- Email: [email protected]
Electrical conduction of a quasi-one dimensional Nb3S4 single crystal
Solid State Communications, Vol. 42, No. 8, pp. 579-582, 1982. Printed in Great Britain.
0038-1098/82/200579-04503.00/0 Pergamon Press Ltd.
ELECTRICAL CONDUCTION OF A QUASI-ONE DIMENSIONAL Nb3S4 SINGLE CRYSTAL Y. Ishihara Faculty of Science, Kanazawa University, Kanazawa, Japan and I. Nakada The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo, Japan (Received 11 December 1981 by W. Sasaki) With respect to single crystals of NbaS4 the electrical resistivity from 2.8 K to 3 0 0 K and the magnetoresistance at 4.2 K were measured. The resistivity is represented as a sum of a temperature independent and an intrinsic temperature dependent component. The temperature dependence of the intrinsic resistivity subjects to T a form between 7 and 50 K above which it becomes weaker than T a approaching a T linear form. This behaviour is discussed in terms of the electron-electron Umldapp scattering. The ratio of the resistivities perpendicular and parallel to the c-axis takes about 15 between room temperature and 50 K. The transverse magnetoresistance is proportional to the magnetic field. The longitudinal magnetoresistance is too small to be measured.
1. INTRODUCTION RECENTLY transition metal chalcogenides with either a quasi-one dimensional or layered structures have attracted considerable interest due to the occurrence of charge density waves [1,2] and superconductivity [3, 4]. Among them NbaS4 was reported by Amberger et al. [5] as a superconducting compound of a quasione dimensional cluster. Its crystal structure is hexagonal [6] with zig-zag Nb-chain running parallel to the direction of the c-axis. The interchain distance between Nb atoms is 2.88 A which is equal to the metallic bonding distance, while the interchain distance is 3.37 A. As a consequence, quasi-one dimensional physical properties may be expected. However, a recent superconductivity, as well as its anisotropy measurement carried out by Biberacher et al. [7] showed that NbaS4 is an anisotropic but three dimensional conductor. Amberger et al. [5] and Biberaeher et al. [7] reported room temperature resistivities to be 120-800/a~2-cm with resistivity ratio p (rT)/p (4.2 K) of 109 and 4 0 - 6 5 , respectively. However, they observed only a monotonic resistivity change in the range from 4 to 300 K, without referring to the detailed temperature dependences. The study of the transport properties of NbaS4 in the normal conducting state is meagre at present. In this communication we shall report on the T a temperature dependence of the resistivity between 7 and 50 K as well as the T linear dependence in the higher
temperature region. Further, the magnetoresistance up to 57 kG at 4.2 K was measured. We have observed the magnetoresistance with positive sign and linear field dependence. 2. EXPERIMENTAL The crystals were prepared by the chemical vapour deposition (CVD) method with iodine as a transport agent following Amberger et al. [5]. The starting material is either elements of Nb or S in stoichiometric proportion or pressed pellets of sintered polycrystalline NbaS4 prepared thereof. The purity of Nb and S is 3N and 6N, respectively. The starting material and the transport agent were put in a quartz ampoule 1.5 cm in diameter and about 15 cm in length which was sealed after evacuation to 1 x 10 -3 torr. The ampoule was placed in a horizontal furnace. The temperature at the centre of the furnace was kept at 900 ° C with temperature gradient of 3 ° C cm -1 . The location of the starting material was adjusted to come to the centre of the ampoule and at the same time to the centre of the furnace. Tiny needle-like single crystals up to several millimetres in length grew after a few weeks. The actual crystals grew nearly at the place where the starting material was put in the ampoule in spite of the temperature gradient. This means that the transport efficiency is rather low, though iodine is indispensable for crystals to grow.
579
580
ELECTRICAL CONDUCTION OF A NbaS4 SINGLE CRYSTAL
The crystal structure analysis has already been made by Ruysink et al. [6] NbaS4 belongs to the hexagonal crystal system. Based on their results the growth crystals were examined with the X-ray powder pattern analysis and identified to be Nb3S4. The needle-like crystals elongated always parallel to the crystallographic c-axis, which was confirmed with the X-ray oscillation photography method. The typical crystal habit is a hexagonal prism. For the electrical measurement crystals with size 3 - 4 mm in length and 0.3-0.8 mm in diameter were selected. To take off deposits on the surface of the as-grown crystals they were soaked in acetone and cleaned by rubbing with a piece of cotton. The electrical resistance was measured mainly for the current flowing in the direction parallel to the c-axis using a conventional d.c. four probe technique. The current lead contacts were soldered with Cerasolzer 279 of Asahi Glass Company ultrasonically. Voltage leads were attached with Dupont 4817 silver paste. For the measurement of the anisotropic resistivity the Montgomery method [8] was used. Electrical leads were contacted by thin sheets of phosphor bronze with sharp edge in soft springs. A superconducting solenoid provided a magnetic field up to 57 kG for the measurement of the magnetoresistance. In the apparatus the specimen was immersed in a liquid helium. This method gave an excellent temperature stability although the experiments were limited to 4.2 K and below. The temperature between 2.8 and 40 K, specimen being either immersed in a liquid helium or in a helium gas atmosphere, was determined with a carbon resistance thermometer. The carbon resistance thermometer was calibrated in the liquid helium range to the vapour pressure of helium and in the higher temperature range to the boiling points of liquid hydrogen and liquid nitrogen. Temperatures between 2.8 and 40 K were also calibrated using a standard resistance vs temperature relation known to hold for the type of the resister used. 3. RESULTS AND DISCUSSION
I (3~
Vol. 42, No. 8
I
r
#
Q
/..
6s
16 6 (a)
°o coooOO o
10 7 o~
16 8
I~9
i
i
101
lO 0
10 2
10 3
T(K)
Fig. 1. The c-axis resistivity vs temperature for Nb3S 4 . Curve (a), as measured; Curve (b), the residual component being subtracted. The anisotropic temperature dependence of the resistivity in the range from 50 K to room temperature obtained using the Montgomery geometry is shown in Fig. 2, where Pll and p± are the resistivity parallel and perpendicular to the c-axis, respectively. Their temperature dependences are quite similar and agree well with those obtained using the linear four probe geometry. The resistivity anisotropy Pl/Pll is about 15 over the temperature region measured. In the temperature region below 50 K nearly the same value ofpi/Pfl was obtained. But as the measurement is as yet preliminary the result was not shown in Fig. 2. -2 10
o P, -3
• 8, /
IO
-4
IO
The curve a in Fig. 1 shows the temperature dependence of the electrical resistivity as measured. As the temperature is lowered the resistivity along the c-axis, i.e., the " - N b - N b - " chain direction, decreases and approaches to a low temperature residual value monotonously. The resistivities for a specimen at 300 and 4.2 K are 6.3 x 10 -s and 3.7 x 10 -7 ~2-cm, respectively. The curve b in the figure shows the temperature dependence of resistivity after the residual value is subtracted from curve a.
-5
IO I
10
lOz T(K)
10 3
Fig. 2. The resistivity of NbaS4 along the c-axis Coil) and in the direction perpendicular to the c-axis (p±).
Vol. 42, No. 8
ELECTRICAL CONDUCTION OF A Nb3S4 SINGLE CRYSTAL
The result suggests that the temperature dependence of the resistivity in the direction along the Nb-chain is described in terms of the Matthiessen's rule [9]. The residual scattering rate for charge carriers is assumed to be temperature independent so that the resistivity p(73 is represented as p(73 = Po + Pl (73, where Po is a residual resistivity and Pl (73 is an intrinsic temperature dependent term. The curve b in Fig. 1 over the temperature range from 7 to 50 K is represented by
p (73 = po + n ~ , where A = 3.2 + 0.1 and B = 1.1 x 10 -11 ~2-cm[KA . At temperatures above 50 K the temperature dependence of p~(T) becomes weaker than T 3"2 and approaches to a T linear form. Materials such as (SN)x [10], certain metals [ 1 1 13] and some semimetals [14] exhibit T 2 dependence of resistivity. Such a temperature dependence has been explained by carrier--carrier Umklapp scattering process. The carder---carrier scattering in single carrier systems has been studied theoretically by Lawrence et al. [15]. They have concluded that the carrier--carrier normal scattering could not contribute to the resistivity. It is a natural result because of the total momentum conservation. Oshiyama, Nakao and Kamimura [16] (ONK, thereafter) have performed a theoretical calculation of the resistivity due to the electron-electron Umklapp scattering based on a quasi-one dimensional model. For example, with respect to metal with two pairs of warped plane-like Fermi surfaces, such as an (SN)x, it has been shown that the electron-electron Umklapp scattering gives the most dominant contribution to the resistivity and the temperature dependence of the resistivity is T n, where 2 ~< n ~< 3, depending on the band parameters. However, when the warping band width is much smaller than k~ T, the resistivity tends to the T linear dependence irrespective of the band parameters. This is the case satisfied at higher temperature regions. There are many examples of the T 2 form as mentioned above [10-14], but few of the T 3 form. Since there is no theoretical work with respect to the band structure of Nb3S4, we cannot further extend our discussion of T 3 form concerned quantitatively at present. However, as Nb3S4 and (SN)x are similar with respect to the crystallographic chain structure, the one is formed of the zig-zag " - N b - " chains and the other also of the zig-zag " - S - N - " chains, resulting to a remarkable anisotropy in the electrical resistance, let us remark a bit concerning the temperature dependence
581
of the resistivity of Nb3S4 based on the model of (SN)x by ONK. The temperature dependence of the electrical resistivity shown by curve b in Fig. 1 is similar to the curve corresponding to n = 3, presented in Fig. 4 of the report of ONK [16]. The case n = 3 means that for a pair of fiat and warped bands where warping is much larger than kB T the electron-electron Umklapp scattering in the neighbourhood of k x = 0 and ky = 0 brings the relaxation for scattering of type T a . This would suggest a possibility for the behaviour of T 3 with Nb3S4 under the similar situation. At higher temperatures the resistivity tends to Tlinear form as the ratio of the warping band width to kB T decreases with increase of temperature. I
~: N "a:
f
,
1.0
fY
d / ?
I--
E.
Ba.i
0.5
/
B//i
X
,.]
2.5
3.0
B=O
?
/ 0
//
3.5
,
4.0
4.5
T(K)
Fig. 3. The temperature dependence of the resistivity of Nb3S4 along the c-axis in the superconducting transition region normalized to p (73/p (4.2 K): B = 0 for no applied magnetic field, B l i and B IIi for the magnetic field applied perpendicular and parallel to the c.axis, respectively. The transition to superconductivity is shown in Fig. 3 for the case of no applied magnetic field and at 1.2 kG. The effect of the current density on the transition temperature Te was examined in the range of 5 - 8 0 A cm -2 , where Tc was independent of the current and was 3.90 K. The Te was by 0.25 K higher than that of Biberacher et al. [7]. As for the residual resistivity ratio p (300 K)/p (4.2 K), Biberacher et al. gave 40--60, while ours are 150-170. Therefore, the increase in T e by 0.25 K would be due to the difference of the quality of the crystals prepared. However, the change of the critical magnetic field against the reduced temperature T I T c confirmed the results of Biberacher et al. [7]. The dependence of the magnetoresistance Ap/po on the magnetic field at 4.2 K is shown in Fig. 4, where Po is the resistivity in the absence of the magnetic field and Ap is the change of the resistivity by the magnetic field. At magnetic field lower than about 2 kG sometimes the magnetoresistance increases steeply as the
582
ELECTRICAL CONDUCTION OF A Nb3S4 SINGLE CRYSTAL 20
f
f
oBJ_
•
i
I
i
i
o-o ''''/°° -
45°i
B
~ B//
o~"
i
~*-
A10
~
,~.,..o
o-'./
'~ 0 -5
I
I
l
I
20
I
40
60
B(kG)
Fig. 4. The dependence of the magnetoresistance on the applied magnetic field. B ± i and B II i, the magnetic field being perpendicular and parallel to the c-axis, repectively; B 45 ° i, the magnetic field being inclined 45 ° to the c-axis. magnetic field is increased. However, as it lacks the reproducibility, it is not an intrinsic effect. The values of magnetoresistance shown in Fig. 4 and in Fig. 5 to appear below are represented by subtracting component in the low magnetic fields. The angular dependences of Ap/po for 54.7 kG at 4.2 K are shown in Fig. 5, where the direction of the magnetic field is turned on the plane including the long axis of the crystal. 0 is the angle between the current and the applied magnetic field and the solid line indicates Isin 0 I.
0 shown in Fig. 5 is subjected to the sine-function means that only the component of the magnetic field perpendicular to the c-axis is effective. This is a natural result that Ap/po = 0 for B II i, where i is the current flowing through the crystal. The transverse magnetoresistance of Nb3S4 is more than an order of magnitude larger than that of (SN)x [17, 18]. In conclusion we must take that the Nb-chains are incompletely separated by surrounding sulfur atoms as to establish a quasi-one dimensional system with respect to the electronic interaction between them. In the region below 50 K, the character of the quasi-one dimensional behaviour is seen in T a form of the resistivity. Above 50 K resistivity takes a usual T linear form. Further study is necessary to explain the field linear magnetoresistance. Acknowledgements - The authors thank Dr A. Oshiyama and Prof. S. Tanuma for helpful discussions. REFERENCES 1. 2. 3. 4. 5.
20
!
i
1
6. 7. 8. 9. 10.
~gl0
11. 12. 0 (~//i)
90 (B,t i)
180 (Bfi)
13.
e(*) Fig. 5. Dependence of the magnetoresistance on the direction of the applied magnetic field at 4.2 K. Strength of the field is 54.7 kG. The transverse magnetoresistance is positive in the range of 3 - 5 7 kG and is proportional to the magnetic field, while the longitudinal magnetoresistance was too low to be measured. That the dependence of Ap/Po on
Vol. 42, No. 8
14. 15. 16. 17. 18.
R.C. Morris, Phys. Rev. Lett. 34, 1164 (1975). N.P. Ong & P. Monceau, Phys. Rev. B16, 3443 (1977). P. Monceau, J. Peyrard, J. Richard & P. Molini6, Phys. Rev. Lett. 39,161 (1977). T. Sambongi, M. Yamamoto, K. Tsutsumi, Y. Shiozaki, K. Yamaya & Y. Abe, J. Phys. Soc. Japan 42, 1421 (1977). E. Amberger, K. Polborn, P. Grimm, M. Dietrich & B. Obst, Solid State Commun. 26,943 (1978). A.F. Ruysink, F. Kadijk, A.J. Wagner & F. JeUinek, Acta Cryst. B24, 1614 (1968). W. Biberacher & H. Schwenk, Solid State Commun. 33,385 (1980). H.C. Montgomery, J. Appl. Phys. 42, 2971 (1971). A. Matttflessen, Rep. Brit. Ass. 32,144 (1862). C.K. Chiang, M.J. Cohen, A.F. Garito & A.J. Heeger, Solid State Commun. 18, 1451 (1976). J.T. Schriempf, J. Phys. Chem. Solids 28, 2581 (1967). A.C. Anderson, R.E. Peterson & J.E. Robinchaux, Phys. Rev. Lett. 20,459 (1968). J.C. Garland & R. Bowers, Phys. Rev. Lett. 21, 1007 (1968). R. Hartman, Phys. Rev. 181,1070(1969). W.E. Lawrence & J.W. Wilkins, Phys. Rev. B7, 2317 (1973). A. Oshiyama, K. Nakao & H. Kamimura, J. Phys. Soc. Japan 45, 1136 (1978). W. Beyer, W.D. Gill & G.B. Street, Solid State Commun. 23,577 (1977). K. Kaneto, M. Yamamoto, K. Yoshino & Y. Inuishi, Solid State Commun. 26, 311 (1978).
0038-1098/82/200579-04503.00/0 Pergamon Press Ltd.
ELECTRICAL CONDUCTION OF A QUASI-ONE DIMENSIONAL Nb3S4 SINGLE CRYSTAL Y. Ishihara Faculty of Science, Kanazawa University, Kanazawa, Japan and I. Nakada The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo, Japan (Received 11 December 1981 by W. Sasaki) With respect to single crystals of NbaS4 the electrical resistivity from 2.8 K to 3 0 0 K and the magnetoresistance at 4.2 K were measured. The resistivity is represented as a sum of a temperature independent and an intrinsic temperature dependent component. The temperature dependence of the intrinsic resistivity subjects to T a form between 7 and 50 K above which it becomes weaker than T a approaching a T linear form. This behaviour is discussed in terms of the electron-electron Umldapp scattering. The ratio of the resistivities perpendicular and parallel to the c-axis takes about 15 between room temperature and 50 K. The transverse magnetoresistance is proportional to the magnetic field. The longitudinal magnetoresistance is too small to be measured.
1. INTRODUCTION RECENTLY transition metal chalcogenides with either a quasi-one dimensional or layered structures have attracted considerable interest due to the occurrence of charge density waves [1,2] and superconductivity [3, 4]. Among them NbaS4 was reported by Amberger et al. [5] as a superconducting compound of a quasione dimensional cluster. Its crystal structure is hexagonal [6] with zig-zag Nb-chain running parallel to the direction of the c-axis. The interchain distance between Nb atoms is 2.88 A which is equal to the metallic bonding distance, while the interchain distance is 3.37 A. As a consequence, quasi-one dimensional physical properties may be expected. However, a recent superconductivity, as well as its anisotropy measurement carried out by Biberacher et al. [7] showed that NbaS4 is an anisotropic but three dimensional conductor. Amberger et al. [5] and Biberaeher et al. [7] reported room temperature resistivities to be 120-800/a~2-cm with resistivity ratio p (rT)/p (4.2 K) of 109 and 4 0 - 6 5 , respectively. However, they observed only a monotonic resistivity change in the range from 4 to 300 K, without referring to the detailed temperature dependences. The study of the transport properties of NbaS4 in the normal conducting state is meagre at present. In this communication we shall report on the T a temperature dependence of the resistivity between 7 and 50 K as well as the T linear dependence in the higher
temperature region. Further, the magnetoresistance up to 57 kG at 4.2 K was measured. We have observed the magnetoresistance with positive sign and linear field dependence. 2. EXPERIMENTAL The crystals were prepared by the chemical vapour deposition (CVD) method with iodine as a transport agent following Amberger et al. [5]. The starting material is either elements of Nb or S in stoichiometric proportion or pressed pellets of sintered polycrystalline NbaS4 prepared thereof. The purity of Nb and S is 3N and 6N, respectively. The starting material and the transport agent were put in a quartz ampoule 1.5 cm in diameter and about 15 cm in length which was sealed after evacuation to 1 x 10 -3 torr. The ampoule was placed in a horizontal furnace. The temperature at the centre of the furnace was kept at 900 ° C with temperature gradient of 3 ° C cm -1 . The location of the starting material was adjusted to come to the centre of the ampoule and at the same time to the centre of the furnace. Tiny needle-like single crystals up to several millimetres in length grew after a few weeks. The actual crystals grew nearly at the place where the starting material was put in the ampoule in spite of the temperature gradient. This means that the transport efficiency is rather low, though iodine is indispensable for crystals to grow.
579
580
ELECTRICAL CONDUCTION OF A NbaS4 SINGLE CRYSTAL
The crystal structure analysis has already been made by Ruysink et al. [6] NbaS4 belongs to the hexagonal crystal system. Based on their results the growth crystals were examined with the X-ray powder pattern analysis and identified to be Nb3S4. The needle-like crystals elongated always parallel to the crystallographic c-axis, which was confirmed with the X-ray oscillation photography method. The typical crystal habit is a hexagonal prism. For the electrical measurement crystals with size 3 - 4 mm in length and 0.3-0.8 mm in diameter were selected. To take off deposits on the surface of the as-grown crystals they were soaked in acetone and cleaned by rubbing with a piece of cotton. The electrical resistance was measured mainly for the current flowing in the direction parallel to the c-axis using a conventional d.c. four probe technique. The current lead contacts were soldered with Cerasolzer 279 of Asahi Glass Company ultrasonically. Voltage leads were attached with Dupont 4817 silver paste. For the measurement of the anisotropic resistivity the Montgomery method [8] was used. Electrical leads were contacted by thin sheets of phosphor bronze with sharp edge in soft springs. A superconducting solenoid provided a magnetic field up to 57 kG for the measurement of the magnetoresistance. In the apparatus the specimen was immersed in a liquid helium. This method gave an excellent temperature stability although the experiments were limited to 4.2 K and below. The temperature between 2.8 and 40 K, specimen being either immersed in a liquid helium or in a helium gas atmosphere, was determined with a carbon resistance thermometer. The carbon resistance thermometer was calibrated in the liquid helium range to the vapour pressure of helium and in the higher temperature range to the boiling points of liquid hydrogen and liquid nitrogen. Temperatures between 2.8 and 40 K were also calibrated using a standard resistance vs temperature relation known to hold for the type of the resister used. 3. RESULTS AND DISCUSSION
I (3~
Vol. 42, No. 8
I
r
#
Q
/..
6s
16 6 (a)
°o coooOO o
10 7 o~
16 8
I~9
i
i
101
lO 0
10 2
10 3
T(K)
Fig. 1. The c-axis resistivity vs temperature for Nb3S 4 . Curve (a), as measured; Curve (b), the residual component being subtracted. The anisotropic temperature dependence of the resistivity in the range from 50 K to room temperature obtained using the Montgomery geometry is shown in Fig. 2, where Pll and p± are the resistivity parallel and perpendicular to the c-axis, respectively. Their temperature dependences are quite similar and agree well with those obtained using the linear four probe geometry. The resistivity anisotropy Pl/Pll is about 15 over the temperature region measured. In the temperature region below 50 K nearly the same value ofpi/Pfl was obtained. But as the measurement is as yet preliminary the result was not shown in Fig. 2. -2 10
o P, -3
• 8, /
IO
-4
IO
The curve a in Fig. 1 shows the temperature dependence of the electrical resistivity as measured. As the temperature is lowered the resistivity along the c-axis, i.e., the " - N b - N b - " chain direction, decreases and approaches to a low temperature residual value monotonously. The resistivities for a specimen at 300 and 4.2 K are 6.3 x 10 -s and 3.7 x 10 -7 ~2-cm, respectively. The curve b in the figure shows the temperature dependence of resistivity after the residual value is subtracted from curve a.
-5
IO I
10
lOz T(K)
10 3
Fig. 2. The resistivity of NbaS4 along the c-axis Coil) and in the direction perpendicular to the c-axis (p±).
Vol. 42, No. 8
ELECTRICAL CONDUCTION OF A Nb3S4 SINGLE CRYSTAL
The result suggests that the temperature dependence of the resistivity in the direction along the Nb-chain is described in terms of the Matthiessen's rule [9]. The residual scattering rate for charge carriers is assumed to be temperature independent so that the resistivity p(73 is represented as p(73 = Po + Pl (73, where Po is a residual resistivity and Pl (73 is an intrinsic temperature dependent term. The curve b in Fig. 1 over the temperature range from 7 to 50 K is represented by
p (73 = po + n ~ , where A = 3.2 + 0.1 and B = 1.1 x 10 -11 ~2-cm[KA . At temperatures above 50 K the temperature dependence of p~(T) becomes weaker than T 3"2 and approaches to a T linear form. Materials such as (SN)x [10], certain metals [ 1 1 13] and some semimetals [14] exhibit T 2 dependence of resistivity. Such a temperature dependence has been explained by carrier--carrier Umklapp scattering process. The carder---carrier scattering in single carrier systems has been studied theoretically by Lawrence et al. [15]. They have concluded that the carrier--carrier normal scattering could not contribute to the resistivity. It is a natural result because of the total momentum conservation. Oshiyama, Nakao and Kamimura [16] (ONK, thereafter) have performed a theoretical calculation of the resistivity due to the electron-electron Umklapp scattering based on a quasi-one dimensional model. For example, with respect to metal with two pairs of warped plane-like Fermi surfaces, such as an (SN)x, it has been shown that the electron-electron Umklapp scattering gives the most dominant contribution to the resistivity and the temperature dependence of the resistivity is T n, where 2 ~< n ~< 3, depending on the band parameters. However, when the warping band width is much smaller than k~ T, the resistivity tends to the T linear dependence irrespective of the band parameters. This is the case satisfied at higher temperature regions. There are many examples of the T 2 form as mentioned above [10-14], but few of the T 3 form. Since there is no theoretical work with respect to the band structure of Nb3S4, we cannot further extend our discussion of T 3 form concerned quantitatively at present. However, as Nb3S4 and (SN)x are similar with respect to the crystallographic chain structure, the one is formed of the zig-zag " - N b - " chains and the other also of the zig-zag " - S - N - " chains, resulting to a remarkable anisotropy in the electrical resistance, let us remark a bit concerning the temperature dependence
581
of the resistivity of Nb3S4 based on the model of (SN)x by ONK. The temperature dependence of the electrical resistivity shown by curve b in Fig. 1 is similar to the curve corresponding to n = 3, presented in Fig. 4 of the report of ONK [16]. The case n = 3 means that for a pair of fiat and warped bands where warping is much larger than kB T the electron-electron Umklapp scattering in the neighbourhood of k x = 0 and ky = 0 brings the relaxation for scattering of type T a . This would suggest a possibility for the behaviour of T 3 with Nb3S4 under the similar situation. At higher temperatures the resistivity tends to Tlinear form as the ratio of the warping band width to kB T decreases with increase of temperature. I
~: N "a:
f
,
1.0
fY
d / ?
I--
E.
Ba.i
0.5
/
B//i
X
,.]
2.5
3.0
B=O
?
/ 0
//
3.5
,
4.0
4.5
T(K)
Fig. 3. The temperature dependence of the resistivity of Nb3S4 along the c-axis in the superconducting transition region normalized to p (73/p (4.2 K): B = 0 for no applied magnetic field, B l i and B IIi for the magnetic field applied perpendicular and parallel to the c.axis, respectively. The transition to superconductivity is shown in Fig. 3 for the case of no applied magnetic field and at 1.2 kG. The effect of the current density on the transition temperature Te was examined in the range of 5 - 8 0 A cm -2 , where Tc was independent of the current and was 3.90 K. The Te was by 0.25 K higher than that of Biberacher et al. [7]. As for the residual resistivity ratio p (300 K)/p (4.2 K), Biberacher et al. gave 40--60, while ours are 150-170. Therefore, the increase in T e by 0.25 K would be due to the difference of the quality of the crystals prepared. However, the change of the critical magnetic field against the reduced temperature T I T c confirmed the results of Biberacher et al. [7]. The dependence of the magnetoresistance Ap/po on the magnetic field at 4.2 K is shown in Fig. 4, where Po is the resistivity in the absence of the magnetic field and Ap is the change of the resistivity by the magnetic field. At magnetic field lower than about 2 kG sometimes the magnetoresistance increases steeply as the
582
ELECTRICAL CONDUCTION OF A Nb3S4 SINGLE CRYSTAL 20
f
f
oBJ_
•
i
I
i
i
o-o ''''/°° -
45°i
B
~ B//
o~"
i
~*-
A10
~
,~.,..o
o-'./
'~ 0 -5
I
I
l
I
20
I
40
60
B(kG)
Fig. 4. The dependence of the magnetoresistance on the applied magnetic field. B ± i and B II i, the magnetic field being perpendicular and parallel to the c-axis, repectively; B 45 ° i, the magnetic field being inclined 45 ° to the c-axis. magnetic field is increased. However, as it lacks the reproducibility, it is not an intrinsic effect. The values of magnetoresistance shown in Fig. 4 and in Fig. 5 to appear below are represented by subtracting component in the low magnetic fields. The angular dependences of Ap/po for 54.7 kG at 4.2 K are shown in Fig. 5, where the direction of the magnetic field is turned on the plane including the long axis of the crystal. 0 is the angle between the current and the applied magnetic field and the solid line indicates Isin 0 I.
0 shown in Fig. 5 is subjected to the sine-function means that only the component of the magnetic field perpendicular to the c-axis is effective. This is a natural result that Ap/po = 0 for B II i, where i is the current flowing through the crystal. The transverse magnetoresistance of Nb3S4 is more than an order of magnitude larger than that of (SN)x [17, 18]. In conclusion we must take that the Nb-chains are incompletely separated by surrounding sulfur atoms as to establish a quasi-one dimensional system with respect to the electronic interaction between them. In the region below 50 K, the character of the quasi-one dimensional behaviour is seen in T a form of the resistivity. Above 50 K resistivity takes a usual T linear form. Further study is necessary to explain the field linear magnetoresistance. Acknowledgements - The authors thank Dr A. Oshiyama and Prof. S. Tanuma for helpful discussions. REFERENCES 1. 2. 3. 4. 5.
20
!
i
1
6. 7. 8. 9. 10.
~gl0
11. 12. 0 (~//i)
90 (B,t i)
180 (Bfi)
13.
e(*) Fig. 5. Dependence of the magnetoresistance on the direction of the applied magnetic field at 4.2 K. Strength of the field is 54.7 kG. The transverse magnetoresistance is positive in the range of 3 - 5 7 kG and is proportional to the magnetic field, while the longitudinal magnetoresistance was too low to be measured. That the dependence of Ap/Po on
Vol. 42, No. 8
14. 15. 16. 17. 18.
R.C. Morris, Phys. Rev. Lett. 34, 1164 (1975). N.P. Ong & P. Monceau, Phys. Rev. B16, 3443 (1977). P. Monceau, J. Peyrard, J. Richard & P. Molini6, Phys. Rev. Lett. 39,161 (1977). T. Sambongi, M. Yamamoto, K. Tsutsumi, Y. Shiozaki, K. Yamaya & Y. Abe, J. Phys. Soc. Japan 42, 1421 (1977). E. Amberger, K. Polborn, P. Grimm, M. Dietrich & B. Obst, Solid State Commun. 26,943 (1978). A.F. Ruysink, F. Kadijk, A.J. Wagner & F. JeUinek, Acta Cryst. B24, 1614 (1968). W. Biberacher & H. Schwenk, Solid State Commun. 33,385 (1980). H.C. Montgomery, J. Appl. Phys. 42, 2971 (1971). A. Matttflessen, Rep. Brit. Ass. 32,144 (1862). C.K. Chiang, M.J. Cohen, A.F. Garito & A.J. Heeger, Solid State Commun. 18, 1451 (1976). J.T. Schriempf, J. Phys. Chem. Solids 28, 2581 (1967). A.C. Anderson, R.E. Peterson & J.E. Robinchaux, Phys. Rev. Lett. 20,459 (1968). J.C. Garland & R. Bowers, Phys. Rev. Lett. 21, 1007 (1968). R. Hartman, Phys. Rev. 181,1070(1969). W.E. Lawrence & J.W. Wilkins, Phys. Rev. B7, 2317 (1973). A. Oshiyama, K. Nakao & H. Kamimura, J. Phys. Soc. Japan 45, 1136 (1978). W. Beyer, W.D. Gill & G.B. Street, Solid State Commun. 23,577 (1977). K. Kaneto, M. Yamamoto, K. Yoshino & Y. Inuishi, Solid State Commun. 26, 311 (1978).