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Raman study of charge-density-wave phase transition in quasi-one-dimensional conductor (TaSe4)2I
~
Solid State Communications, Vol.53,No.9, pp.767-771, Printed in Great Britain.
1985.
0038-|098/85 $3.00 + .00 Pergamon Press Ltd.
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION IN QUASI-ONE-DIMENSIONAL CONDUCTOR (TaSe4)2I
Tomoyuki Sekine, Taisaku Seino, Mitsuru Izumi and Etsuyuki Matsuura Institute of Physics, University of Tsukuba, Sakura-mura, Ibaraki 305, Japan (received 22 November 1984 by W. Sasaki)
Polarized Raman spectra were obtained in the quasi-one-dimensional conductor (TaSe4)2I above and below the charge-density-wave (CDW) transition temperature (Tc=263 K). The Raman intensities of many peaks become intenser and two of the phonon peaks shift to higher frequency with decreasing temperature. Moreover a new broad peak at about 90 em-1 and a new peak around 166 cm-I appear in the lowtemperature phase. The polarization characteristic shows that the former is assigned to totally symmetric mode. The damping constant of the phonon at 90 cm-1 increases markedly with increasing temperature. The frequency shifts to higher frequency as the temperature increases and the coupling coefficient is approximately proportional to (Tc-T) I/2. This peak becomes Raman active owing to the CDW phase transition. The temperature dependence of the damping constant and the frequency shift may have a relation to the dynamical properties of the CDW phase transition.
During the last decade, it has been shown that many quasi-one-dimensional conductors undergo a Peierls transition, i.e., the formation of charge-denslty wave (CDW) with a periodic lattice distortion connected with a condensation of the 2-~F phonon mode. Here-~F is the Fermi wave vector. The CDW opens up a gap at the Fermi surface-~:±~F and the materials show semiconducting properties below the transition temperature T c. Among the quasi-onedimensional conductors, much attention has been paid to transition-metal trichalcogenides, because they show nonlinear transport properties due to the motion of the CDW. Recently much interest has been aroused not only in transition-metal trichalcogenides but also in a new family of halogenated transition-metal tetrachalcogenides (MX4)nY, where M=Nb or Ta, Y=Br or I and n=2, 3 or 10/3, because such intriguing phenomena of the transport properties were found also in (TaSe4)2I [I-4], (NbSe4)2I [5] and (NbSe4)10/31 [4,6]. In (TaSe4)2I, Wang et al. [I] have found out a resistive anomaly due to the formation of an incommensurate CDW at Tc=263 K. The remarkable electric-field and frequency dependence of the conductivity and the current oscillations have been observed in the low-temperature phase [1-4,7]. Sherwin et al. [8] have reported the observation of chaotic ac responce in the CDW state. Fujishita et al. [5] have observed the incommensurate superlattice reflections at points-~=(±O.05,±0.05, ±0.085) by X-ray diffraction. These superlattice reflections were confirmed by electron diffraction [9], although t h e - ~ v e c t o r s are
slightly different from those obtained by the X-ray diffraction. In the CDW states there are two types of collective modes, i.e., the amplitude and phase modes [10]. In spite of much effort to observe these collective modes in the quasi-one-dimensional conductors, the success in the observation is limited only in K2Pt(CN)4Br 0 3"3.2H20 (KCP) [11,12], deuterated KCP [13] and K0.3MoO 3 [14]. The purpose of this paper is to study the CDW phase transition of (TaSe4)2I and to observe the amplitude mode by means of Raman scattering. Single crystals of (TaSe4)2I were synthesized in a quartz ampoule by vapour transport method in a two-zone furnace. The stoichiometric mixture of the constituents in the high-temperature zone was heated at 600Oc and the other zone was kept at 450°C for a few weeks. In our samples the CDW phase transition was observed at 263 K by the resistivity measurement. In the Raman-scattering measurement we used single crystals of about 1xlx4 mm3 with (100), (010) and (001) surfaces. The orientation was carried out by the X-ray diffraction. The large cross section of the sample permits us to measure Raman scattering on the (001) surface. Raman-scattering measurement was carried out using 5145-~ line of argonion laser in conventional backscattering configuration. The scattered light was detected by the usual photon-counting method. At room temperature (TaSe4)2I has a te~ragonal structure of the space group I422 (D~) [15]. The crystal is composed of two TaSe 4 chains and two iodine columns running 767
768
RAMAN STUDY OF CHARGE-DENSITY-WAVE
along the c axis in a unit cell. In each TaSe 4 chain, Ta atom is coordinated to eight Se atoms in a slightly distorted rectangular antiprism. The TaSe 4 chains are well separated from one another by the iodine columns. This structure provides quasi-one-dimensional character to this crystal. Four molecules of TaSe 4 per chain are located within one c length and then there are four molecules of (TaSe4)2I in a unit cell. The lattice vibrations at the center of Brillouin zone are represented as 15A1+I7A2+I3B1+15B2+36E
PHASE TRANSITION
VoI° 53, No. 9
295 K a(bc)~"
• •
l
_
;'T
.,f. B-
c(ab)T
Z
,•
(-
,
. ,
Among them one of the A 2 modes and one of the E modes are acoustic, 16 A 2 modes are infrared active, 15 A I modes, 13 B I modes and 15 B 2 modes are Raman active, and 35 E modes are Raman and infrared active. With a=[100], b= [010] and c=[001], the Raman tensors of Ramanactive phonons are written by
[
6 6
],
w.,
•
•~1.
,~ a ( b b ) ~
,.
and 0=[001],
A
.'%;"
~.
B
i- i
t,
"
"xl--
&2
;
RI >. :
Ai
a(cc)~
Z
ILl IX
i
.
c(b'b')E
•
b':[ITO]
,
""
I-
•
and with a':[110],
,"%~.
.*
these
,% A 1 . B 2 a
• c(a'b')~' ;,. ::. 100
' ::
are written by
0
;
B :"
"r'q
200
FREQUENCY
[
300
(cm -1)
Fig. I Polarized Raman spectra at 295 K. a, b, c, a' and b' represent [100], [010], [001], [110] and lIT0] axes, respectively. Figures I and 2 show polarized Raman spectra at 295 K and 78 K, respectively. At 295 K we observe the A I modes in the a(cc)~ spectrum, the B I modes in the c(a'b')~ spectrum, the B 2 modes in the c(ab)~ spectrum and the E modes in the a(bc)~ spectrum, while both the A I and B I modes appear in the a(bb)~ spectrum and both the A I and B 2 modes in the c(b'b')~ spectrum• The Ranan intensities of many peaks increase at 78 K, in particular, those of the AI, B I and B2 modes near 270 cm -I. At 78 K there appears a new BI phonon peak at 166 cm -I near the 158-cm-1"B 1 phonon peak in the c(a'b')~ and a(bb)~ spectra. (Here in the low-temperature phase, we shall use the same notation of the phonon symmetry as that in the high-temperature phase.) The 188-cm -I B I mode and the 189-cm -I B 2 mode shift considerably to higher frequency at 78 K in the c(a'b')~ and c(ab)~ spectra, respectively. Therefore the 188 cm -I peak which consists of the B I mode at 188 cm -I and the A I mode at 184 cm -I in the a(bb)~ spectrum splits into two peaks at 78 K. In the c(b'b')~ spectrum, the B2 mode at 189 cm -I is superimposed on the A I mode at 184 cm-1 at 295 K and similar splitting was observed at 78 K. The remaining peaks scarcely shift.
The most important feature is that a new broad peak appeared at 92 cm -I . This peak was observed only in the a(cc)~ spectrum• This fact shows that this belongs to the totally symmetric mode. We shall focus on the temperature dependence of the phonon peak at 92 cm -I in the a(cc)~ polarization configuration. Figure 3 shows the low-frequency Raman spectra between 6 K and 294 K. At 6 K a broad peak is observed at 90 cm -I and a small peak at 65 cm -I. The higher-frequency peak broadens remarkably with increasing temperature. Its frequency shifts slightly to higher frequency as the temperature increases. It disappears at about 245 K. On the other hand, the lower-frequency peak remains observable even above Tc=263 K. In order to determine precisely the frequency, the damping constant and the coupling coefficient of the higher-frequency peak, we fitted the Raman spectra by a spectral function [16] using the method of least squares, 2
O(~)=(n(~)+l)
2 E Kilmx(~,~i,Fi)+bg i=l
' (I)
Vol. 53, No. 9
769
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
where 2 2 X(~ '~i ' ri) = (~ -~i -2i
r±~)
-1
"::
(2)
Here ~I (0>2), rl (r2) and K I (K2) are the frequency, the damping constant and the coupling coefficient of the higher-frequency phonon (the lower-frequency phonon), n(~) is the Bose factor, b E is the background and is assumed to be independent of m. The parameters ml, rl and K I obtained are shown in Figs. 4, 5 and 6, respectively. The frequency of the higher-frequency peak increases slightly and the damping constant increases remarkably with increasing temperature. The coupling coefficient decreases as the temperature increases. The solid curve in Fig. 6 shows the relation KI=(Tc-T) I/2. The phonon, whlch is R ~ a n inactive or does not exist at the r point above T O and becomes Raman active below Tc, has the coupling coefficient proportional to the order parameter <~>, so that we obtain the following relation if we use the mean-field theory [16]; K = < ¢ > = (Tc_T) 1/2
"A ....
".
A,.
",,
. 2,4,.
.
245 K
•
A,.
•
", •
~
¢.-
"A
'
• "'.''.'5"
173 K
•
, ' ~ -.~ ~ . . . . "
.
."
".
~
.
. f k
=>,
..
e
_/'~.
%~e
1/.,2 K
o
•
•
• •
,.O L.. al
•
>. i-u3 z LI.I I--Z
(3)
"%:
A..,~#~=..
112K
"'/~"
44 Z
k
78 K •
a(bc)~
•
~
"\
6K
,•
c(ab)c"
:
,,
I
/!
•
A
•
I
I
80 FREQUENCY ( c m -1)
••
a(bb)a
I
40
Fig. 3 Temperature dependence of the low-frequency Raman spectrum in the a(ec)~ polarization configuration. The solid curves show the spectra fitted by Eqs. (I) and (2).
X 1
: .
I
120
s
a(cc)a 120 Z tlJ I-Z
c (b'b')T
110 7 E ~I00 >-
xt
U
z bJ
m 90
%
--
•
•
.
c(a'b')c
%
~
it
,,
".
": x :%)-
i
0 bJ m~ h
I
I
I
I
tt
80I 0
I I I I 100 20O FREOUENCY (cm -I)
I 300
F i g . 2 P o l a r i z e d Raman s p e c t r a a t 78 K. a , b , c , a ' and b ' r e p r e s e n t [ 1 0 0 ] , [ 0 1 0 ] , [ 0 0 1 ] , [ 1 1 0 ] and [ I T O ] a x e s i n t h e h i g h - t e m p e r a t u r e p h a s e , respectively.
0
I
I I I 100 200 TEMPERATURE (K)
Tc il 30O
F i g . 4 T e m p e r a t u r e dependence o f t h e f r e q u e n c y ~I of the 90-cm-I Raman peak•
770
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
t
L; v I--
I
I
I
I
z
540
/
I--
I
J
u~ z 0 u (.D
E20
13.. IE
Tc
I
I I I 100 200 TEMPERATURE (K)
il 300
Fig. 5 Temperature dependence of the damping constant F I of the 90-cm -I Raman peak. The solid curve indicates Kurihara's theory written by Eqs. (4) and (6) with an adjustable parameter F 0 .
"~ 5 i
"£-
I
I
I
I
I
Vol. 53, No. 9
is a phonon which is a Raman-inactive optical mode at the F point above Tc and becomes Raman active below T c. If we assume the latter two cases, it seems difficult to explain the temperature dependence of the damping constant. Although the phonons in the latter two cases should have strongly temperature-dependent intensities, they are not expected to have strongly temperature-dependent damping constants, because they are quite ordinary modes with-k'=O in the lowtemperature phase. In this sense, the temperature dependence observed in the damping constant is quite anomalous and suggests that it may have a relation to the dynamical properties of the CDW phase transition. The frequency of the amplitude mode, however, is expected to decrease on approaching Tc. The frequency of the 90-cm -I phonon observed in (TaSe4)2I has opposite temperature dependence. But this fact does not necessarily deny the possibility that it is an amplitude mode. Similar temperature dependence of the frequency and the damping constant has been observed in the amplitude modes of KCP [11] and deuterated KCP [13], i.e., the frequency increases considerably with increasing temperature, and the damping constant increases remarkably as the temperature increases. Kurihara [17] calculated the damping constant of KCP by using a nonlinear amplitude-phase interaction Hamiltonian, and he obtained the temperature dependence of the damping constant of the amplitude mode as follows:
I
F (T) = F 0 c o t h (T O/T)
(4)
with F0=~ LLI
)2) }1/2]
(5)
and T0=~/4
o
/ [4{~(i_(2~/~
0
100
200
300
TEMPERATURE (K) Fig. 6 Temperature dependence of the coupling coefficient K I of the 90-cm -I Raman peak. The solid curve shows the relation KI~ (Te-T) I/2, where Tc=263 K.
This equation explains well the temperature dependence of the coupling coefficient K I of the 90-cm -I phonon, as shown in Fig. 6. This fact indicates that this phonon is closely related to the CDW phase transition at 263 K. We can consider the following three cases as an origin of this phonon: (i) it is an amplitude mode, (ii) it is a simple "folded mode other than the amplitude mode or the phase mode which is folded from k{O point to the F point by the formation of the superlattice and (iii) it
(6)
Here ~ is the effective mass of the collective modes divided by the electron band mass and ~ and ~ are the frequencies of the amplitude and phase modes, respectively. Since U and ~¢ have been obtained by the experiments other than the Raman scattering in KCP, Kurihara [17] applied this equation to the damping constants observed by the Raman scattering [11] without any adjustable parameters and he obtained an excellent agreement. In (TaSe4)2I, the values of U and ~ have not been obtained yet. We, therefore, determined F0 in Eq. (5) by fitting the theoretical value to the experimental one, and then we obtained the calculated curve shown by the solid curve in Fig. 5 using ~e=90 cm -I. It agrees well with the experimental data. The Peierls distortion affects the cc component of the dielectric susceptibility tensor parallel to the chain direction. Since the Raman cross section is proportional to the square of an appropriate susceptibility derivative, only the cc component of Raman tensor is affected by the Peierls distortion in the first-order Raman scattering. The amplitude mode should therefore be observed for the incident and scattered beams polarized parallel
Vol. 53, No. 9
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
to the c axis [11]. This agrees with the polarization characteristic of the 90-om -I Raman peak.
The temperature dependence of the damping constant and the polarization characteristic of the 90-cm -I phonon suggest the possibility of the amplitude mode. But the temperature dependence of the frequency shift still cannot be understood. Kurihara's theory [17] cannot explain the frequency shift of the amplitude mode in KCP, whose frequency increases with increasing temperature towards T c. Kurihara reported that the coupling of the amplitude mode to the motion of water molecules surrounding the Pt(CN) 4 chain is important in the frequency shift in KCP. The importance of the coupling of the CDW to the water stretching mode has been demonstrated experimentally by Steigmeier et al. [13] through the isotope shift of the amplitude-mode frequency in deuterated KCP. And they reported that the decoupled frequencies of the CDW amplitude modes are higher than those observed in the Raman scattering of KCP and deuterated KCP. They suggested that the rotations of the water molecules would diminish the coupling between the water and the Pt-chain which could be the origin of the temperature dependence of the frequency of the amplitude mode. In (TaSe4)2I , the iodine atoms are located in between the TaSe 4 chains, and therefore the coupling of the amplitude mode to the motion of the iodine atoms may affect effectively the frequency of the amplitude mode. But the model of KCP cannot simply be applied to the present case, because there does not exist internal motion of the iodine atom in (TaSe4)2I. Recently Fujishita et al. [18] reported by the X-ray diffraction that the Peierls distor-
tion is induced by the condensation of a transverse acoustic (TA) phonon with polarization perpendicular to the c axis in (TaSe4)2I. Also in K0 3MoO 3 the Peierls transition at 180 K resuits from the condensation of TA phonon [19], and the softening of the amplitude mode is small [14,19]. The condensation of the TA phonon cannot induce directly the CDW. The CDW can be induced only if the longitudinal elastic distortion follows the condensation of the TA phonon. The condensation of TA phonon, which is a trigger of the formation of the CDW in (TaSe4)2I , may give the anomalous behaviour of the 90-cm -I phonon observed by the present experiment. At present we think that there is a possibility that the 90-cm -I phonon is an amplitude mode, although it is necessary to clarify the nature of the amplitude mode by other experiments, in particular, the inelastic neutron scattering. In conclusion, we have observed Raman spectra in the quasi-one-dimensional conductor (TaSe4)2I. The Raman peak at about 90 cm-I reveals anomalous temperature dependence in its frequency and its damping constant. The temperature dependence of the coupling coefficient shows clearly that it is related to the CDW phase transition. The temperature dependence of the damping constant agrees with that of the amplitude mode calculated by Kurihara in KCP. We suggest that there is a possibility that the 90-cm -1 phonon is the amplitude mode, although the frequency shift still cannot be understood.
Acknowledgement-The authors would like to thank Y. Koguchi for her assistance in the experiments.
References
[I] Z.Z. Wang, M.C. Saint-Langer, P. Monceau, M. Renard, P. Gressier, A. Meerschaut, L. Guemas and J. Rouxel: Solid State Commun. 46, 325 (1983). [2] M. Maki, M. Kaiser, A. Zettl and G. Gruner: Solid State Commun. 46, 497 (1983). [3] P. Gressier, A. Meerschaut, L. Guemas, J. Rouxel and P. Monceau: J. Solid State Chem. 51, 121 (1984). [4] A. Meerschaut: Proc. Int. Symposium on Nonlinear Transport and Related Phenomena in Inorganic Quasi One Dimensional Conductors, Sapporo, 1983 p. 231. [5] H. Fujishita, M. Sato and S. Hoshino: Solid State Commun. 49, 313 (1984). [6] Z.Z. Wang, P. Monceau, M. Renard, P. Gressier, L. Guemas and A. Meerschaut: Solid State Commun. 47, 439 (1983). [7] G. Mozurkewich, M. Maki and G. GrUner: Solid State Commun. 48, 453 (1983). [8] M. Sherwin, R. Hall and A. Zettl: Phys. Rev. Lett. 53, 1387 (1984). [9] C. Roucau, R. Ayroles, P. Gressier and A. Meerschaut: J. Phys. C 17, 2993 (1984).
771
[10] P.A. Lee, T.M. Rice and P.W. Anderson: Solid State Co,lnun. 14, 703 (1974). [11] E.F. Steigmeier, R. Loudon, G. Harbeke, H. Auderset and G. Scheiber: Solid State Commun. 17, 1447 (1975). [12] P. BrGes-ch and H.R. Zeller: Solid State Commun. 14, 1037 (1974); P. Br~esch, S. Str~ssle-r--and H.R. Zeller: Phys. Rev. B12, 219 (1975). [13] E.F. Steigmeier, D. Baeriswyl, G. Harbeke H. Auderset and G. Scheiber: Solid State Commun. 20, 661 (1976). [14] G. Travaglini, I. M~rke and p. Wachter: Solid State Commun. 45, 289 (1983). [15] P. Gressier, L. Guemas and A. Meerschaut: Acta Cryst. B38, 2877 (1982). [16] P.A. Fleury: -~mments on Solid State Phys. IV, 167 (1972). [17] S. Kurihara: J. Phys. Soc. Jpn. 48, 1821 (1980). [18] H. Fujishita, M. Sato, S. Sato and S. Hoshino: to be published in J. Phys. C. [19] M. Sato, H. Fujishita, S. Sato and S. Hoshino: submitted to J. Phys. C.
Solid State Communications, Vol.53,No.9, pp.767-771, Printed in Great Britain.
1985.
0038-|098/85 $3.00 + .00 Pergamon Press Ltd.
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION IN QUASI-ONE-DIMENSIONAL CONDUCTOR (TaSe4)2I
Tomoyuki Sekine, Taisaku Seino, Mitsuru Izumi and Etsuyuki Matsuura Institute of Physics, University of Tsukuba, Sakura-mura, Ibaraki 305, Japan (received 22 November 1984 by W. Sasaki)
Polarized Raman spectra were obtained in the quasi-one-dimensional conductor (TaSe4)2I above and below the charge-density-wave (CDW) transition temperature (Tc=263 K). The Raman intensities of many peaks become intenser and two of the phonon peaks shift to higher frequency with decreasing temperature. Moreover a new broad peak at about 90 em-1 and a new peak around 166 cm-I appear in the lowtemperature phase. The polarization characteristic shows that the former is assigned to totally symmetric mode. The damping constant of the phonon at 90 cm-1 increases markedly with increasing temperature. The frequency shifts to higher frequency as the temperature increases and the coupling coefficient is approximately proportional to (Tc-T) I/2. This peak becomes Raman active owing to the CDW phase transition. The temperature dependence of the damping constant and the frequency shift may have a relation to the dynamical properties of the CDW phase transition.
During the last decade, it has been shown that many quasi-one-dimensional conductors undergo a Peierls transition, i.e., the formation of charge-denslty wave (CDW) with a periodic lattice distortion connected with a condensation of the 2-~F phonon mode. Here-~F is the Fermi wave vector. The CDW opens up a gap at the Fermi surface-~:±~F and the materials show semiconducting properties below the transition temperature T c. Among the quasi-onedimensional conductors, much attention has been paid to transition-metal trichalcogenides, because they show nonlinear transport properties due to the motion of the CDW. Recently much interest has been aroused not only in transition-metal trichalcogenides but also in a new family of halogenated transition-metal tetrachalcogenides (MX4)nY, where M=Nb or Ta, Y=Br or I and n=2, 3 or 10/3, because such intriguing phenomena of the transport properties were found also in (TaSe4)2I [I-4], (NbSe4)2I [5] and (NbSe4)10/31 [4,6]. In (TaSe4)2I, Wang et al. [I] have found out a resistive anomaly due to the formation of an incommensurate CDW at Tc=263 K. The remarkable electric-field and frequency dependence of the conductivity and the current oscillations have been observed in the low-temperature phase [1-4,7]. Sherwin et al. [8] have reported the observation of chaotic ac responce in the CDW state. Fujishita et al. [5] have observed the incommensurate superlattice reflections at points-~=(±O.05,±0.05, ±0.085) by X-ray diffraction. These superlattice reflections were confirmed by electron diffraction [9], although t h e - ~ v e c t o r s are
slightly different from those obtained by the X-ray diffraction. In the CDW states there are two types of collective modes, i.e., the amplitude and phase modes [10]. In spite of much effort to observe these collective modes in the quasi-one-dimensional conductors, the success in the observation is limited only in K2Pt(CN)4Br 0 3"3.2H20 (KCP) [11,12], deuterated KCP [13] and K0.3MoO 3 [14]. The purpose of this paper is to study the CDW phase transition of (TaSe4)2I and to observe the amplitude mode by means of Raman scattering. Single crystals of (TaSe4)2I were synthesized in a quartz ampoule by vapour transport method in a two-zone furnace. The stoichiometric mixture of the constituents in the high-temperature zone was heated at 600Oc and the other zone was kept at 450°C for a few weeks. In our samples the CDW phase transition was observed at 263 K by the resistivity measurement. In the Raman-scattering measurement we used single crystals of about 1xlx4 mm3 with (100), (010) and (001) surfaces. The orientation was carried out by the X-ray diffraction. The large cross section of the sample permits us to measure Raman scattering on the (001) surface. Raman-scattering measurement was carried out using 5145-~ line of argonion laser in conventional backscattering configuration. The scattered light was detected by the usual photon-counting method. At room temperature (TaSe4)2I has a te~ragonal structure of the space group I422 (D~) [15]. The crystal is composed of two TaSe 4 chains and two iodine columns running 767
768
RAMAN STUDY OF CHARGE-DENSITY-WAVE
along the c axis in a unit cell. In each TaSe 4 chain, Ta atom is coordinated to eight Se atoms in a slightly distorted rectangular antiprism. The TaSe 4 chains are well separated from one another by the iodine columns. This structure provides quasi-one-dimensional character to this crystal. Four molecules of TaSe 4 per chain are located within one c length and then there are four molecules of (TaSe4)2I in a unit cell. The lattice vibrations at the center of Brillouin zone are represented as 15A1+I7A2+I3B1+15B2+36E
PHASE TRANSITION
VoI° 53, No. 9
295 K a(bc)~"
• •
l
_
;'T
.,f. B-
c(ab)T
Z
,•
(-
,
. ,
Among them one of the A 2 modes and one of the E modes are acoustic, 16 A 2 modes are infrared active, 15 A I modes, 13 B I modes and 15 B 2 modes are Raman active, and 35 E modes are Raman and infrared active. With a=[100], b= [010] and c=[001], the Raman tensors of Ramanactive phonons are written by
[
6 6
],
w.,
•
•~1.
,~ a ( b b ) ~
,.
and 0=[001],
A
.'%;"
~.
B
i- i
t,
"
"xl--
&2
;
RI >. :
Ai
a(cc)~
Z
ILl IX
i
.
c(b'b')E
•
b':[ITO]
,
""
I-
•
and with a':[110],
,"%~.
.*
these
,% A 1 . B 2 a
• c(a'b')~' ;,. ::. 100
' ::
are written by
0
;
B :"
"r'q
200
FREQUENCY
[
300
(cm -1)
Fig. I Polarized Raman spectra at 295 K. a, b, c, a' and b' represent [100], [010], [001], [110] and lIT0] axes, respectively. Figures I and 2 show polarized Raman spectra at 295 K and 78 K, respectively. At 295 K we observe the A I modes in the a(cc)~ spectrum, the B I modes in the c(a'b')~ spectrum, the B 2 modes in the c(ab)~ spectrum and the E modes in the a(bc)~ spectrum, while both the A I and B I modes appear in the a(bb)~ spectrum and both the A I and B 2 modes in the c(b'b')~ spectrum• The Ranan intensities of many peaks increase at 78 K, in particular, those of the AI, B I and B2 modes near 270 cm -I. At 78 K there appears a new BI phonon peak at 166 cm -I near the 158-cm-1"B 1 phonon peak in the c(a'b')~ and a(bb)~ spectra. (Here in the low-temperature phase, we shall use the same notation of the phonon symmetry as that in the high-temperature phase.) The 188-cm -I B I mode and the 189-cm -I B 2 mode shift considerably to higher frequency at 78 K in the c(a'b')~ and c(ab)~ spectra, respectively. Therefore the 188 cm -I peak which consists of the B I mode at 188 cm -I and the A I mode at 184 cm -I in the a(bb)~ spectrum splits into two peaks at 78 K. In the c(b'b')~ spectrum, the B2 mode at 189 cm -I is superimposed on the A I mode at 184 cm-1 at 295 K and similar splitting was observed at 78 K. The remaining peaks scarcely shift.
The most important feature is that a new broad peak appeared at 92 cm -I . This peak was observed only in the a(cc)~ spectrum• This fact shows that this belongs to the totally symmetric mode. We shall focus on the temperature dependence of the phonon peak at 92 cm -I in the a(cc)~ polarization configuration. Figure 3 shows the low-frequency Raman spectra between 6 K and 294 K. At 6 K a broad peak is observed at 90 cm -I and a small peak at 65 cm -I. The higher-frequency peak broadens remarkably with increasing temperature. Its frequency shifts slightly to higher frequency as the temperature increases. It disappears at about 245 K. On the other hand, the lower-frequency peak remains observable even above Tc=263 K. In order to determine precisely the frequency, the damping constant and the coupling coefficient of the higher-frequency peak, we fitted the Raman spectra by a spectral function [16] using the method of least squares, 2
O(~)=(n(~)+l)
2 E Kilmx(~,~i,Fi)+bg i=l
' (I)
Vol. 53, No. 9
769
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
where 2 2 X(~ '~i ' ri) = (~ -~i -2i
r±~)
-1
"::
(2)
Here ~I (0>2), rl (r2) and K I (K2) are the frequency, the damping constant and the coupling coefficient of the higher-frequency phonon (the lower-frequency phonon), n(~) is the Bose factor, b E is the background and is assumed to be independent of m. The parameters ml, rl and K I obtained are shown in Figs. 4, 5 and 6, respectively. The frequency of the higher-frequency peak increases slightly and the damping constant increases remarkably with increasing temperature. The coupling coefficient decreases as the temperature increases. The solid curve in Fig. 6 shows the relation KI=(Tc-T) I/2. The phonon, whlch is R ~ a n inactive or does not exist at the r point above T O and becomes Raman active below Tc, has the coupling coefficient proportional to the order parameter <~>, so that we obtain the following relation if we use the mean-field theory [16]; K = < ¢ > = (Tc_T) 1/2
"A ....
".
A,.
",,
. 2,4,.
.
245 K
•
A,.
•
", •
~
¢.-
"A
'
• "'.''.'5"
173 K
•
, ' ~ -.~ ~ . . . . "
.
."
".
~
.
. f k
=>,
..
e
_/'~.
%~e
1/.,2 K
o
•
•
• •
,.O L.. al
•
>. i-u3 z LI.I I--Z
(3)
"%:
A..,~#~=..
112K
"'/~"
44 Z
k
78 K •
a(bc)~
•
~
"\
6K
,•
c(ab)c"
:
,,
I
/!
•
A
•
I
I
80 FREQUENCY ( c m -1)
••
a(bb)a
I
40
Fig. 3 Temperature dependence of the low-frequency Raman spectrum in the a(ec)~ polarization configuration. The solid curves show the spectra fitted by Eqs. (I) and (2).
X 1
: .
I
120
s
a(cc)a 120 Z tlJ I-Z
c (b'b')T
110 7 E ~I00 >-
xt
U
z bJ
m 90
%
--
•
•
.
c(a'b')c
%
~
it
,,
".
": x :%)-
i
0 bJ m~ h
I
I
I
I
tt
80I 0
I I I I 100 20O FREOUENCY (cm -I)
I 300
F i g . 2 P o l a r i z e d Raman s p e c t r a a t 78 K. a , b , c , a ' and b ' r e p r e s e n t [ 1 0 0 ] , [ 0 1 0 ] , [ 0 0 1 ] , [ 1 1 0 ] and [ I T O ] a x e s i n t h e h i g h - t e m p e r a t u r e p h a s e , respectively.
0
I
I I I 100 200 TEMPERATURE (K)
Tc il 30O
F i g . 4 T e m p e r a t u r e dependence o f t h e f r e q u e n c y ~I of the 90-cm-I Raman peak•
770
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
t
L; v I--
I
I
I
I
z
540
/
I--
I
J
u~ z 0 u (.D
E20
13.. IE
Tc
I
I I I 100 200 TEMPERATURE (K)
il 300
Fig. 5 Temperature dependence of the damping constant F I of the 90-cm -I Raman peak. The solid curve indicates Kurihara's theory written by Eqs. (4) and (6) with an adjustable parameter F 0 .
"~ 5 i
"£-
I
I
I
I
I
Vol. 53, No. 9
is a phonon which is a Raman-inactive optical mode at the F point above Tc and becomes Raman active below T c. If we assume the latter two cases, it seems difficult to explain the temperature dependence of the damping constant. Although the phonons in the latter two cases should have strongly temperature-dependent intensities, they are not expected to have strongly temperature-dependent damping constants, because they are quite ordinary modes with-k'=O in the lowtemperature phase. In this sense, the temperature dependence observed in the damping constant is quite anomalous and suggests that it may have a relation to the dynamical properties of the CDW phase transition. The frequency of the amplitude mode, however, is expected to decrease on approaching Tc. The frequency of the 90-cm -I phonon observed in (TaSe4)2I has opposite temperature dependence. But this fact does not necessarily deny the possibility that it is an amplitude mode. Similar temperature dependence of the frequency and the damping constant has been observed in the amplitude modes of KCP [11] and deuterated KCP [13], i.e., the frequency increases considerably with increasing temperature, and the damping constant increases remarkably as the temperature increases. Kurihara [17] calculated the damping constant of KCP by using a nonlinear amplitude-phase interaction Hamiltonian, and he obtained the temperature dependence of the damping constant of the amplitude mode as follows:
I
F (T) = F 0 c o t h (T O/T)
(4)
with F0=~ LLI
)2) }1/2]
(5)
and T0=~/4
o
/ [4{~(i_(2~/~
0
100
200
300
TEMPERATURE (K) Fig. 6 Temperature dependence of the coupling coefficient K I of the 90-cm -I Raman peak. The solid curve shows the relation KI~ (Te-T) I/2, where Tc=263 K.
This equation explains well the temperature dependence of the coupling coefficient K I of the 90-cm -I phonon, as shown in Fig. 6. This fact indicates that this phonon is closely related to the CDW phase transition at 263 K. We can consider the following three cases as an origin of this phonon: (i) it is an amplitude mode, (ii) it is a simple "folded mode other than the amplitude mode or the phase mode which is folded from k{O point to the F point by the formation of the superlattice and (iii) it
(6)
Here ~ is the effective mass of the collective modes divided by the electron band mass and ~ and ~ are the frequencies of the amplitude and phase modes, respectively. Since U and ~¢ have been obtained by the experiments other than the Raman scattering in KCP, Kurihara [17] applied this equation to the damping constants observed by the Raman scattering [11] without any adjustable parameters and he obtained an excellent agreement. In (TaSe4)2I, the values of U and ~ have not been obtained yet. We, therefore, determined F0 in Eq. (5) by fitting the theoretical value to the experimental one, and then we obtained the calculated curve shown by the solid curve in Fig. 5 using ~e=90 cm -I. It agrees well with the experimental data. The Peierls distortion affects the cc component of the dielectric susceptibility tensor parallel to the chain direction. Since the Raman cross section is proportional to the square of an appropriate susceptibility derivative, only the cc component of Raman tensor is affected by the Peierls distortion in the first-order Raman scattering. The amplitude mode should therefore be observed for the incident and scattered beams polarized parallel
Vol. 53, No. 9
RAMAN STUDY OF CHARGE-DENSITY-WAVE PHASE TRANSITION
to the c axis [11]. This agrees with the polarization characteristic of the 90-om -I Raman peak.
The temperature dependence of the damping constant and the polarization characteristic of the 90-cm -I phonon suggest the possibility of the amplitude mode. But the temperature dependence of the frequency shift still cannot be understood. Kurihara's theory [17] cannot explain the frequency shift of the amplitude mode in KCP, whose frequency increases with increasing temperature towards T c. Kurihara reported that the coupling of the amplitude mode to the motion of water molecules surrounding the Pt(CN) 4 chain is important in the frequency shift in KCP. The importance of the coupling of the CDW to the water stretching mode has been demonstrated experimentally by Steigmeier et al. [13] through the isotope shift of the amplitude-mode frequency in deuterated KCP. And they reported that the decoupled frequencies of the CDW amplitude modes are higher than those observed in the Raman scattering of KCP and deuterated KCP. They suggested that the rotations of the water molecules would diminish the coupling between the water and the Pt-chain which could be the origin of the temperature dependence of the frequency of the amplitude mode. In (TaSe4)2I , the iodine atoms are located in between the TaSe 4 chains, and therefore the coupling of the amplitude mode to the motion of the iodine atoms may affect effectively the frequency of the amplitude mode. But the model of KCP cannot simply be applied to the present case, because there does not exist internal motion of the iodine atom in (TaSe4)2I. Recently Fujishita et al. [18] reported by the X-ray diffraction that the Peierls distor-
tion is induced by the condensation of a transverse acoustic (TA) phonon with polarization perpendicular to the c axis in (TaSe4)2I. Also in K0 3MoO 3 the Peierls transition at 180 K resuits from the condensation of TA phonon [19], and the softening of the amplitude mode is small [14,19]. The condensation of the TA phonon cannot induce directly the CDW. The CDW can be induced only if the longitudinal elastic distortion follows the condensation of the TA phonon. The condensation of TA phonon, which is a trigger of the formation of the CDW in (TaSe4)2I , may give the anomalous behaviour of the 90-cm -I phonon observed by the present experiment. At present we think that there is a possibility that the 90-cm -I phonon is an amplitude mode, although it is necessary to clarify the nature of the amplitude mode by other experiments, in particular, the inelastic neutron scattering. In conclusion, we have observed Raman spectra in the quasi-one-dimensional conductor (TaSe4)2I. The Raman peak at about 90 cm-I reveals anomalous temperature dependence in its frequency and its damping constant. The temperature dependence of the coupling coefficient shows clearly that it is related to the CDW phase transition. The temperature dependence of the damping constant agrees with that of the amplitude mode calculated by Kurihara in KCP. We suggest that there is a possibility that the 90-cm -1 phonon is the amplitude mode, although the frequency shift still cannot be understood.
Acknowledgement-The authors would like to thank Y. Koguchi for her assistance in the experiments.
References
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771
[10] P.A. Lee, T.M. Rice and P.W. Anderson: Solid State Co,lnun. 14, 703 (1974). [11] E.F. Steigmeier, R. Loudon, G. Harbeke, H. Auderset and G. Scheiber: Solid State Commun. 17, 1447 (1975). [12] P. BrGes-ch and H.R. Zeller: Solid State Commun. 14, 1037 (1974); P. Br~esch, S. Str~ssle-r--and H.R. Zeller: Phys. Rev. B12, 219 (1975). [13] E.F. Steigmeier, D. Baeriswyl, G. Harbeke H. Auderset and G. Scheiber: Solid State Commun. 20, 661 (1976). [14] G. Travaglini, I. M~rke and p. Wachter: Solid State Commun. 45, 289 (1983). [15] P. Gressier, L. Guemas and A. Meerschaut: Acta Cryst. B38, 2877 (1982). [16] P.A. Fleury: -~mments on Solid State Phys. IV, 167 (1972). [17] S. Kurihara: J. Phys. Soc. Jpn. 48, 1821 (1980). [18] H. Fujishita, M. Sato, S. Sato and S. Hoshino: to be published in J. Phys. C. [19] M. Sato, H. Fujishita, S. Sato and S. Hoshino: submitted to J. Phys. C.