Origin of the structural transition in TiSe2

~

Solid State Communications, Voi.39, pp. I167-I170. Pergamon Press Ltd. 1981. Printed in Great Britain.

ORIGIN OF THE STRUCTURAL

Department

TRANSITION

0038-I098/81/351167-04502.00/0

IN TISe 2

John H. Gaby, B. DeLong, F. C. Brown of Physics and Materials Research Laboratory, University at Urbana-Champalgn, Urbana, IL 61801

Department of Physics,

R. Kirby University of Nebraska,

Lincoln,

NB

of Illinois

68588

and

Laboratolre de Physique (Recieved

F. L~vy Appllqu~e, EPF, Lausanne,

Switzerland

March 1981 by A. A. Maradudin)

Thermoelectric power and electron diffraction measurements have been made on well characterized crystals of TiSe2, ZrxTi I xSe2 and VxTi I xSe2 in an effort to determine the importance of charge-carriers to the periodic lattice distortion. When the energy bands are uncrossed by alloying with Zr, the superlattice is critically suppressed. This result and the effect of vanadium doping, as well as earlier investigations, suggest that both electrons and holes are crucial. Superlattlce formation in these systems appears to be due to interaction between carriers and a particular zone boundary phonon. Fermi surface nesting alone is not sufficient to account for the instability.

The group IVb transition metal diselenide TiSe 2 undergoes a much studied periodic lattice di~t~rtlon at a transition temperature T = 200 c K. ",~ This transition is unusual compared to the charge density wave transitions which occur in the group Vb layered crystals such as TaS 2 or TaSe 2. For one thing TISe 2 is semimeta~l~c with small pockets of electrons and holes. J'~ The transition in TiSe 2 involves a zone boundary wavevector and a commensurate 2a o x 2a o x 2c o superlattice without the occurance of an incommensurate phase. The mechanism for the phase transition in TiSe 2 ~as been discussed by a number of authors. Wilson ~ for example has sng~ested the excitonic insulator mechanism, Hughes, ~ a ba~d Jahn-Teller effect, and White and Lucovsky, a soft-mode transition suppressed by carriers. A crucial question is whether or not electrons and holes are important to superlattice formation. We address this question below and show that the transition is suppressed by alloying with zirconium at a critical composition corresponding to uncrossing of electron and hole energy ba~ds. Very recently Yoshida and Motizuki have calculated both the bare electronic susceptibility x°(q) and the accurate or re-normallzed x(ql) which includes the wave number q and mode dependence I of the electron-lattice interaction. In order to accomplish this feat, the initial electronic structure was obtalned 3 by a tight binding fit to Zunger and Freeman's calculated energy bands at high symmetry points in the Brillouln zone. The remarkable result of this work is that little or no divergence in x°(q) is found even at the zone boundary. The driving force for the transition cannot be nesting o f the Fermi surface in the simple

sense. On the other hand, Yoshida and Motizuki find a uniquely high x(ql) for waveveetors q spanning L to r (electron-hole pockets) and for the particular zone boundary Eu mode which is related to the observed superlat~ice and which is known to be a quasl-soft mode. When the atomic displacements for three of these symmetry related E modes are superimposed, the metal-chalcog~n bonds of the IT crystal structure twist in an easy liberation, as shown in Fig. 1 which is a view of the three atomic planes in a sandwich layer. Notice that this motion tends to bring titanium and selenium atoms together into molecular TiSe 2 units. Thus the transition is partly chemical i n nature as implied by Thompson some years ago. I0 On the other hand, ~btizuki and coworkers show that the driving force for the transition is not Just soft mode anti-ferroelectric behavior nor Fermi surface nesting alone, rather it includes the effect of nesting, plus strong electron-phonon interaction with renormallzed electron as well as phonon energies. If the above i d e a s are correct it would seem that the phase transition could be suppressed by the elimination of carriers either through uncrossing the energy bands or possibly by localizing electrons or holes. In the present work control over the instability was accomplished by varying x in the system ZrxTil_xSe 2 and also by studying VxTil_xSe 2 around x - O.Ol. Transport measurements were carried out, especially thermoelectric power as a function of temperature, in order to ascertain the sign of the residual carriers. The presence or absence of a superlattice was determined by diffraction using an electron microscope with a cold stage. Results on the zirconium alloys are consistent 1167

1168

ORIGIN OF THE STRUCTURAL TRANSITION IN TiSe 2

@

©

T i atom C) Se atom above plane

Se atom below plane Fig.

l(a)

Showing a part of the hexagonal crystal structure of TiSe 2 looking down onto a sandwich layer. The arrows indicate atomic displacements when the commensurate superlattice forms below 200 K (Ti atom displacements are actually somewhat larger than Se atom displacements).

with a continuous uncrossing of energy bands with increasing x. The charge density wave is critically suppressed at an alloy composition corresponding to zero band gap. The results on the vanadium system are more difficult to interpret, however, they strongly suggest that electrons become localized, and when this happens the transition tends to be suppressed. Single crystal samples of TiSe2, Zr~TiL_xSe 2 and VxTii_xSe 2 were grown in silica tu~es by vapor phase reaction using iodine as a transporting agent. 13 In general, low growth temperatures and excess selenium were used to favor stolchlometry. The compounds and alloys were synthesized before growth and repeatedly transported to improve homogeneity. After growth, chemical composition was checked by energy dispersive x-ray spectroscopy; x-ray and electron diffraction were also employed for further characterization. Preclsion thermoelectric power measurements were ,made in the layered plane by clamping a sample between insulated copper blocks within a double walled can which could be lowered into a liquid helium cryostat. Helium gas was used as a heat exchange medium. Small heaters were employed and temperatures were electronically controlled using platinum resistance thermometers. A differential gold-lron thermocouple was used to determine the small difference in temperature between the two copper blocks. The various voltages, were fed through an analog switch to a nanovoltmeter under control by a micro-computer. Repeated measurements were made for a given temperature in order to average small drifts during the experiment. The results of resistivity and Hall measurements were also available for several of the materials studied, however we emphasize thermoelectric power because it is relatively free of contact resistance, phase shift and magnetic

Vol. 39, No.

|I

effects which can cause trouble especially at low temperature. Under normal conditions we expect the sign of the thermopower to b~ a good indication of the dominant carriers. 2 In layered crystals, the thermoelectric effect can he quite large. It is also very sensitive to the formation of energy gaps when a phase transition takes place. The lowest curve in Fig. 2 with data points indicated by solid circles is the thermopower S(uVolts/0K) for pure TiSe 2 (the other curves are for V doped material and will be discussed

o

-~ee 7

0

%

:~ ~

• I ,'" 50 Z tQd " ."

50%. /

i ~50 T (°K)

J 200

j I . 250 . 306 •"

350

.." ~'~-z.,.

-I00 1

-~50[

"e~

""~"

-200

Fig. 2

Thermoelectric power S versus T for pure and vanadium doped VxTil_xSe 2. The differently marked points correspond to the following compositions: e,x = 0.00; • ,x = 0.009; A,x = 0.01; e,x = 0.02.

later). Careful magnetic susceptibility versus temperature measurements for this sample showed that it transformed at [95K indicating relatively good stoichlometry. This thermoelectric power curve for TISe 2 is very similar to that reported by DiSalvo et al I except that near 30K S changes sign at higher temperature indicating more excess t i t a n i ~ , and therefore slightly higher electron density. These data indicate that the inflection point near 200K can be associated with the transition. In any case, the rapid decrease in S near 200K is due to energyband gap formation and the filling of hole states as the charge density wave sets in. At still lower temperature when the energy gaps associated with the charge density wave are fully developed, the thermopower S decreases more-or-less monotonically to zero as T goes to zero. From the sign of S and the magnitude of the conductivity it appears that at low tenperature electrons dominate in metallic or near metallic conduction. Except at ~ e lowest temperatures S can be approximated by L ~ S = AT + B/T

(1)

This can be shown by plating ST versus T 2 which is nearly a straight llne in the range 45 to [25K. The first or diffusive term dominates at high temperature whereas phonon drag (second term of Eq. i) is appreciable bel0~ 100K and apparently can be represented by the I/T term well below the Debye temperature. Small electron pockets in the e-band help to explain this result. TiSe 2 is a semimetal with a band overlap of

ORIGIN OF THE STRUCTURAL TRANSITION IN TiSe 2

Vol. 39, No. II

0.2 eV, whereas ZrSe 2 is a semiconductor with a bandgap of about 1 eV. Both substances have the same crystal structure and somewhat similar valence charge density. 13 One expects that the mixed crystal system Zr _Til_xSe. will have intermediate bandgaps an~ little disorder. Resistivity m e a s ~ m e n t s indicate that this is indeed the case. ~' H o r e o v e ~ recent extended x-ray absorption EXAFS work ~ indicates that most if not all the zirconi,-, below x = 0.21 substitutes for titanium. If the energy bands shift proportional to composition a linear plot of bandgap E 2 versus composition x crosses zero bandgap clos~ to x - 0.15. We find that a superlattice is readily observed by electron diffraction in TiSe 2 but have been unable to observe a superlattlce at low temperature in ZrSe 2. Extensive transmission electron microscope observations with a cold stage show that superlattlces form in the Zr alloys for composition x = 0 . 0 3 , 0.07, 0.11 but not for x = 0.21. Moreover, some samples from a tube which analyzes 14% transform, others do not. The phase transition seems to be critically suppressed for x in the range 14 to 15%. This is further verified by reslstlvit[4measurements for various values of composition. ~

T (°K)

5O

%'

,

I00

150

I

I

I

300

350

I

I

I

%

-40

%

O

Se ee~

" - •% ~

ZOO 250

•

-80

X =0.03 +~ . I ~ •

"%. "o...~

m -120

X : 0.II

+

.-"-,,,

(o)

: ^.o---d

--. O~

-160 T(°K)

0(

.

5O

I00

I

I

150 I

200

250

300

350

I

I

I

[

< -40 %.,

_X : 0 . 1 4 (nontransforming)

9 ._ v O9

-80 ee

(b)

.. e e •

-120 Fig. 3(a)

e•

Thermopower S versus T for ZrxTil_xSe z for x = 0.03 and x = 0.11, transforming crystals.

Figure 3 shows the thermopower of three samples with x ,, 0.03, 0.1l and 0.14. In the case of the lightly doped sample, electron diffraction shows that the phase transition is still present, but the higher temperature data in Fig. 3a shows that the hole contribution to the thermopower has been reduced. (Compare the curve for p u r e Time 2 in Fig. 2.) ~ would expect the electron contribution to be similarly reduced, except for the presence of excess electrons due to a slight excess of Ti. Below 50K, the plateau due to phonon drag is still apparent, but considerably reduced, probably due to disorder. When the Zr concentration is increased to about 14% a thermoelectric power curve as shown in Fig. 3b is obtained in the case of a crystal which does not transform at least down to liquid nitrogen temperature in the electron microscope. The thermopower data gives no evidence for a contribution due to holes nor for the occurance of a phase transition. In fact, the sign, magnitude and temperature dependence of Fig. 3b is very similar to that observed for relatively stolchlometr ic TIS? which does not transform. Before s,,-marizlng these results let us discuss the V doped TiSe 2 materials. The upper curves in Fig. 2 show the temperature dependence of thermopower in VxTi I xSe2 for the fractions x - 0.009, 0.01 and O.02. These values of x bracket the special concentration x = 0.01 which has been shown to produce a striking increase in resistivity an~, negative magnetoresistance at low temperature, 6 probably due to Anderson localization. I / In general the effect of impurities such as vanadlmn is complicated. However, the Hall coefficient in these crystals 18 is positive just like the thermopower data of Fig. 2 above 150K. The decrease and change in sign of S at low temperature in the doped crystals is due to the charge density wave phase transition for which it appears that T c is depressed more-or-less continuously with increasing V concentration. Electron dffraction experiments showed that the superlattlce could be detected at low temperature in VxTil x-Se" for x - 0.009, 0.01 and 0.02 but not for x-> 0.z03. Notice that the thermopower becomes negative at sufficiently low temperature in the cases shown because charge density wave formation occurs in all these samples and they also all probably contain a small excess of electrons due to nonstolchlometry. The exact nature of transport under these conditions is an open question. Here it should be kept in mind that the density of_yanad~lum when x = 0.01 is only about 1.5 x 1020 cm-3, considerably less than the density of electrons and hole~6(5 x i0 20 c m --3 ) present in the pure semlmetal. If Anderson localization actually occurs in the x = 0.01 vanadium doped sample, the thermopower measurements at low temperature yield s l g n l f ~ a n t new information. For example, Mort et al. argue that, for conduction by excitation tO a mobility edge Ec, the thermopower is given by S - (k/e) [Zc-Ef)/kT + I]

(b)

Thermopower S versus T for Zr0,1~Ti0.86Sez, non-transforming crystals.

I169

(2)

which increases as T goes to zero. For conduction by hopping at the Fermi level ~ the ther-

ORIGIN OF THE STRUCTURAL TRANSITION IN TiSe 2

I170

mopower would be given as for a metal by S = (~2/3) (k2T/e) d In=/dE

(3)

which increases from zero with t e m p e r a t u r e . Thermopower data on the one percent vanadium doped crystal down to at least 2.5K are in better agreement with Eq. 3 than with Eq. 2, suggestin 8 that conduction at low temperature is by hopping at EF rather than by excitation to Ec• Finally, we summarize the picture which is beginnln E to e m e r g e concerning the origin of the periodic lattice distortion in TISe 2. Superlattice formation in this compound appears to be due to an interaction between electrons and holes and a particular zone boundary phonon which is driven soft as in a Kohn anomaly. This mode softening and the libration described in Fig. I may be in p a r t a tendency of the crysta~ structure, however the recent theoretical work v suggests that electrons and holes are essential to the instability. The experimental results

Vol. 39, No. II

reported here, as well as earlier work on excess tltanium, 1'2 support the view that electrons and holes plus strong electron lattice interaction are necessary for superlattice formation. Furthermore, this is supported by the fact that the superlattice is critically suppressed in ZrxTi1_xSe 2 when the electron and hole bands are uncrossed. It is highly unlikely that disorder is the controlling factor. The results on VxTil_xSe 2 are also very suggestive. Further work on the interesting possibility of electron localization and the nature of transport in the vanadium alloy system is underway. Acknowledgement--The authors would like to acknowledge the assistance and helpful suggestions of K. C. Woo, A. H. Thompson, B. Davies, R. J. Miller, W. Fabian, S. Hulbert, K. C. Hsleh, K. Bourque, and R. Allgeyer. The assistance of D. Pappert is much appreciated. The work was supported In part by grants from the National Science Foundation OME 77-23999 and 79-10025.

REFERENCES I. F. J. DiSalvo, D. E. Moncton, and J. V. Waszczak, Physical Review BI4, 4321 (1976). 2. K. C. Woo, F. C. Brown and W. L. McMillan, Physical Review B14, 3242 (1976). 3. A. Zunger and A. J. Freeman, Physical Review BI7, 1839 (1978). 4. C. H. Chen, W. Fabian, F. C. Brown, K. C. Woo, B. Davies, B. DeLong and A. H. Thompson, Physical Review B2~I 615 (1980). 5. J. A. Wilson, Solid State Communications, 551 (1977). 6. R. P. Rughes, Journal of Physics CiO, L319 (1977). 7. R. M. Nhfte and G. Lucovsky, Nuovo Clmento 38B~ 280 (1977)o 8. Y. Yoshlda and K. Motlzukl, Journal of the Physical Society of Japan ~ 898 (1980). 9. N. Wakabayashl, H. G. Smith, K. C. Woo, and F. C. Brown, Solid State Communlcatlons,

ii.

12. 13. [4. 15. 16. 17.

18.

2_~s, 923 (1978). 10.

A. H. Thompson, Physical Review Letters 34, 520 (1975).

19.

The vanadium doped crystals were grown and characterized by F. Levy and Y. Froldevaux, Journal of Physics C12, 473 (1979) - T h e zirconium doped samples were prepared at the University of Nebraska. F. J. Blair, Thermoelectrlc-Power of Metals, Plenum, New York (1978). J. yon Boehm, I{. Isomakl and P. Kruslus, Physica Scripta 22, 523 (1980). R. Kirby, R. Fagerquist and W. N. Nieveen, to be published. B. M. Davies and F. C. Brown, t o be published. F. J. DiSalvo and J. V. Waszczak, Physical Review El_~7 3801 (1978). S. Uchlda, K. T a n a b e , K. Q