange.
Weinterpretourresultsinconnectionwithrecentlypub-
studies. The scattering was excited by propagating in
lished neutron scattering data and with the concept of
h100i direction 514.5 nm light from a 200 mW Ar+-ion
interactionofphononswithinternalrelaxationalmotion.
laser, focused to a 0.1 mm spot. The scattered light was
As a result of this work, we present our view on the pic- ◦
collected at an angle of 90 with respect to the incident
tureofstructuraltransformationsinPMNcrystalandon
beam (i.e., in h010i direction) by a double-grating ISA
the origin of its Raman spectrum.
Jobin Yvon spectrometer equipped with a Hamamatsu
photomultiplier R-649. For most of the measurements,
the slits were opened to 1.7 cm−1. However, in order to
II. EXPERIMENTAL SETUP AND RESULTS acquire more precise data in the central peak region, at
the temperatures close to the maximum of the dielectric
WehaveinvestigatedtheRamanscatteringfromh100i constant ( 100 < T < 350 K), the slits were narrowed
cut PMN single crystal. The crystal was grown by the to 0.5 cm−1. Each polarization of the scattered light,
high temperature solution technique using 30 wt% PbO hx|zz|yi (VV) and hx|zx|yi (VH), was measured sepa-
as flux. The growth conditions were optimized based on rately. Inordertoexcludedifferencesinsensitivityofthe
the pseudo-binary phase diagram established for PMN monochromator to different polarizations of the light, a
andPbO55. Theas-growncrystalexhibitsapseudo-cubic circular polarizer was used in front of the entrance slit.
morphologywithh100icubgrowthsteps. Ah100i/h110i Forcontrolpurposes,wealsotookmeasurementswithout
cub-orientedcrystalofavolumeof53mm3 wascutfrom polarization analysis. Finally, to protect the photomul-
a large as-grown crystal and polished with fine diamond tiplier from the strong Raleigh scattering, the spectral
paste (down to 0.25 mm). It showed very high optical regionfrom -4 to +4 cm−1 was excluded fromthe scans.
qualityandsatisfiedtherequirementsforlightscattering The data were collected in the temperature range from
4
CP
CP
A
A
15 (a) (b)
14
13
12 C
B
11 D
E
)
its10 C D E B
n 1000 K
u 9
1000 K
.
b 8
r
a
( 7 800 K
y 700 K 800 K
it 6 650 K 700 K
s
n 600 K 650 K
e 5
nt 600 K
I 4
3 C 550 K
1C
2 2 D 450 K 550 K
1 D2 E1 E2 450 K
1 300 K 300 K
200 K 200 K
0 100 K 100 K
0 200 400 600 800 1000 0 200 400 600 800 1000
Wavenumber (cm-1) Wavenumber (cm-1)
FIG. 2: Examples of Raman scatteting spectra measured in VV (a) and VH (b) geometries upon cooling from 1000 to100 K.
1000to 100K.The coolingratewas0.5-1K/min. Every Thesespectrawepresentinuncorrected,”as-measured”,
50-20Kthetemperaturewasstabilizedandthespectrum form.
recorded. We agree with Ref.24 that the reproducibility AscanbeseenfromFigs. 1and2,ourspectraarecon-
of the spectra in the temperature range approximately sistent with those from Refs.14 and24. In the high tem-
between200and350Kwasnotverygood. Inthisrange, peratureregion,atypicalspectrumconsistsoftwostrong
thespectraexhibitedastrongdependenceonthecooling lines centered approximately at 45 cm−1 and 780 cm−1
rate and other experimental conditions. (labelled A and B) and of three broad bands (C, D, E).
Fig.1 presents examples of light scattering spectra Line A exhibits fine structure, which is explicitly seen
measured at different temperatures without polarization on the spectra measured with polarization analysis (see
analysis. Tofacilitatecomparison,wecorrectedthespec- Figs. 2 and 3). Lowering temperature leads to the split-
tra by the Bose population factor: ting of the broad bands C, D and E into a number of
narrowerlines (labelled by indices)andto appearanceof
new line F.
n(f)+1, for Stokes part AsseenfromFig. 1,startingfrom1000K,thereduced
F(f,T)= , (1)
( n(f), for anti-Stokes part intensity of the scattering, first grows until the temper-
ature of ∼ 700 K then sharply decreases to a minimum
where locatedclosetotheBurnstemperatureTd ≈620K,after
whichitincreasesagain. At∼550Kitsstrengthgetsre-
n(f)=(exp(hf/kT)−1)−1. stored. Belowthistemperature,theintensitiesofthema-
jor lines (especially A and B) are determined primarely
Figure 2 demonstrates scattering spectra measured in by the Bose factor. I.e. being corrected by it, they do
VV(a)andVH(b)geometriesatdifferenttemperatures. not show significant temperature changes, demonstrat-
5
VV A VH
7 CP 7 (45 cm-1)
A 1000 K 1000 K
6 (45 cm-1) 6 CP
) 7
u.5 5 6
. 5
a 4
(
y 4 4 3
2
t
i 1
ens3 C (B780 cm-1) 3 00 20 40 60 80 100
t
n2 D 2
I
E C D
1 1 E B
0 0
0 200 400 600 800 1000 0 200 400 600 800 1000
7 7
CP
6 110 K 6 A 110 K
(45 cm-1)
) 7
. 6
u5 5
(a.4 CP (A45 cm-1) B(780 cm-1) 4 345
y 2
nsit3 C1 C2 D1 3 010 20 40 60 80 100
e D
nt2 2
I1 D2 F E1 E2 1 C F E B(780 cm-1)
0 0
0 200 400 600 800 1000 0 200 400 600 800 1000
Wavenumber (cm-1) Wavenumber (cm-1)
FIG.3: ExamplesofmultiplepeakdecompositionofRamanspectrameasuredat1000and110Kboth,inVVandVHgeometry.
For convenience, major peaks are labeled with letters. Inserts show examples of fits for the line A using the model of the two
coupled harmonic oscillators, as described in Discussion.
ing characteristic first-order behavior. The shape simi- electricfield-inducedferroelectricphasetransition23,the
larity of the low- and high- temperature spectra shows shape of the spectra is relatively stable.
that even at 1000 K the scattering has first-order char- A comprehensive analysis of our data and their com-
acter. In the perfecly cubic crystal,first-orderscattering parisonwithresultsofotherexperimentsallowstounder-
isprohibited. Therefore,oneshouldassumethepresence standthe meaning of the mentioned abovetemperatures
of distortions in the form of lower symmetry clusters, T ≈ 620 K, T ≈ 350 K and T ≈ 210 K in the tem-
d f do
like Fm3m or R3m. At high temperature, these clusters perature evolution of the Raman spectra and the lattice
might be present in the dynamic form, having short life- structure.
time. Lowering the temperature, their lifetime increases
andtheybecomeprogressivelymorestatic. Theobserved
aroundT decreaseofRamanintensityisalsoclearlyseen III. MULTIPLE-PEAK DECOMPOSITION OF
d
in Fig. 2. However, there are no reports on this effect SPECTRA PROCEDURE.
in the literature; it might have been overlooked. This
intensity drop indicates worsening of the optical quality To be able to analyze the data, we decomposed the
of the crystal. In our opinion, it is consistent with the measured spectra using multiple peak fitting procedure.
formation of Fm3m clusters in their evolution from dy- It was found that satisfactory fit could be achieved with
namictostaticform. Thesplittingofpeaksisassociated the assumption that the central peak has a Lorentzian
with the development of R3m clusters. The first signs of shape and that each of the other peaks is described by
the splitting appear at T . Strarting from T ∼ 350 K the spectral response function, i.e. damped harmonic
d f
(which is also close to where the dispersion of the di- oscillator, modified by the population factor (1):
electricconstantappears),thiseffectbecomesevenmore
definite and the intensities of the components begin to
Γ f2f
grow. Below T ∼ 210 K, which is the temperature of Φ ∼ i 0i F(f,T) , (2)
do i (f2−f2)2+Γ2f2
0i i 0i
6
whereΓ andf arethedampingconstantandthemode
i 0i
frequency.
VV
As all of the peaks are much better resolved at low 3.5 VH
temperatures, we started our fitting procedure at the
s) 3.0
low-temperature end of the data set (at 110 K) and, nit
then, observed the evolution of the peaks with increas- b. u 2.5
ing temperature (i.e., in order, opposite to the order of ar 2.0
measuring). At the same time, we tried to minimize the y (
sit 1.5
number of peaks necessary to achieve a reasonably good n
fit. The controldata set (measured without polarization nte 1.0
I
analysis) has been used to calibrate the positions and 0.5
(a)
widths of the weak and poorely resolved peaks from the 0.0
VV and VH data sets. Since a large number of parame- 0 200 400 600 800 1000
45
ters is involved,resultsofa particularfit maydepend on
40
their initial values. To stabilize the results, the best-fit
35
values of parameters obtained at the previous temper-
ature were used as initial values for the next one. In -1m) 30
25
this manner, several sets of fits were obtained and an- M (c 20
alyzed. It is remarkable, that in all of them the major
H
15
parametersshowedthesametrendsofbehavior,confirm- W
H 10
ingtheimportanceofthementionedabovetemperatures:
T ≈620±50K,T ≈350±25KandT ≈210±25K. 5 (b)
d f do
0
ThesetrendsaresummarizedinTableII. Oneofthesets
0 200 400 600 800 1000
have been selected to report the most interesting results Temperature (K)
in detail. Examples of the fits at the temperatures of
1000 and 110 K in VV and VH geometries are shown in
Fig. 3. For clarity, we describe the observed phenomena
from high to low temperatures, following the same order FIG. 4: Temperature dependencies of the intensity (a) and
as in measurements (unless the opposite stated). half-width (b) of the Lorentzian approximation for the cen-
tral peak in VV (circles) and VH (triangles) geometries of
experiment.
IV. MOST INTERESTING RESULTS OF
DECOMPOSITION AND THEIR ANALYSIS.
tering studies of similar system56. The similarity of the
A. Central peak. CP behavior in these two very different materials, sug-
geststhatthetemperatureevolutionofthepolarclusters
Thetemperaturedependencesofthefittingparameters inPbMg1/3Nb2/3O3 passesthroughthe similarstagesas
forthecentralpeak(CP)arepresentedinFig. 4. Circles in KTa0.85Nb0.15O3 (KTN), however, it is not accompa-
correspondtotheVVandtrianglestotheVHcomponent nied by appearance of the long-range order.
of the peak. The existence of the CP is a direct conse- Starting from the high-temperature end (Fig. 4), the
quenceofthelatticerelaxations,whichareverysensitive first important feature is the strong and narrow scat-
totherestrictionsimposedbythelow-symmetryclusters. tering in the VV geometry accompanied by a relatively
Ifrelaxationsarefast48,theCPislow-intenseandbroad, weak scattering in the VH geometry. This indicates the
whereastheirslowingcausesgrowthandnarrowingofthe presenceofasymmetricslowrelaxationalmotion,involv-
peak. ing 180o reorientations of ions. Lowering the temper-
We would like to point out a striking similarity of ature, starting from ∼ 900 K, a cessation of this mo-
thetemperaturebehavioroftheCPinPbMg1/3Nb2/3O3 tioncausesanintensity decreaseofthe CP.Slow atfirst,
(Fig. 4) and in KTa Nb O (Fig.3 in Ref.53) crys- thisdecreasebecomessharperandreachesminimumnear
0.85 0.15 3
tals. We have shown53 that the temperature behavior of T ≈ 620 K. The prohibition of 180o reorientations in-
d
the CP in KTN can be explained by the model involv- troduces anisotropy into the lattice causing the distin-
ing the relaxational motion of off-centered Nb ions and guishability between Mg and Nb occupied cites and to
its progressive restriction with temperature decrease. In formation in the 1:1 ordered areas of the superstructure
the cubic phase,Nbionsareallowedtoreorientamongst with, on average,Fm3m symmetry. It also imposes first
eight equivalent <111> directions. The appearance of restrictionsonthe reorientationalmotionofthe dynami-
the PNR’s followed by a sequence of phase transitions cal R3m polar nanoregions. Now, they can reorient only
down to a rhombohedral R3m phase, limits the ion mo- amongstfour neighboring<111>directions,forming,on
tion to four, two and, finally, locks it in only one site. average, tetragonal-like distortions. These processes are
Thismodelisinagreementwiththediffuseneutronscat- accompanied by the appearance of large (of the order of
7
TABLEII:Majorpeaksandtheirresponsetothetemperaturerestrictionsonionmotion. Onlychangingpropertiesareshown.
T ≈620 K is also characterized by thetotal loss of intensity of scattered light.
d
Peak Polari- RegionI.Unrestricted RegionII.Restricted RegionIII.Formation of
zation dynamical clusters dynamical clusters static R3m clusters
T&(T =620 K) (T =620 K)&T&(T =350 K) (T =350 K)&T
d d pr pr
Central VV Intensity decreases Intensityincreases Intensity has a maximum at 300 K
broadens narrows
VH Intensity decreases Intensityincreases Intensity has a maximum at 300 K
width has a maximum at 450 K
Peak A VV Softens, broadens Hardens and narrows
VH-I Broadens Broadens Broadens
VH-II Softens Hardens,intensity has minimum at 400 K Broadens and grows
Peak C VV Hardens and narrows Finestructure appears Splits in two
VH Softens Hardensand narrows Narrows
Peak D VV Splitsin two
VH Softens Hardens Softens and narrows
Peak F VV VVcomponent appears VH component appears
Peak E VV Finestructure appears Splits in two, VH appears
Peak B VV Hardening Hardening VH appears
wavelength of light) dynamic fluctuations causing wors- The discrepancy occurs due to the difference in experi-
ening of the optical quality of the sample. mental technique. In the centralpeak region,we did the
measurementswithmuchhigherresolution(0.5cm−1,as
With further decrease of the temperature, the opti-
comparedto2cm−1fromRef.54). Consequently,wewere
cal quality of the crystal improves. From ∼ 550 K, the
able to provide a more correct separation of the slow re-
four-cite reorientational motion of the PNR’s starts to
laxationsfromtheelasticscattering,whichwasespecially
slow down, which is marked by the narrowing of the
important at low temperatures.
VV component of the CP and increase of its VV and
VH intensities. The simultaneous broadening of the VH
componentuptothe maximumat∼450K,indicatesre-
arrangements in the crystalline structure leading to the B. Line A.
appearanceofthenewtypeofrestrictionsontheionmo-
tion. Analogy with KTN suggests that below ∼ 450 K
Figure 5 presents the temperature evolutionof the fit-
the motionof R3mclustersbecomes limited to twoneig-
ting parameters of the peak A, showing its position (a),
boring <111> orientations, averaging in monoclinic-like
reduced intensity (b) and damping constant (c). This
distortions. Such a rearrangement causes some decrease
peak has a triplet structure, containing one component
in intensity of the VV component (with minimum at
inVV(circles)andtwocomponentsinVH(upanddown
∼ 400 K), while the VH intensity keeps growing. Be-
triangles) geometries. The fitting parameters for this
low ∼ 400 K, the slowing down of the two-site relax-
peak exhibit changes at mentioned above temperatures
ational motion causes narrowing the CP and increase of
T , T and T , confirming their importance for the
d f do
intensities ofboth components. FromT ≈350K,these
f structural evolution of the crystal. However, the origin
effects become especially dramatic. Further temperature
of this peak (see Table. I) requires qlarification. From
decrease, starting from ∼ 300 K, leads to the complete
a comparison with the frequencies of the phonon modes
prohibition of intersite reorientational motion of R3m
determined from neutron scattering, it is clear that this
clusters, i.e. to appearance of static R3m clusters. This
line cannot be due to the zone center soft TO mode
1
is marked by a sharp decrease in intensity of both com-
(black stars in Fig. 5). On the other hand, the lower
ponents ofthe CP.Atthe temperatureT ≈210K,the
do frequency VH component, and possibly the VV compo-
process of conversion of PNR’s from dynamic to static
nentcouldbeduetothedisorder-inducedzoneboundary
form (freezing) is primarily finished. Below this temper-
scattering on TA phonon (white stars in Fig. 5). How-
ature,thecentralpeakisnarrowanditsintensityissmall
ever,thehigherfrequencyVHcomponentwouldstillnot
in both scattering geometries.
be accounted for.
We should mention that the result of our analysis of In an attempt to account for both VH components
the VV componentofthe CP exhibits similartendencies simultaneously, we have tried to make use of a coupled
to those in Ref.54, except at the low temperature end. oscillatormodel. Intheapproximationoflinearcoupling
8
VV Neutron data First oscillator Neutron data
VH-I TO (ZC) Second oscillator TO (ZC)
70 VH-II TA (ZB) 70 TA (ZB)
-1Position (cm) 456000 (a) -1Position (cm) 5600 (a)
40
0 200 400 600 800 1000 0 200 400 600 800 1000
45
ensity 00..56 -1cm) 3450
ed int 00..34 ping ( 2350
uc 0.2 m 20
ed 0.1 (b) Da 15 (b)
R
0.0 10
0 200 400 600 800 1000 0 200 400 600 800 1000
10
55
-1m) 4550 -1m) 8
g (c 3450 g (c 6
Dampin 12235050 (c) Couplin 024 (c)
10
0 200 400 600 800 1000 0 200 400 600 800 1000
Temperature (K)
Temperature (K)
FIG. 5: Temperature dependences of the fitting parameters: FIG. 6: Temperature dependences of the fitted parameterst
position (a), reduced intensity (b) and damping constant (c) of the line A VH component (located at 45 cm−1) using the
for the triplet line A (located at around 45 cm−1). Phonon model of coupled harmonic oscillators. From top to bot-
frequencies, measured by neutron spectroscopy43,44,45,46, are tom: resonant frequencies (a), damping constants (b) and
shown for comparizon. couplingconstant(c). Phononfrequencies,measuredbyneu-
tron spectroscopy43,44,45,46, are shown for comparizon.
between two harmonic oscillators57 this approachgains:
approximated as S = 22.3 cm−1 and S = 20.6 cm−1.
1 2
The other parameters as a function of temperature are
CY −BZ
showninFig.6: the best-fit frequencies (a), the damping
I(ω)=[n(ω)+1] ,
B2+C2 constants (b) and the coupling coefficient (c).
(cid:18) (cid:19)
The examples of the fits (inserts in Fig.3) demon-
where
strate that this model gives a good approximation to
the shape of the peak A. However, a comparizon of the
B =(ω12−ω2)(ω22−ω2)+ω2(γ122−γ1γ2)−ω1ω2∆212, best-fit frequencies (Fig. 6a) with the neutron scatter-
C =ω[γ1(ω22−ω2)+γ2(ω12−ω2)−2(ω1ω2)1/2∆12γ12], ing data43,44,45,46 rules out the possibility to explain the
Y =S12(ω22−ω2)+S22(ω12−ω2)−2S1S2(ω1ω2)1/2∆12, higher-frequency VH component by the interaction be-
Z =ω(S12γ2+S22γ1−2S1S2γ12). tween ZC TO1 (black stars) and ZB TA (white stars)
modes. The lower frequency oscillator can still be asso-
Intheseequationsω andω aretheresonantfrequencies, ciatedwithdisorder-inducedscatteringonZB TAmode.
1 2
γ and γ are the damping constants, S and S are the The possible explanation of the presence of two VH
1 2 1 2
structure factors for two oscillators,∆ and γ are the components in the peak A can be in the correspondence
12 12
real and imaginary parts of the coupling constant. toTAmodeswithdifferentpolarizationsindifferentcrys-
It was shown58, that a unitary transformation can be talline planes of a distorted lattice. (A similar effect we
found, which would set either real or imaginary part of have seen in monodomain KTa1−xLixO3, where one or
the coupling to be equal to zero. We have chosen to the other TA polarization was observed, depending on
use imaginary coupling and set ∆ = 0. We also set the orientation of the electric field.) These differently
12
the structure factors S and S to be the same at all polarizedmodesareinfluencedbythepolarnanoregions,
1 2
temperatures. The rest of the parameters were treated which explains the increase of damping (Fig. 6b) and
as being temperature dependent. In the result of fitting, coupling (Fig. 6c) coefficients with lowering tempera-
wehavefoundthatthe valuesofstructurefactorscanbe ture.
9
It is also necessary to point out an observation con- 7. It also exhibits similar temperature tendency to that
cerning the temperature dependences of the frequencies described in Ref.59. Detailed understanding of this phe-
ofthecomponentsofthetripletAinapproximationofin- nomenon requires further work, and it is a subject of
dependentoscillators(Fig. 5a). Thesedependencesseem separate paper.
to show anomalies at intersections with ZC TO modes
1
(black stars). For example, the VV component exhibits
deeps at ∼ 700 and 350 K and VH-I component has a
knee at ∼400 K.
96 300
VV
94 250 788
-1m) 8889946802 2-2Dn(-73) (cm)112050500000 Tpr -1Position (cm) 777788880246 (a)
n (c 8802 100 200 Tem3p0e0rature (4K00) 500 0 200 400 600 800 1000
D 7768 Tpr sity 2.0
74 en 1.6
7702 100 200 300 400 500 600 700 ced int 01..82
u
Temperature (K) ed 0.4 (b)
R
0.0
0 200 400 600 800 1000
90
FthIeGl.in7e:EA.mThpelitiundseertofdesmploitntsintrgatbeesttwheaetnththisespcolimttpinognefonltlsowosf -1m) 8805
c
thecritical dependence. g ( 7705
n
pi 65
m 60
Da 55 (c)
50
C. The most important parameters of other lines. 0 200 400 600 800 1000
Temperature (K)
Among the changes occuring to the Raman spectrum
withcoolingthesample,thesplittingofthephononlines
desrves special attention, since such a splitting is a di- FIG. 8: Temperaturedependencies of thefitting parameters:
rect indicator of the modifications of the local structure. position (a), reduced intensity (b) and damping constant (c)
As we already mentioned, the splitting occurs to the of the line B (located at ∼780 cm−1.)
lines C, D, and E, which is especially well seen in the
VV geometry (Fig. 2a). At high temperatures, their
widths are very big, so the lines almost merge in a sin-
gle broad shoulder. Lowering the temperature, they be-
come more discernible and the fine structure gradually Finally, we would like to stop on the line B located at
develops. The first signs of it appear at T ≈ 620 K. the upper end of the spectrum. Fig. 8 demonstrates the
d
BelowT ≈350K,the fine structurebecomes moreob- fittingparamentersforthisline: position(a),reducedin-
pr
vious. These observations support the expressed above tensity(b), anddampingcoefficient(c). Thislineisvery
idea that the scattering originates from the distorted re- strongintheVVgeometrybutitisratherweakintheVH
gions. Highly dynamic and disordered at high tempera- one(i.e. characterizedbyA symmetry). Itseemstobe
1g
ture, they become progressivelymore static with cooling theleastinfluencedbytheorderingprocessesinthecrys-
down, and their motion becomes more correlated. This tal. However, the temperature evolution of its parame-
process is reflected by the temperature evolution of the ters reflects development of the low-temperature phase,
lines C, D, and E. confirming the expressed above ideas about formation
Below the temperature of T ≈ 350 K, the splitting of dynamic polar clusters at T ≈ 620 K, their slowing
pr d
value of the line E exhibits especially interesting trend. down,andappearanceofthestaticorderatT ≈350K.
pr
As seen from Fig. 7, with temperature decrease be- AsitisseenfromtheTableI,the appearanceofthis line
low T the distance between the E-line components in- in the Raman spectrum has several contradictory expla-
pr
creases. Moreover,this increase exhibits the characteris- nations. However, according to the recent first-principle
ticorderparameterbehavior,followingthe(T −T)−1/2 calculations42, this mode most likely is a consequence of
pr
dependence, which is demonstrated in the insert to Fig. oscillations of oxygen ions.
10
V. CONCLUSION tions on ionic motion and, starting from T ≈ 350 K,
pr
to the appearance of the static polar nanoregions. At
This paper offers a comprehensive analysis of the Ra- Tdo ≈210K,theformationofthelow-temperaturephase
man scattering spectra of PbMg Nb O in the tem- is primarily finished. The shape of the phonon lines is
1/3 2/3 3
peraturerangebetween100and1000K.Fromouranaly- determined by multiphonon processesinvolving phonons
sis,thestructuralevolutionofthelatticeoccursinseveral with different polarizations propagating in different di-
stages. Evenat1000K,thePMNcrystalischaracterized rections, which interact with dynamic and static disor-
bythepresenceofdynamicdistortionsofthelatticefrom der.
cubic symmetry, which are responsible for existence of
first-orderRamanscatteringatsuchahightemperature.
At the Burns temperature Td ≈ 620 K, the first restric- VI. ACKNOWLEDGEMENT
tions on the reorientational motion of the off-centered
ions appear. These restrictions lead to slowing of the
Authors are very grateful to D.La-Orauttapong and
motion and growth of correlations between neighboring
G.Yong for useful advice and helpful discussions. This
regionswithR3msymmetry. Theyalsointroducedistin-
work was partially supported by the ONR grant
guishabilitybetweensitesoccupiedbyMgandNb,which
#N00014-99-1-0738.
causesonsetofFm3msymmetryinthe1:1orderedareas.
Further cooling leads to progressive growth of restric-
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