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Transport and elastic anomalies in ZrTe3
Solid State Communications,Vo1.49,No.l1, pp.l031-1033, 1984 Printed in Great Britain.
0038-1098/84 $3.00 + .OO Pergamon Press Ltd.
TRANSPORT AND ELASTIC ANOMALIES IN ZrTeB S.Takahashi' and T.Sambongi Department of Physics, Hokkaido University, Sapporo 060 Japan and J.W.Brill and W.Roark Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506 USA (Received 22 November 1983 by H. Kamimura)
Anomalies were observed in electrical resistivity components, Hall coefficient and Young's modulus of semimetallic ZrTe near 63~. The results suggest that a structural phase transition, a.,. the onset of a charge density wave, occurs. Analysis indicates that the hole band is more strongly affected by the transition, resulting in the strong renormalization of the elastic modulus.
Group Vb-transition metal trichalcogenides (V-MXS) are now widely accepted as typical quasi one dimensional conductors. On the other hand, group IVb-metal trichalcogenides (IV-MXS) have attracted much less attention, partly because all of them, except ZrTeS, are non-metallic. The crystal structurelof IV-MX3 is simpler than that of V-MXS; it consists of only one kind of triangular prismatic chain. Within the unit cell there are two chains (running in the b-direction), connected by inversion symmetry to each other. There are two variants in the arrangement of chains. ZrS3, ZrSeg and HfS3 possess the ordinary one, which is referred to as type A. Structures of TiS3, ZrTe3 and HfSeS belong to the other, type B, which is connected to type A by the relation xB=l-x where x is the fractional c-coordinate of tht'atom position within the unit cell. The cross section of prisms in the type A configuration is approximately isosceles-triangular,while that in the type B is more distorted. In 1958, McTaggart' measured the electrical resistivity of all existing IV-MX3 at room temperature. He found that, in general, the resistivity of Hf-chalcogenides is higher than that of Zr-compounds and that sulfides, selenides and tellurides are more insulating in that order. The trends of magnetic susceptibility3 and optical band gap1 are in good agreement with the McTaggart's findings; magnetic susceptibility of these compounds is negative and temperature-independent,and the optical gap is larger for the heavier metal compounds. Among IV-MX3, ZrTeg is the only one which is metallic; it is supposedly a semi-metal but with an electronic structure different from those of V-MX3. To find a unified feature of chain-structuredMXS as low dimensional conductors, we have been studying the properties of ZrTeS. We have found anomalies in the transverse conductivities and Hall coefficient at 63K and that it becomes a three dimensional superconductorbelow 2K with an anisotropic
In this paper we upper critical field.4 examine the possibility that it undergoes a structural phase transition, e.g. charge density wave formation, at 63K. Single crystals of ZrTeS were prepared by the iodine transport method. Weighted amounts of 3N Zr (MRC, Marz grade) and 6N Te were reacted for a few weeks in the temperature gradient 750-7oo"c. X-ray examination confirmed the parameters determined by Brattas and Kjekshusl : monoclinic, a=5.897A, b=3.926A, c=ll.llA and 8=97.82". The electrical resistivity was measured by the usual four probe method. At room temperature, values of the resiswere found as tivity components pb, pa and p 2.5, 1.8 and 20x1g4 Ccm , resp&c*tively.The largest is ock; the van der Waals gap is crossed in this direction. Contrary to V-MXS, pb has a slightly larger value than p . The ratio pa/pb was also obtained by the Montgomery method as (O.SS+O.lO) at 300K, consistent with the above resulS. The small value of pa is a result of strong coupling between chains. The temperature dependence of pb is shown in Fig. 1. It is metallic throughout the temperature range measured, but the temperature derivative dpb/dT shows a sharp knee at 55K. This anomaly is quite reproducible; it was observed in every sample examined. Above 56K, pb is linear in temperature, T, while it is quadratically dependent on T below 54K. The derivative is continuous at 55K, so pb below 55K is larger than that extrapolated from above. The transverse components, p and p , are shown in Fig. 2 and 3. Humps werl obse&d in both components. The maximum is located at 55K (knee in pb) and the temperature of extremum derivative, T , was observed at 63K+2K. The residual resistgnce ratios (p(300K)/pT4K))were % 35, 8 and 4 along the b-, a- and c*-axes respectivetly. No clear correlation between T and the residual resistance ratio was found.P As
OPresent address: Alps Electric,Inc., Yukigaya, Tokyo 145 Japan 1031
1032
Vol. 49, No:11
TRANSPORT AND ELASTIC ANOMALIES IN ZrTe3
RH infers that the mobility of electrons is larger than that of holes. The magnitude of RR increases near T = 63K, consistent with the conductivity inc8ease.
Fig.1 Resistivity along the b-axis and its temperature derivative vs. temperature.
Fig.2 Resistivity along the a-axis and its temperature derivative.
To check whether the anomalies in the transport properties were due to the presence of a phase transition, in particular a structural transition,we measured the Young's modulus along the b-axis, E, and internal friction, tans using a vibrating reed technique described in detail elsewhere5 . Two crystals, of typical dimensions 0.2 mm x 2 mm x 1 pm, were mounted as cantilevers by gluing one end with silver paint to a copper support, and the frequency, foam, and quality factor, Q, of the fundamental flexural resonance of each were measured as functions of temperature. Relative changes in the modulus with temperature could be measured very precisely, although the absolute magnitude of the modulus could only be estimated to an order of magnitude due to the difficulty in measuring the sam le thickness. We found that E~~xIO"~ dyne/cms , comparable to the metallic V-MK3 compounds.6 Changes in the quality factor, measured by monitoring the amplitude of the resonance, give d_frectlychanges in the internal friction, AQ =Atan6. The relative change in modulus vs. temperature for one sample is shown in the inset of Fig.4; both samples showed very similar results. A sharp minimum, indicating a phase transition, is observed. The transition temperatures of the two samples, taken as the temperatures of the modulus minima, were T =63.1K and 63.5K. The modulus and internal ftiction near T are shown in detail in Fig.4. The internal fr%ction peaks a few degrees below T (at 61K for both samples) , as expected for a pRase transition. No ther-
0
50 loo150200250
Fig.3 Resistivity along the c*-axis . Inset: Hall coefficient. T(K) shown in Fig.3 pc* shows, at high temperature, negative curvature, which has been observed in TaSe3 and many Al5 compounds, but for which no unified explanation has been given. Hall coeffcient, RR, measured with the current along the b-axis and the magnetic field parallel to c*, is shown in the inset of Fig.3. If ZrTe3 is semi-metallic, the negative sign of
Fig.4 Relative change in Young's modulus, R/RO, and internal friction l/Q vs. temperature from 50K to 75K for a reed of ZrTe with ambient resonant frequency f =641H?. Inset: E/E0 vs. temperature f!om OK-250K.
ma1 hysteresis (T
L > p,“- (ubyoaH) vaH= FbH_“,H u,“-(ObL/UaL)V a so that V aH-(ubL/uaL)v
An analysis of the transport anomalies is given below to estimate what kind of structural transition occurs at 63K. The simple two-band model is used in two different approaches. The first is to assume that the carrier density is unchanged and that the anomalies are due to a change in the transverse mobility (i.e. that it is not a CDW transition). The Hall coefficient RH in the present configuration is given by
= (l/B)
c~~~/bs~u~
+
oab
2,
(1)
where the conductivity tensor in the two band
where n(p) and u>O (v>O) are the density and mobility of electrons (holes) respectively. in the low B limit is given
(3) L From the present experimental results, (-R,,) >(-%I” and ‘I Ub =ab =ua =2aa (4). L
H
H
L
where the prefix H(L) denotes the high (low) temperature phase, (3) gives
a
L
>
IlbylbL
=
0
(5)
Here we have assumed that the ralation p is equivalent to ubH=ubL and vbH=vbL. wt:;I’&, the following relation is given: H L V 2 2v a a The scattering mechanism which comes in below T reduces the transverse hole mobility effective-P 1Y. Since the crystal structure is well defined at room temperature, the new scattering mechanism is due to, for example, long-range modification of the trigonal chain arrangement, with the chai.nitself kept rigid. The alternative approach is to assume that the anomalies at T are due to a partial vanishing of the Fe& surface by e.g. charge density wave formation. For simplicity, no change in the mobility is assumed. Since it is difflcult to conceive that a vanishing of the Fermi surface sheet perpendicular to the b-axis does not affect p it is assumed that a piece of the Fermi surfacbe'which is longer along the b*-axis partially vanishes at T . Hence the b*-component of the effective mass iR that sheet is large. If the hole sheet is columnar and the electron sheet is more isotropic, reduction of hole density occurs below T . Conductivity components at high tempera&e are U
\
1033
TRANSPORT AND ELASTIC ANOMALIES IN ZrTe3
Vol. 49, No. II
H = nolel(ua+va)
=no(ej
(l+a)p,
aH ob = where CX=V while be&
(7)
/u
and
Ia p
u
i3=vb/pb
,
L =nolelua(l+ca) aL
'b
=n,lelub(l+03)
(8)
where Sn is the hole density below T . Relations (49, (7) and (8) give 6'2. .pH The experimental result of (-RH )>(-RH >>O is rewritten as l-SW3 l-a8 (l+Sa)(l+SB) ' (l+a)(l+8) (9) Because of the relation O
1034
TRANSPORT
AND ELASTIC ANOMALIES
ting reed result: A, (iXIe3)~lOOh(NbSe ), where h is the electron-phonon coupling coastant (for the condensing band), i.e. the Te-p band is expected to couple more strongly to acoustic phonons than the metal d-band. The large X
IN ZrTe3
Vol. 49, No.
should be related to the relatively high value of the superconducting transition temperature of 2K.4 Acknowlegement-The authors at HKU acknowlege M.Ido and H.Fukuyama for helpful discussions. REFERENCES
1) L.Brattas
2) 3) 4) 5) 6)
and A.Kjekshus, Acta Chem.Scand. 26,3441 (1972) F.K. McTaggart, Austr.J.Chem. 11,445 (1958) H.Haraldsen, A.Kjekshus, E.Rost and A. Steffensen, Acta Chem. Stand. 17, 1283 (1963) S.Takahashi and T.Sambongi, J. Physique 44 supplement c-3, 1733 (1983) J.W. Brill, Solid State Commun. 41,925 (1982) J.W. Brill, Mol.Cryst.Liq.Cryst.81,107 (1982)
7) A.W. Higgs and J.C. Gill, Solid State Commun. 47,737 (1983) 8) R.M. Fleming, D.E. Moncton and D.B.McWhan, Phys.Rev. Bl8, 5560 (1978) 9) M.Bannatz, L.R.Testardi and F.J.DiSalvo, Phys.Rev.Bl2, 4367 (1975) 10) H.W. Myron, B.N.Harman and F.S.khumalo, .I. Phys.Chem.Solids,42,263 (1981)
II
0038-1098/84 $3.00 + .OO Pergamon Press Ltd.
TRANSPORT AND ELASTIC ANOMALIES IN ZrTeB S.Takahashi' and T.Sambongi Department of Physics, Hokkaido University, Sapporo 060 Japan and J.W.Brill and W.Roark Department of Physics and Astronomy, University of Kentucky, Lexington, KY 40506 USA (Received 22 November 1983 by H. Kamimura)
Anomalies were observed in electrical resistivity components, Hall coefficient and Young's modulus of semimetallic ZrTe near 63~. The results suggest that a structural phase transition, a.,. the onset of a charge density wave, occurs. Analysis indicates that the hole band is more strongly affected by the transition, resulting in the strong renormalization of the elastic modulus.
Group Vb-transition metal trichalcogenides (V-MXS) are now widely accepted as typical quasi one dimensional conductors. On the other hand, group IVb-metal trichalcogenides (IV-MXS) have attracted much less attention, partly because all of them, except ZrTeS, are non-metallic. The crystal structurelof IV-MX3 is simpler than that of V-MXS; it consists of only one kind of triangular prismatic chain. Within the unit cell there are two chains (running in the b-direction), connected by inversion symmetry to each other. There are two variants in the arrangement of chains. ZrS3, ZrSeg and HfS3 possess the ordinary one, which is referred to as type A. Structures of TiS3, ZrTe3 and HfSeS belong to the other, type B, which is connected to type A by the relation xB=l-x where x is the fractional c-coordinate of tht'atom position within the unit cell. The cross section of prisms in the type A configuration is approximately isosceles-triangular,while that in the type B is more distorted. In 1958, McTaggart' measured the electrical resistivity of all existing IV-MX3 at room temperature. He found that, in general, the resistivity of Hf-chalcogenides is higher than that of Zr-compounds and that sulfides, selenides and tellurides are more insulating in that order. The trends of magnetic susceptibility3 and optical band gap1 are in good agreement with the McTaggart's findings; magnetic susceptibility of these compounds is negative and temperature-independent,and the optical gap is larger for the heavier metal compounds. Among IV-MX3, ZrTeg is the only one which is metallic; it is supposedly a semi-metal but with an electronic structure different from those of V-MX3. To find a unified feature of chain-structuredMXS as low dimensional conductors, we have been studying the properties of ZrTeS. We have found anomalies in the transverse conductivities and Hall coefficient at 63K and that it becomes a three dimensional superconductorbelow 2K with an anisotropic
In this paper we upper critical field.4 examine the possibility that it undergoes a structural phase transition, e.g. charge density wave formation, at 63K. Single crystals of ZrTeS were prepared by the iodine transport method. Weighted amounts of 3N Zr (MRC, Marz grade) and 6N Te were reacted for a few weeks in the temperature gradient 750-7oo"c. X-ray examination confirmed the parameters determined by Brattas and Kjekshusl : monoclinic, a=5.897A, b=3.926A, c=ll.llA and 8=97.82". The electrical resistivity was measured by the usual four probe method. At room temperature, values of the resiswere found as tivity components pb, pa and p 2.5, 1.8 and 20x1g4 Ccm , resp&c*tively.The largest is ock; the van der Waals gap is crossed in this direction. Contrary to V-MXS, pb has a slightly larger value than p . The ratio pa/pb was also obtained by the Montgomery method as (O.SS+O.lO) at 300K, consistent with the above resulS. The small value of pa is a result of strong coupling between chains. The temperature dependence of pb is shown in Fig. 1. It is metallic throughout the temperature range measured, but the temperature derivative dpb/dT shows a sharp knee at 55K. This anomaly is quite reproducible; it was observed in every sample examined. Above 56K, pb is linear in temperature, T, while it is quadratically dependent on T below 54K. The derivative is continuous at 55K, so pb below 55K is larger than that extrapolated from above. The transverse components, p and p , are shown in Fig. 2 and 3. Humps werl obse&d in both components. The maximum is located at 55K (knee in pb) and the temperature of extremum derivative, T , was observed at 63K+2K. The residual resistgnce ratios (p(300K)/pT4K))were % 35, 8 and 4 along the b-, a- and c*-axes respectivetly. No clear correlation between T and the residual resistance ratio was found.P As
OPresent address: Alps Electric,Inc., Yukigaya, Tokyo 145 Japan 1031
1032
Vol. 49, No:11
TRANSPORT AND ELASTIC ANOMALIES IN ZrTe3
RH infers that the mobility of electrons is larger than that of holes. The magnitude of RR increases near T = 63K, consistent with the conductivity inc8ease.
Fig.1 Resistivity along the b-axis and its temperature derivative vs. temperature.
Fig.2 Resistivity along the a-axis and its temperature derivative.
To check whether the anomalies in the transport properties were due to the presence of a phase transition, in particular a structural transition,we measured the Young's modulus along the b-axis, E, and internal friction, tans using a vibrating reed technique described in detail elsewhere5 . Two crystals, of typical dimensions 0.2 mm x 2 mm x 1 pm, were mounted as cantilevers by gluing one end with silver paint to a copper support, and the frequency, foam, and quality factor, Q, of the fundamental flexural resonance of each were measured as functions of temperature. Relative changes in the modulus with temperature could be measured very precisely, although the absolute magnitude of the modulus could only be estimated to an order of magnitude due to the difficulty in measuring the sam le thickness. We found that E~~xIO"~ dyne/cms , comparable to the metallic V-MK3 compounds.6 Changes in the quality factor, measured by monitoring the amplitude of the resonance, give d_frectlychanges in the internal friction, AQ =Atan6. The relative change in modulus vs. temperature for one sample is shown in the inset of Fig.4; both samples showed very similar results. A sharp minimum, indicating a phase transition, is observed. The transition temperatures of the two samples, taken as the temperatures of the modulus minima, were T =63.1K and 63.5K. The modulus and internal ftiction near T are shown in detail in Fig.4. The internal fr%ction peaks a few degrees below T (at 61K for both samples) , as expected for a pRase transition. No ther-
0
50 loo150200250
Fig.3 Resistivity along the c*-axis . Inset: Hall coefficient. T(K) shown in Fig.3 pc* shows, at high temperature, negative curvature, which has been observed in TaSe3 and many Al5 compounds, but for which no unified explanation has been given. Hall coeffcient, RR, measured with the current along the b-axis and the magnetic field parallel to c*, is shown in the inset of Fig.3. If ZrTe3 is semi-metallic, the negative sign of
Fig.4 Relative change in Young's modulus, R/RO, and internal friction l/Q vs. temperature from 50K to 75K for a reed of ZrTe with ambient resonant frequency f =641H?. Inset: E/E0 vs. temperature f!om OK-250K.
ma1 hysteresis (T
L > p,“- (ubyoaH) vaH= FbH_“,H u,“-(ObL/UaL)V a so that V aH-(ubL/uaL)v
An analysis of the transport anomalies is given below to estimate what kind of structural transition occurs at 63K. The simple two-band model is used in two different approaches. The first is to assume that the carrier density is unchanged and that the anomalies are due to a change in the transverse mobility (i.e. that it is not a CDW transition). The Hall coefficient RH in the present configuration is given by
= (l/B)
c~~~/bs~u~
+
oab
2,
(1)
where the conductivity tensor in the two band
where n(p) and u>O (v>O) are the density and mobility of electrons (holes) respectively. in the low B limit is given
(3) L From the present experimental results, (-R,,) >(-%I” and ‘I Ub =ab =ua =2aa (4). L
H
H
L
where the prefix H(L) denotes the high (low) temperature phase, (3) gives
a
L
>
IlbylbL
=
0
(5)
Here we have assumed that the ralation p is equivalent to ubH=ubL and vbH=vbL. wt:;I’&, the following relation is given: H L V 2 2v a a The scattering mechanism which comes in below T reduces the transverse hole mobility effective-P 1Y. Since the crystal structure is well defined at room temperature, the new scattering mechanism is due to, for example, long-range modification of the trigonal chain arrangement, with the chai.nitself kept rigid. The alternative approach is to assume that the anomalies at T are due to a partial vanishing of the Fe& surface by e.g. charge density wave formation. For simplicity, no change in the mobility is assumed. Since it is difflcult to conceive that a vanishing of the Fermi surface sheet perpendicular to the b-axis does not affect p it is assumed that a piece of the Fermi surfacbe'which is longer along the b*-axis partially vanishes at T . Hence the b*-component of the effective mass iR that sheet is large. If the hole sheet is columnar and the electron sheet is more isotropic, reduction of hole density occurs below T . Conductivity components at high tempera&e are U
\
1033
TRANSPORT AND ELASTIC ANOMALIES IN ZrTe3
Vol. 49, No. II
H = nolel(ua+va)
=no(ej
(l+a)p,
aH ob = where CX=V while be&
(7)
/u
and
Ia p
u
i3=vb/pb
,
L =nolelua(l+ca) aL
'b
=n,lelub(l+03)
(8)
where Sn is the hole density below T . Relations (49, (7) and (8) give 6'2. .pH The experimental result of (-RH )>(-RH >>O is rewritten as l-SW3 l-a8 (l+Sa)(l+SB) ' (l+a)(l+8) (9) Because of the relation O
1034
TRANSPORT
AND ELASTIC ANOMALIES
ting reed result: A, (iXIe3)~lOOh(NbSe ), where h is the electron-phonon coupling coastant (for the condensing band), i.e. the Te-p band is expected to couple more strongly to acoustic phonons than the metal d-band. The large X
IN ZrTe3
Vol. 49, No.
should be related to the relatively high value of the superconducting transition temperature of 2K.4 Acknowlegement-The authors at HKU acknowlege M.Ido and H.Fukuyama for helpful discussions. REFERENCES
1) L.Brattas
2) 3) 4) 5) 6)
and A.Kjekshus, Acta Chem.Scand. 26,3441 (1972) F.K. McTaggart, Austr.J.Chem. 11,445 (1958) H.Haraldsen, A.Kjekshus, E.Rost and A. Steffensen, Acta Chem. Stand. 17, 1283 (1963) S.Takahashi and T.Sambongi, J. Physique 44 supplement c-3, 1733 (1983) J.W. Brill, Solid State Commun. 41,925 (1982) J.W. Brill, Mol.Cryst.Liq.Cryst.81,107 (1982)
7) A.W. Higgs and J.C. Gill, Solid State Commun. 47,737 (1983) 8) R.M. Fleming, D.E. Moncton and D.B.McWhan, Phys.Rev. Bl8, 5560 (1978) 9) M.Bannatz, L.R.Testardi and F.J.DiSalvo, Phys.Rev.Bl2, 4367 (1975) 10) H.W. Myron, B.N.Harman and F.S.khumalo, .I. Phys.Chem.Solids,42,263 (1981)
II