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Pressure enhancement of charge density wave formation in VSe2; The role of coulomb correlations
Solid State Communications, Vol. 27,pp. 169—173. © Pergamon Press Ltd. 1978. Printed in Great Britain
0038—1098/78/0708—0169 $02.00/0
PRESSURE ENHANCEMENT OF CHARGE DENSITY WAVE FORMATION IN VSe2 THE ROLE OF COULOMB CORRELATIONS* R.H. Friendt and D. Jerome Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France and D. M. Schleich~and P. Molinié Laboratoire de Chimie Minérale A, B.P. 1044, 44037 Nantes, France (Received 23 February 1978 by P. G. de Gennes) We have followed the pressure dependence of the onset and lock-in CDW transitions in VSe2 by measurements of resistivity and Hall effect up to 30 kbar. (The onset transition appears as a break in the slope of the resistivity, and the lock-in as 1% temperature hysteresis). Both transition temperatures rise at 0.8 K kbar~.We attribute this behaviour to pressure broadening of the d conduction band in the presence of strong electron Coulomb repulsion. THE STUDY of charge density wave (CDW) formation in the group V transition metal dichalcogenides [1, 2] has been largely concentrated on the 4d and Sd metals, and the only vanadium dichalcogenide that can easily be prepared, IT VSe2, has received less attention. It is however an interesting material in that CDW formation is relatively weak, and that the CDW superlattice is different from that observed in the IT tantalum dichalcogenides. Conductivity and susceptibility measurements [3—6] show an anomaly at around 110K, and electron diffraction [7] shows the appearance of a 4 x 4 incommensurate superlattice at this temperature. The superlattice is initially 2% incommensurate, but at 40K has become commensurate. The weak anomaly in resistivity at the normal—incommensurate transition, and the nature of the incommensurate—commensurate lock-in transition, where the superlattice does not rotate to form the commensurate phase as in IT TaSe2 and IT TaSe2, are more common with the 2H polytype of TaSe2 [8] than with the IT polytypes. There is little change in transport properties at the lock-in transition in 2H TaSe2, no more than 1% temperature hysteresis in the resistivity, which has been measured to follow the lock-in transition under pressure [9]. We have measured the resistivity and Hall coefficient of VSe2 under pressure as a function of temperature to follow ___________ *
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Work supported in part by DGRST Contract No. 77-7-0549. .
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Permanent address: Cavendish Laboratory, Carnbndge, U.K. Supported in part by N.S.F. Grant No. 39737. 169
the CDW formation. We have found temperature hysteresis in the resistivity, similar to that in 2H TaSe2, at around 70K at 1 bar, which is at the temperature of the lock-in seen in electron diffraction on the crystals we used [10]. Thus we have been able to follow both the normal—incommensurate, onset transition and the lock-in transition under pressure. In contrast to all the IT and 2H polytypes previously investigated [9, 11—15], CDW formation in VSe2 is enhanced under pressure. We relate this behaviour to the narrow d band in VSe2 [16] and the larger Coulomb interaction between the conduction electrons derived from the 3d V orbitals, cornpared to 4d Nb and Sd Ta. VSe2 is always found to grow metal rich, with the excess V taking up sites between the layers, and possessing localised moments which show up as a Curie tail in the low temperature magnetic susceptibility. Measurements of susceptibility can, therefore, be used to characterise batches of VSe2. Crystals used for these experiments were grown by selenium vapour transport in a temperature gradient of 830 780°C,with excess Se present, conditions similar to those used by van Bruggen and Haas [4]. The magnetic susceptibility of ground crystals was measured using a Faraday balance and is shown in Fig. 1. The CDW onset transition shows up as a fall in susceptibility below 100 K. Fitting the Curie tail to x = x~+ C/T, where y~.is the almost temperature independent intrinsic susceptibility gives = 2.47 x l0~emumole~and C= 4.32 x iO~ ernu Kmole~; the fitted curve is shown as the solid line in Fig. 1. Also shown is C/T, which represents the intrinsic behaviour of the VSe2. To determine the V excess from the value of C -+
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Fig. 1. Molar susceptibility vs temperature for the VSe2 used in the high pressure experiments. The solid line is the Curie fit to the low temperature regime of the measured data (.). Also shown (.) is )(e~) XCurie—
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I (K) requires knowledge of the effective moment on the interlayer hence the valence consider 31s V, theand most probable valencestate. state,We and that that V 1B• the is closestate to its valueVofin2.83 Thismoment is the valence ofspin-only the interlayer V I5Sa [17J and V5Se8 [181, and in V5S8 spin—orbit coupling reduces the effective moment to 2.3 PB [17]. A small degree ofspin—orbit coupling is consistent with the anisotropy in the Curie susceptibility reported by van Bruggen and Hass [4] for their theof 2-83PB we VSe2. deduceTaking V excess effective to be Di Salvo and Waszczak [6] also 0.5% inmoment our samples. choose V3~for the interlayer V. but van Bruggen and Haas [4] take V2~,and Bayard and Sienko [5] choose V~nevertheless the value of C can be used to compare the stoichiometries of different batches of crystals. In view of the sensitivity of the CDW transitions, particularly the lock-in, to the presence of impurities [6, 191, we do not consider that the V excess in our samples is much larger than 0.5%. Helium gas was used as the pressure transmitting medium up to 8 kbar [201. Over the whole temperature range of measurement, the helium remained gaseous, and pressure was stabilised to within 20 bar in the pressure intensifier which remained at room temperature and which was in communication with the sample pressure cell. At 15 kbar and above a mixture of isopentane and isoamylalcohol was used in a pressure intensifying teflon cell system [21]. Temperature was
Fig. 2. Warmingcurves (solid) for andVSe cooling (dashed) resistivity vs temperature 2 at different pressures. measured with a Cu—constant thermocouple inside the pressure cell next to the samples. The standard technique of a low frequency (70 Hz) alternating current with phaselock voltage measurement was used to measure resistivity and Hall effect, with 4 and 5 sample contacts Using a stabiised source [22] andrespectively. a PAR 186 phaselock amplifiercurrent a stability of better than 1 in 1 o~over 24 hr was obtained, allowing easy detection of the 1% hysteresis at the lock-in transition. Hall effect measurements were made in a CuBe cell in a field of 20 kG from a superconducting solenoid around the pressure system. The two transitions in resistivity at atmospheric pressure can be seen in Fig. 2. Electron diffraction experiments [10] on crystals from this batch showed the 4 x 4 superlattice to be 6% incommensurate at 90K, falling to < 1% at 72 K, when it is commensurate to within experimental accuracy. We have taken the onset transition to be at the temperature where the resistivity first deviates from its high temperature behaviour; this is the temperature at which the susceptibility first falls, and is 108K in these crystals. Definition of the lockin transition temperature from resistivity measurements is more arbitrary, although the maxim resistivity hysteresis is at 66 K.
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T (K) Fig. 3. Hall effect vs temperature for VSes at 1 bar and 8 kbar.
Under pressure both transitions move to higher temperatures, as is shown in Fig. 2. The range of hysteresis for the helium gas experiment at 8 kbar is still narrow, and the extended temperature range at higher pressures may be a consequence of slight pressure inhomogeneities in the isopentane/isoarnylalcohol mixture which is solid at these temperatures and pressures. Hall effect measurements are shown in Fig. 3; at 1 bar the data is similar to that previously reported [4, 51, and at 8 kbar the low temperature rise which signals the onset transition has moved to a higher temperature. The pressure-temperature phase diagram is shown in Fig. 4. The onset transition rises at 0.8 K kbar-’ ; the lock-in transition also rises at a similar rate although the change in width of the hysteresis loop with pressure prevents precise determination of the rate. It is not possible to say much about the behaviour of the lock-in transition without knowledge of how the incommensurability of the CDW superlattice changes with pressure. We note however that in contrast to VSe.2,the lock-in transition of 2H TaSel at 90 K falls rapidly and is suppressed entirely above 15 kbar [9]. The pressure dependence of the onset transition is more significant, and is a further example of the anomalous behaviour of VSes. The CDW transition temperature in VSez at 1 bar is appreciably lowered from the value that may be expected from comparison with the IT Nb and Ta dichalcogenides (see Table I), and either the application of pressure, or Nb doping [24] raises this temperature.
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Fig. 4. Onset (0) and lock-in (n) CDW transition temperatures in VSes as a function of pressure, as derived from the resistivity measurements of Fig. 2. The onset was taken as the temperature at which the resistivity first deviates from its high temperature behaviour. For the lock-in transition, n is at the temperature of the maximum resistivity hysterisis, and the bars indicate the limits at which the hysterisis has fallen to 20% of its maximum value. Recent photoemission experiments [ 161 have shown an occupied d bandwidth of only - 0.3 eV, and it is this very much narrower d band that is found in IT TaSes and IT TaSes (see Table 1) that distinguishes VSes from the 4d and 5d materials. This narrow d band does not appear in the band structure calculated by Wooley and Wexler [25], who find little difference between VSes and TaSes. However VSes has an anomalously high c/u ratio, of 1.821 [26], and so a strong trigonal distortion of the octahedral field around the V, which splits the tzzptriplet into a dXY, d,l_ ,,z doublet and a d, * level. For such a trigonal distortion the d,z level will be lowest [27], and if the splitting of the d,l and dxy, d,p_g levels is a substantial fraction of the band broadening of these levels, the lowering of the half occupied dzz band can be interpreted as the driving force of a band Jahn-Teller distortion [28] which increases the c/c ratio. Note that the increased occupation of the d band from Li intercalation decreases the c/u ratio, in spite of the Li introduced between the layers. This is consistent with occupation of the d%,,, dxg_,.z levels by the Li valence electron which will take place if the Coulomb repulsion U for the d states is larger than the d,a bandwidth. Coulomb repulsion between the conduction electrons
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Table 1. CDW onset (T0) and lock-in (Td) distortion tern- electron—phonon matrix element. In the tight-binding peratures and occupied d bandwidths as seen in photomodel of Barili~[30] I V (transfer integral) emission, for the iT polytype group Vdichalcogenides. bandwidth, so the electron—phonon coupling term on IT NbSe2 is not stable at room temperature, and Td was estimated in [19] from the behaviour of Ti doped the LHS will be small for the narrow V d band. Esti/TNbSe2, for which the ITpolyiype is stable as far as mates of(2Uq P~)-several eV [31] are2/Mc~.,2 of Ti0~~Nb0~Se2. similar of 2Iwe consider for the magnitude 2H Nb and to Taestimated materials values [321, and T 0 (K) Td (k) Occupied that in VSe2 these terms are almost equal. Pressure (or d bandwidth (eV) Nb doping) will increase the d bandwidth and hence 2/Mw2, and when 212/Mc,,2 is close to (2UQ V~) VSe2 110 70 0.3 (c) 21 TaS 2 350 (a) 1.5 (b) the overall rate of increase of the LHS will be enhanced. TaSe2 470 (a) 1.15 (d) Thus it can dominate any decrease in x~coming from a NbSe2 425 (b) fall in the density of states and impairment of the Fermi-surface nesting, which accounts for the negative (a) Ref. [2]. (b) Ref. [19]. (c) Ref. [16]. (d) Ref. [23]. dT0/dP observed in the Nb and Ta dichalcogenides [13, 14] CDW formation in VSe2 is therefore stabiised will always oppose CDW formation which involves by the increase in d bandwidth under pressure. bringing the electr~nscloser together on average. We A similar situation exists for the quasi one-dimenconsider that the larger repulsion between the 3d elecsional charge transfer salt TTF—TCNQ, in which the trons from V compared to 44 and Sd Nb and Ta, Pierls distortion on the ‘fl’F stacks also rises in tempera. together with the narrow d band, can account for the ture under pressure [31]. Coulomb repulsion in the relatively weak CDW formation in VSe2, and its narrow TTF conduction band inhibits CDW formation enhancement under pressure. at atmospheric pressure, and it is the reduction of the The than and Heine [29] criterion for CDW formeffects of the Coulomb repulsion with an increase in ation at wavevector q is bandwidth that stabiises the CDW under pressure. 1/Xq 212 Mw(q)2 Acknowledgements We thank F.J. Di Salvo, H.P. (2U~ Vq) Hughes, J. Rouxel, B.G. Silbernagel, G.J. Tatlock and where Uq and ~ are the average Coulomb and A.D. Yoffe for many useful discussions. We thank G. exchange energies at wavevector q, Xq the Lindhart Malfait and A. Andrieux for their skilful technical function, M~.,(q)2the lattice force constant and I the assistance. ‘~‘
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REFERENCES 1.
SCRUBY C.D., WILLIAMS P.M. & PARRY G.S.,Phil. Mag. 31, 255 (1975).
2.
WILSON J.A., DI SALVO F.J. & MAHAJAN S., Adv. Phys. 24, 117 (1975).
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THOMPSON A.H. & SILBERNAGEL B.G., Bull. Am. Phys. Soc. 21,260(1976). VAN BRUGGEN C.F. & HAAS C., Solid State Commun~20, 251 (1976).
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BAYARD M. & SIENKO M.J., Solid State Commun. 20, 251 (1976).
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DI SALVO F.J. & WASZCZAK J.V., J. de Phys. Suppl. C4, 37, 157 (1976). WILLIAMS P.M., Crystallography and C,ystal Chemistry ofMaterials with Layered Structures, (Edited by LEVY F.), Vol. 2. Reidel, Dordrecht (1976). MONCTON D.E., AXE J.D. & DI SALVO F.J.,Phys. Rev. Lett. 34, 734 (1975);Phys. Rev. B16, 801 (1977). CHU C.W., TESTARDI L.R., DI SALVO FJ. & MONCTON D.E.,Phys. Rev. B14, 464 (1976); Similar experiments on poorer quality 2H TaSe 2 performed at Orsay [JEROME D., BERTHIER C., MOLINIE P. & ROUXEL J., J. de Phys. Suppl. C4, 37, 125 (1976)] showed some indication of a rise in Td with pressure. We consider it important to repeat these experiments on good quality samples in a helium gas pressure system to eliminate any effects of strain that is present in oil systems.
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TATLOCK G.J. (private communication).
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GRANT A.J., GRIFFITHS T.M., PITT G.D. & YOFFE A.D.,J. Phys. C7, L249 (1974).
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SILBERNAGEL B.G., THOMPSON A.H. & GAMBLE F.R., 20th Conf on Magnetism andMagnetic Materials (Edited by WOLFE H.C.), p. 380. A.I.P. Proceedings (1975). DI SALVO F.J., WILSON J.A., BAGLEY B.G. & WASZCZAK J.V., Phys. Rev. B12, 2220 (1975).
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MALFAIT G. & JEROME D., Rev. Phys. App!. 4,467 (1969).
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DELAPLACE R., MALFAIT G. & JEROME D., Rev. Phys. AppL 11, 327 (1976).
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FRIEND R.H. & BETT N. (to be published). TRAUM M.M., SMITH N.y. & DI SALVO F.J.,Phys. Rev. Lett. 32, 1241 (1974).
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SCHNEEMEYER L. & SIENKO M.J., 15th Annual Solid State Physics Conference, Warwick (unpublished) (1978). WOOLLEY A.M. & WEXLER G.,J. Phys. ClO, 2601 (1977).
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WHITTINGHAM M.S. & GAMBLE F.R.,Mat. Res. Bull. 10,363 (1975).
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MATTHEISS L.F.,Phys. Rev. B8, 3719 (1973).
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HUGHES H.P.,J. Phys. ClO, L319 (1977). CHAN S.K. & HEINE V.,J. Phys. F3, 795 (1973).
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BARISI~S.,Phys. Rev. B5, 932 and 941 (1972).
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FRIEDEL J., The Physics ofMetals, (Edited by ZIMAN J.M.), Chap. 8. Cambridge University Press (1969).
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FRIEND R.H., MIUAK M. & JEROME D. Phys. Rev. Lett. 40, 1048 (1978).
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PRESSURE ENHANCEMENT OF CHARGE DENSITY WAVE FORMATION IN VSe2 THE ROLE OF COULOMB CORRELATIONS* R.H. Friendt and D. Jerome Laboratoire de Physique des Solides, Université Paris-Sud, 91405 Orsay, France and D. M. Schleich~and P. Molinié Laboratoire de Chimie Minérale A, B.P. 1044, 44037 Nantes, France (Received 23 February 1978 by P. G. de Gennes) We have followed the pressure dependence of the onset and lock-in CDW transitions in VSe2 by measurements of resistivity and Hall effect up to 30 kbar. (The onset transition appears as a break in the slope of the resistivity, and the lock-in as 1% temperature hysteresis). Both transition temperatures rise at 0.8 K kbar~.We attribute this behaviour to pressure broadening of the d conduction band in the presence of strong electron Coulomb repulsion. THE STUDY of charge density wave (CDW) formation in the group V transition metal dichalcogenides [1, 2] has been largely concentrated on the 4d and Sd metals, and the only vanadium dichalcogenide that can easily be prepared, IT VSe2, has received less attention. It is however an interesting material in that CDW formation is relatively weak, and that the CDW superlattice is different from that observed in the IT tantalum dichalcogenides. Conductivity and susceptibility measurements [3—6] show an anomaly at around 110K, and electron diffraction [7] shows the appearance of a 4 x 4 incommensurate superlattice at this temperature. The superlattice is initially 2% incommensurate, but at 40K has become commensurate. The weak anomaly in resistivity at the normal—incommensurate transition, and the nature of the incommensurate—commensurate lock-in transition, where the superlattice does not rotate to form the commensurate phase as in IT TaSe2 and IT TaSe2, are more common with the 2H polytype of TaSe2 [8] than with the IT polytypes. There is little change in transport properties at the lock-in transition in 2H TaSe2, no more than 1% temperature hysteresis in the resistivity, which has been measured to follow the lock-in transition under pressure [9]. We have measured the resistivity and Hall coefficient of VSe2 under pressure as a function of temperature to follow ___________ *
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Work supported in part by DGRST Contract No. 77-7-0549. .
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Permanent address: Cavendish Laboratory, Carnbndge, U.K. Supported in part by N.S.F. Grant No. 39737. 169
the CDW formation. We have found temperature hysteresis in the resistivity, similar to that in 2H TaSe2, at around 70K at 1 bar, which is at the temperature of the lock-in seen in electron diffraction on the crystals we used [10]. Thus we have been able to follow both the normal—incommensurate, onset transition and the lock-in transition under pressure. In contrast to all the IT and 2H polytypes previously investigated [9, 11—15], CDW formation in VSe2 is enhanced under pressure. We relate this behaviour to the narrow d band in VSe2 [16] and the larger Coulomb interaction between the conduction electrons derived from the 3d V orbitals, cornpared to 4d Nb and Sd Ta. VSe2 is always found to grow metal rich, with the excess V taking up sites between the layers, and possessing localised moments which show up as a Curie tail in the low temperature magnetic susceptibility. Measurements of susceptibility can, therefore, be used to characterise batches of VSe2. Crystals used for these experiments were grown by selenium vapour transport in a temperature gradient of 830 780°C,with excess Se present, conditions similar to those used by van Bruggen and Haas [4]. The magnetic susceptibility of ground crystals was measured using a Faraday balance and is shown in Fig. 1. The CDW onset transition shows up as a fall in susceptibility below 100 K. Fitting the Curie tail to x = x~+ C/T, where y~.is the almost temperature independent intrinsic susceptibility gives = 2.47 x l0~emumole~and C= 4.32 x iO~ ernu Kmole~; the fitted curve is shown as the solid line in Fig. 1. Also shown is C/T, which represents the intrinsic behaviour of the VSe2. To determine the V excess from the value of C -+
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Fig. 1. Molar susceptibility vs temperature for the VSe2 used in the high pressure experiments. The solid line is the Curie fit to the low temperature regime of the measured data (.). Also shown (.) is )(e~) XCurie—
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I (K) requires knowledge of the effective moment on the interlayer hence the valence consider 31s V, theand most probable valencestate. state,We and that that V 1B• the is closestate to its valueVofin2.83 Thismoment is the valence ofspin-only the interlayer V I5Sa [17J and V5Se8 [181, and in V5S8 spin—orbit coupling reduces the effective moment to 2.3 PB [17]. A small degree ofspin—orbit coupling is consistent with the anisotropy in the Curie susceptibility reported by van Bruggen and Hass [4] for their theof 2-83PB we VSe2. deduceTaking V excess effective to be Di Salvo and Waszczak [6] also 0.5% inmoment our samples. choose V3~for the interlayer V. but van Bruggen and Haas [4] take V2~,and Bayard and Sienko [5] choose V~nevertheless the value of C can be used to compare the stoichiometries of different batches of crystals. In view of the sensitivity of the CDW transitions, particularly the lock-in, to the presence of impurities [6, 191, we do not consider that the V excess in our samples is much larger than 0.5%. Helium gas was used as the pressure transmitting medium up to 8 kbar [201. Over the whole temperature range of measurement, the helium remained gaseous, and pressure was stabilised to within 20 bar in the pressure intensifier which remained at room temperature and which was in communication with the sample pressure cell. At 15 kbar and above a mixture of isopentane and isoamylalcohol was used in a pressure intensifying teflon cell system [21]. Temperature was
Fig. 2. Warmingcurves (solid) for andVSe cooling (dashed) resistivity vs temperature 2 at different pressures. measured with a Cu—constant thermocouple inside the pressure cell next to the samples. The standard technique of a low frequency (70 Hz) alternating current with phaselock voltage measurement was used to measure resistivity and Hall effect, with 4 and 5 sample contacts Using a stabiised source [22] andrespectively. a PAR 186 phaselock amplifiercurrent a stability of better than 1 in 1 o~over 24 hr was obtained, allowing easy detection of the 1% hysteresis at the lock-in transition. Hall effect measurements were made in a CuBe cell in a field of 20 kG from a superconducting solenoid around the pressure system. The two transitions in resistivity at atmospheric pressure can be seen in Fig. 2. Electron diffraction experiments [10] on crystals from this batch showed the 4 x 4 superlattice to be 6% incommensurate at 90K, falling to < 1% at 72 K, when it is commensurate to within experimental accuracy. We have taken the onset transition to be at the temperature where the resistivity first deviates from its high temperature behaviour; this is the temperature at which the susceptibility first falls, and is 108K in these crystals. Definition of the lockin transition temperature from resistivity measurements is more arbitrary, although the maxim resistivity hysteresis is at 66 K.
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T (K) Fig. 3. Hall effect vs temperature for VSes at 1 bar and 8 kbar.
Under pressure both transitions move to higher temperatures, as is shown in Fig. 2. The range of hysteresis for the helium gas experiment at 8 kbar is still narrow, and the extended temperature range at higher pressures may be a consequence of slight pressure inhomogeneities in the isopentane/isoarnylalcohol mixture which is solid at these temperatures and pressures. Hall effect measurements are shown in Fig. 3; at 1 bar the data is similar to that previously reported [4, 51, and at 8 kbar the low temperature rise which signals the onset transition has moved to a higher temperature. The pressure-temperature phase diagram is shown in Fig. 4. The onset transition rises at 0.8 K kbar-’ ; the lock-in transition also rises at a similar rate although the change in width of the hysteresis loop with pressure prevents precise determination of the rate. It is not possible to say much about the behaviour of the lock-in transition without knowledge of how the incommensurability of the CDW superlattice changes with pressure. We note however that in contrast to VSe.2,the lock-in transition of 2H TaSel at 90 K falls rapidly and is suppressed entirely above 15 kbar [9]. The pressure dependence of the onset transition is more significant, and is a further example of the anomalous behaviour of VSes. The CDW transition temperature in VSez at 1 bar is appreciably lowered from the value that may be expected from comparison with the IT Nb and Ta dichalcogenides (see Table I), and either the application of pressure, or Nb doping [24] raises this temperature.
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Fig. 4. Onset (0) and lock-in (n) CDW transition temperatures in VSes as a function of pressure, as derived from the resistivity measurements of Fig. 2. The onset was taken as the temperature at which the resistivity first deviates from its high temperature behaviour. For the lock-in transition, n is at the temperature of the maximum resistivity hysterisis, and the bars indicate the limits at which the hysterisis has fallen to 20% of its maximum value. Recent photoemission experiments [ 161 have shown an occupied d bandwidth of only - 0.3 eV, and it is this very much narrower d band that is found in IT TaSes and IT TaSes (see Table 1) that distinguishes VSes from the 4d and 5d materials. This narrow d band does not appear in the band structure calculated by Wooley and Wexler [25], who find little difference between VSes and TaSes. However VSes has an anomalously high c/u ratio, of 1.821 [26], and so a strong trigonal distortion of the octahedral field around the V, which splits the tzzptriplet into a dXY, d,l_ ,,z doublet and a d, * level. For such a trigonal distortion the d,z level will be lowest [27], and if the splitting of the d,l and dxy, d,p_g levels is a substantial fraction of the band broadening of these levels, the lowering of the half occupied dzz band can be interpreted as the driving force of a band Jahn-Teller distortion [28] which increases the c/c ratio. Note that the increased occupation of the d band from Li intercalation decreases the c/u ratio, in spite of the Li introduced between the layers. This is consistent with occupation of the d%,,, dxg_,.z levels by the Li valence electron which will take place if the Coulomb repulsion U for the d states is larger than the d,a bandwidth. Coulomb repulsion between the conduction electrons
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Table 1. CDW onset (T0) and lock-in (Td) distortion tern- electron—phonon matrix element. In the tight-binding peratures and occupied d bandwidths as seen in photomodel of Barili~[30] I V (transfer integral) emission, for the iT polytype group Vdichalcogenides. bandwidth, so the electron—phonon coupling term on IT NbSe2 is not stable at room temperature, and Td was estimated in [19] from the behaviour of Ti doped the LHS will be small for the narrow V d band. Esti/TNbSe2, for which the ITpolyiype is stable as far as mates of(2Uq P~)-several eV [31] are2/Mc~.,2 of Ti0~~Nb0~Se2. similar of 2Iwe consider for the magnitude 2H Nb and to Taestimated materials values [321, and T 0 (K) Td (k) Occupied that in VSe2 these terms are almost equal. Pressure (or d bandwidth (eV) Nb doping) will increase the d bandwidth and hence 2/Mw2, and when 212/Mc,,2 is close to (2UQ V~) VSe2 110 70 0.3 (c) 21 TaS 2 350 (a) 1.5 (b) the overall rate of increase of the LHS will be enhanced. TaSe2 470 (a) 1.15 (d) Thus it can dominate any decrease in x~coming from a NbSe2 425 (b) fall in the density of states and impairment of the Fermi-surface nesting, which accounts for the negative (a) Ref. [2]. (b) Ref. [19]. (c) Ref. [16]. (d) Ref. [23]. dT0/dP observed in the Nb and Ta dichalcogenides [13, 14] CDW formation in VSe2 is therefore stabiised will always oppose CDW formation which involves by the increase in d bandwidth under pressure. bringing the electr~nscloser together on average. We A similar situation exists for the quasi one-dimenconsider that the larger repulsion between the 3d elecsional charge transfer salt TTF—TCNQ, in which the trons from V compared to 44 and Sd Nb and Ta, Pierls distortion on the ‘fl’F stacks also rises in tempera. together with the narrow d band, can account for the ture under pressure [31]. Coulomb repulsion in the relatively weak CDW formation in VSe2, and its narrow TTF conduction band inhibits CDW formation enhancement under pressure. at atmospheric pressure, and it is the reduction of the The than and Heine [29] criterion for CDW formeffects of the Coulomb repulsion with an increase in ation at wavevector q is bandwidth that stabiises the CDW under pressure. 1/Xq 212 Mw(q)2 Acknowledgements We thank F.J. Di Salvo, H.P. (2U~ Vq) Hughes, J. Rouxel, B.G. Silbernagel, G.J. Tatlock and where Uq and ~ are the average Coulomb and A.D. Yoffe for many useful discussions. We thank G. exchange energies at wavevector q, Xq the Lindhart Malfait and A. Andrieux for their skilful technical function, M~.,(q)2the lattice force constant and I the assistance. ‘~‘
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