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High magnetic field quantum transport in the low temperature density wave state of the purple bronze KMo6O17
Synthetic Metals, 55-57 (1993) 2725-2730
2725
HIGH MAGNETIC FIELD QUANTUM TRANSPORT IN THE LOW TEMPERATURE DENSITY WAVE STATE OF THE PURPLE BRONZE KMo~17
A. ROTGER +, C. SCHLENKER +, J. DUMAS +, J. MARCUS +, S. DUBOIS*, A. AUDOUARD*, L. BROSSARD*, J.P. ULMET*, S. ASKENAZY* (+) CNRS, Laboratoire d'Etudes des Propri6t6s Electroniques des Solides, BP166, 38042 Grenoble Cedex 9 (France) (*) CNRS, Service National des Champs Magn6tiques Puls6s et Laboratoire de Physique des Solides, INSA, Complexe Scientifique de Rangueil, 31077 Toulouse Cedex (France)
ABSTRACT The resistivity of the purple bronze KMo6017 has been studied between 1.9K and 300K with pulsed magnetic fields up to 37 T. Several anomalies are found on the curves Ap(B)/p and p(T) for different field orientations. Shubnikov-de Haas oscillations are observed at low temperatures. The results are discussed in relation with the Fermi surface topology.
INTRODUCTION The purple bronze KMo6017 belongs to the class of the low dimensional metallic molybdenum bronzes which show anisotropic Fermi surfaces and charge density wave (CDW) instabilities[ 1]. Among these compounds, KMo6017 is a quasi-two dimensional metal due to a trigonal layered structure including MoO6 octahedra separated by K + ions and MoO4 tetrahedra. The resistivity along the c-axis, perpendicular to the (a,b) conducting layers, is about 500 times higher than in the (a,b) plane. In this compound, a Peierls instability occurs at Tp = 110K towards a metallic state due to a partial opening of gaps on the Fermi surface. Band structure calculations, based on a quasi-two dimensional tight-binding approach, lead to three bands crossing the Fermi level [2]. They may be decomposed into three quasi-lD bands along the three symetrically equivalent directions in the (a*, b*) plane [3]. In this so-called hidden nesting model, one finds exactly the nesting vector (a*/2, 0,0) and equivalents, as observed by diffuse x-ray scattering. All physical properties[4,6] are consistent with a gap opening at 110K. The CDW properties of KMo6017 under hydrostatic pressure were also explored[7]. In contrast to other low dimensional CDW compounds, Tp increases with pressure. 0379-6779/93/$6.00
© 1993 - Elsevier Sequoia. All rights reserved
2726
In the CDW state, several properties measured with applied magnetic fields perpendicular to the layers are still unexplained. The magnetic susceptibility versus temperature shows a minimum at -70K and a maximum at -20K for fields parallel to the c-axis[4]. It has been suggested that a spin density wave instability may take place at Ta - 20K in low fields. Hall effect measurements [5,8] indicate an electron type conductivity above Tp and a hole type one below Tp . The large anisotropic positive magnetoresistance observed below Tp has been attributed to the effect of the magnetic field on the closed orbits related to the small electron and hole pockets left at the Fermi surface by the CDW gap openings[l]. While the magnetotransport of quasi-one dimensional metals hag been extensively studied, the field dependent properties of quasi-two dimensional metals have received little attention. Only some layered dichalcogenides have been studied under a magnetic field ; their large positive magnetoresistance has been attributed to magnetic breakdown through CDW gaps [9]. In an effort to clarify the magnetotransport of K M o 6 O I 7 , we have performed high field measurements, up to 37T and down to 1.9K using the pulsed fields provided by the Service National des Champs MagnEtiques Puls6s at Toulouse. Preliminary results are given in Ref.[10]. EXPERIMENTAL RESULTS The crystals were grown by the conventional electrocrystallization method, as described elsewhere [6]. The electrical resistance has been measured with the four-contact method in pulsed fields up to 37T, as described in Ref.[11]. The current was passed in the (a,b) plane and the applied field was either perpendicular or parallel to the layers. Figure 1 shows recordings of the resistivity as a function of temperature at different magnetic fields, perpendicular to the applied current and parallel to the layers. The magnetoresistance is extremely large below - l l 0 K . An increase of the slope of the curve p(T) is observed at ~ 26K, whatever the magnetic field. This behaviour might be related to an instability taking place at this temperature. Figure 2 shows the resistivity curves as a function of temperature obtained for magnetic fields perpendicular to the layers. The kink at - 26K is still observed. A new and unexplained bump appears around 150K. ....
10
, ....
I ....
~ ....
i ....
t
. . . .
7
c
8 !
=b
6
'i
m-I
[]
37T
•
30T
0
20T
•
5T
'
0T
, ....
, ....
, ....
, ....
~ 0
""
4
."
:'-"
.'-"""
1
0
.... 0
, ....
B,c
o
"n~~q~o,~" ~ 2
....
6
= .... i .... F .... I .... I .... SO 100 150 200 250 300
• o
0
•
0
ST OT
~ .....................
50
100
150
200
250
T(K) T(K)
Figure 1. Resistivity as a function of temperature for magnetic field in the plane of the layers. Figure 2. Same as in Figure 1 for magnetic field parallel to the c-axis.
300
2727
Figure 3 shows the transverse magnetoresistance at low temperatures for magnetic fields perpendicular to the layers. Superimposed on a large positive magnetoresistance four pronounced and broad oscillations are observed at 5T, 8.2T, 22T and 33T respectively. At 22T, the oscillatory part of the magnetoresistance amounts to -50% of the normal magnetoresistance. The curves of the magnetoresistance versus B, with B parallel to the c-axis, exhibit a downwards curvature for temperatures T< 100K, and upwards curvature above - 100K, as shown in Figure 4. 25
20 o_ 15 ov 10
.g 5
0 0
5
10
15
20 25 B(Tesla)
30
35
40
Figure 3. Oscillatory behavior of the transverse magnetoresistance at low temperatures. Field parallel to the c-axis.
15
1 .... , .... , ..., ....
, ,.
-'"'1''"1""1''"1""1'"'1''"1"
,
. . . .
,
. . . .
,
.... ,...
0.8 c,.
10 o.
0.6
o '
0.4
5 50K
0.2
0
0 0
5
10
15
20
25
30
35
40
5
10
B('resla)
15
20
25
30
35
40
B(Tcsla)
Figure 4. Magnetoresistance as a function of temperature below 100K (a) and above(b). For a magnetic field in the plane of the layers, the magnetoresistance curves show a downwards curvature below - 26K and upwards above 26K, as shown in Figure 5. In this configuration, no oscillation of the magnetoresistance is observed. For fields parallel and perpendicular to the c-axis, a semi-classical fit
Ap/p =
(l~effB)2 is obtained
below a critical field which decreases as the temperature decreases. For T< 100K, the temperature dependence of the effective mobility I~eff is found to obey the empirical law: P-eff = Aexp(-T/To) with To = 30K for B parallel to the c-axis and To= 38K for B perpendicular to the c-axis, as shown in Figure 6. The effective mobility laeff is extremely large : for example, ~.teff= 7x103cm2/Vs at 25K, for B parallel to the c-axis.
2728 14
0.8
12
0.7 tlal
. . . .
I0
0.5
8
Ct. v
6
,
. . . .
,
. . . .
,
. . . .
,
c
. . . .
,
.
.
.
.
.
.
.
.
.
77~
I
1
/
] 100K
i
4
•
2
~ 5 o ~
0
. . . .
0.4
v
%
,
l
5
26K
10
0.2 0.1 0
Q.
,
15 20 B(Tesla)
25
30
35
4O
B(Tesla)
Figure 5. Magnetoresistance curves for magnetic field in the plane of the layers below - 2 6 K (a) and above (b). ., , Q I i , , i , ~ , i , , , i , , , i , , , "~" 0.8 Q,kB//c 0.6 ~.~ 0.4 0.2
,,,,,, 0
20
S"?,,'-?-r7~-,-~-,-~,,, 40
60
8o
~00
120
T(K) Figure 6. Effective mobility as a function of temperature.
DISCUSSION AND CONCLUSIONS We ascribe the oscillatory behavior of the magnetoresistance shown in Figure 3 to Shubnikovde Haas (SdH) oscillations, due to oscillations of the density of states at the Fermi level, caused by quantization of electron energy in the presence of the magnetic field. According to this model, the oscillations obey the formula: I/Bn = (n-v'/) (1/BF) where BF = l~A/rce with A the extremal cross sectional area of the Fermi surface perpendicular to B and 0
2729
w h e r e TD is the Dingle temperature. A good fit to the data is obtained for m* ~0.1 m0 but a significant departure from the fit appears above -30K. This may be related to the kink in the magnetoresistance curves shown in Figure 1. 0.3
I
I
I
i
[.-, 0.25
T= 1.9K
0.2
Y
0.15 0.1 0.05
I
0
I
0
I
1
quantum
2
number
n
Figure 7. Reciprocal magnetic fields 1/Bn corresponding to the maxima of the oscillations as a function of the quantum number n.T= 1.9K. 0.7
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
0.6 0.5 0.4 0.3 0.2 0.1 0 10
20
30
40
50
60
70
T(K)
Figure 8. Amplitude of the n= 2 oscillation corresponding to Bn= 8.2T as a function of temperature.Solid curve is a fit to the data with A0 = 0.66, mr = 0.095, as described in the text. In summary, our results confh-m the anisotropic character of this compound. The resistivity kink and other anomalies observed previously at 26K under magnetic field could be related either to a field induced readjustment of the nesting vector of the CDW or to the onset of an additional density wave instability, possibly spin density wave.Further experiments are in progress to elucidate this point. REFERENCES 1 "Low Dimensional Elecla'onic Properties of Molybdenum Bronzes and Oxides", ed. C. Sehlenker (Kluwer Pub. , 1989). 2 M.H. Whangbo, E. Canadell, C. Schlenker, J. Am. Chem. Soc. 109 (1987) 6308. 3 M.H. Whangbo, E. Canadell, P. Foury, J.P. Pouget, Science 252 (1991) 96.
2730
4 R. Buder, J. Devenyi, J. Dumas, J. Marcus, J. Mercier, C. Schlenker, J. Phys. Lett. 43 (1982) L59. 5 E. Bervas, R.W. Cochrane, J. Dumas, C. Filippini, J. Marcus, C. Schlenker, in "Charge Density Waves in Solids", Lecture Notes in Physics, Vol.217 (Springer Verlag, 1984), p. 144. 6 C. Schlenker, J. Dumas, C. Filippini, H. Guyot, J. Marcus, G. Fourcaudot, Philos. Mag. 52 (1985) 643. 7 J. Beille, A. Rotger, J. Dumas, C. Schlenker, Philos. Mag. Lett. 64 (1991) 221. 8 C. Schlenker, J. Dumas, C. Filippini, M. Boujida, Phvsica Scriota T 29 (1989) 55. 9 M. Naito, S. Tanaka, J. Phvs.Soc.Jnn 51 (1982) 219; 228. 10 A. Rotger, J. Dumas, J. Marcus, C. Se,lalenker, J.P. Ulmet, A. Audouard, S. Askenazy, Synth. Metals 41-43 (1991) 4013. 11 J.P. Ulmet, A. Khmou, P. Auban, L. Bach~re, Solid State Commun. 58 (1986) 753. 12 S. Askenazy, in "New Developments in Semiconductors", Part IV, ed. P.R. Wallace, R. Harris, M.J.Zuckermann, Nooddhoff Int. Pub., Leyden (1990); A.B. Pippard,"Magnetoresistance in metals", Cambridge University Press (1989), p.36.
2725
HIGH MAGNETIC FIELD QUANTUM TRANSPORT IN THE LOW TEMPERATURE DENSITY WAVE STATE OF THE PURPLE BRONZE KMo~17
A. ROTGER +, C. SCHLENKER +, J. DUMAS +, J. MARCUS +, S. DUBOIS*, A. AUDOUARD*, L. BROSSARD*, J.P. ULMET*, S. ASKENAZY* (+) CNRS, Laboratoire d'Etudes des Propri6t6s Electroniques des Solides, BP166, 38042 Grenoble Cedex 9 (France) (*) CNRS, Service National des Champs Magn6tiques Puls6s et Laboratoire de Physique des Solides, INSA, Complexe Scientifique de Rangueil, 31077 Toulouse Cedex (France)
ABSTRACT The resistivity of the purple bronze KMo6017 has been studied between 1.9K and 300K with pulsed magnetic fields up to 37 T. Several anomalies are found on the curves Ap(B)/p and p(T) for different field orientations. Shubnikov-de Haas oscillations are observed at low temperatures. The results are discussed in relation with the Fermi surface topology.
INTRODUCTION The purple bronze KMo6017 belongs to the class of the low dimensional metallic molybdenum bronzes which show anisotropic Fermi surfaces and charge density wave (CDW) instabilities[ 1]. Among these compounds, KMo6017 is a quasi-two dimensional metal due to a trigonal layered structure including MoO6 octahedra separated by K + ions and MoO4 tetrahedra. The resistivity along the c-axis, perpendicular to the (a,b) conducting layers, is about 500 times higher than in the (a,b) plane. In this compound, a Peierls instability occurs at Tp = 110K towards a metallic state due to a partial opening of gaps on the Fermi surface. Band structure calculations, based on a quasi-two dimensional tight-binding approach, lead to three bands crossing the Fermi level [2]. They may be decomposed into three quasi-lD bands along the three symetrically equivalent directions in the (a*, b*) plane [3]. In this so-called hidden nesting model, one finds exactly the nesting vector (a*/2, 0,0) and equivalents, as observed by diffuse x-ray scattering. All physical properties[4,6] are consistent with a gap opening at 110K. The CDW properties of KMo6017 under hydrostatic pressure were also explored[7]. In contrast to other low dimensional CDW compounds, Tp increases with pressure. 0379-6779/93/$6.00
© 1993 - Elsevier Sequoia. All rights reserved
2726
In the CDW state, several properties measured with applied magnetic fields perpendicular to the layers are still unexplained. The magnetic susceptibility versus temperature shows a minimum at -70K and a maximum at -20K for fields parallel to the c-axis[4]. It has been suggested that a spin density wave instability may take place at Ta - 20K in low fields. Hall effect measurements [5,8] indicate an electron type conductivity above Tp and a hole type one below Tp . The large anisotropic positive magnetoresistance observed below Tp has been attributed to the effect of the magnetic field on the closed orbits related to the small electron and hole pockets left at the Fermi surface by the CDW gap openings[l]. While the magnetotransport of quasi-one dimensional metals hag been extensively studied, the field dependent properties of quasi-two dimensional metals have received little attention. Only some layered dichalcogenides have been studied under a magnetic field ; their large positive magnetoresistance has been attributed to magnetic breakdown through CDW gaps [9]. In an effort to clarify the magnetotransport of K M o 6 O I 7 , we have performed high field measurements, up to 37T and down to 1.9K using the pulsed fields provided by the Service National des Champs MagnEtiques Puls6s at Toulouse. Preliminary results are given in Ref.[10]. EXPERIMENTAL RESULTS The crystals were grown by the conventional electrocrystallization method, as described elsewhere [6]. The electrical resistance has been measured with the four-contact method in pulsed fields up to 37T, as described in Ref.[11]. The current was passed in the (a,b) plane and the applied field was either perpendicular or parallel to the layers. Figure 1 shows recordings of the resistivity as a function of temperature at different magnetic fields, perpendicular to the applied current and parallel to the layers. The magnetoresistance is extremely large below - l l 0 K . An increase of the slope of the curve p(T) is observed at ~ 26K, whatever the magnetic field. This behaviour might be related to an instability taking place at this temperature. Figure 2 shows the resistivity curves as a function of temperature obtained for magnetic fields perpendicular to the layers. The kink at - 26K is still observed. A new and unexplained bump appears around 150K. ....
10
, ....
I ....
~ ....
i ....
t
. . . .
7
c
8 !
=b
6
'i
m-I
[]
37T
•
30T
0
20T
•
5T
'
0T
, ....
, ....
, ....
, ....
~ 0
""
4
."
:'-"
.'-"""
1
0
.... 0
, ....
B,c
o
"n~~q~o,~" ~ 2
....
6
= .... i .... F .... I .... I .... SO 100 150 200 250 300
• o
0
•
0
ST OT
~ .....................
50
100
150
200
250
T(K) T(K)
Figure 1. Resistivity as a function of temperature for magnetic field in the plane of the layers. Figure 2. Same as in Figure 1 for magnetic field parallel to the c-axis.
300
2727
Figure 3 shows the transverse magnetoresistance at low temperatures for magnetic fields perpendicular to the layers. Superimposed on a large positive magnetoresistance four pronounced and broad oscillations are observed at 5T, 8.2T, 22T and 33T respectively. At 22T, the oscillatory part of the magnetoresistance amounts to -50% of the normal magnetoresistance. The curves of the magnetoresistance versus B, with B parallel to the c-axis, exhibit a downwards curvature for temperatures T< 100K, and upwards curvature above - 100K, as shown in Figure 4. 25
20 o_ 15 ov 10
.g 5
0 0
5
10
15
20 25 B(Tesla)
30
35
40
Figure 3. Oscillatory behavior of the transverse magnetoresistance at low temperatures. Field parallel to the c-axis.
15
1 .... , .... , ..., ....
, ,.
-'"'1''"1""1''"1""1'"'1''"1"
,
. . . .
,
. . . .
,
.... ,...
0.8 c,.
10 o.
0.6
o '
0.4
5 50K
0.2
0
0 0
5
10
15
20
25
30
35
40
5
10
B('resla)
15
20
25
30
35
40
B(Tcsla)
Figure 4. Magnetoresistance as a function of temperature below 100K (a) and above(b). For a magnetic field in the plane of the layers, the magnetoresistance curves show a downwards curvature below - 26K and upwards above 26K, as shown in Figure 5. In this configuration, no oscillation of the magnetoresistance is observed. For fields parallel and perpendicular to the c-axis, a semi-classical fit
Ap/p =
(l~effB)2 is obtained
below a critical field which decreases as the temperature decreases. For T< 100K, the temperature dependence of the effective mobility I~eff is found to obey the empirical law: P-eff = Aexp(-T/To) with To = 30K for B parallel to the c-axis and To= 38K for B perpendicular to the c-axis, as shown in Figure 6. The effective mobility laeff is extremely large : for example, ~.teff= 7x103cm2/Vs at 25K, for B parallel to the c-axis.
2728 14
0.8
12
0.7 tlal
. . . .
I0
0.5
8
Ct. v
6
,
. . . .
,
. . . .
,
. . . .
,
c
. . . .
,
.
.
.
.
.
.
.
.
.
77~
I
1
/
] 100K
i
4
•
2
~ 5 o ~
0
. . . .
0.4
v
%
,
l
5
26K
10
0.2 0.1 0
Q.
,
15 20 B(Tesla)
25
30
35
4O
B(Tesla)
Figure 5. Magnetoresistance curves for magnetic field in the plane of the layers below - 2 6 K (a) and above (b). ., , Q I i , , i , ~ , i , , , i , , , i , , , "~" 0.8 Q,kB//c 0.6 ~.~ 0.4 0.2
,,,,,, 0
20
S"?,,'-?-r7~-,-~-,-~,,, 40
60
8o
~00
120
T(K) Figure 6. Effective mobility as a function of temperature.
DISCUSSION AND CONCLUSIONS We ascribe the oscillatory behavior of the magnetoresistance shown in Figure 3 to Shubnikovde Haas (SdH) oscillations, due to oscillations of the density of states at the Fermi level, caused by quantization of electron energy in the presence of the magnetic field. According to this model, the oscillations obey the formula: I/Bn = (n-v'/) (1/BF) where BF = l~A/rce with A the extremal cross sectional area of the Fermi surface perpendicular to B and 0
2729
w h e r e TD is the Dingle temperature. A good fit to the data is obtained for m* ~0.1 m0 but a significant departure from the fit appears above -30K. This may be related to the kink in the magnetoresistance curves shown in Figure 1. 0.3
I
I
I
i
[.-, 0.25
T= 1.9K
0.2
Y
0.15 0.1 0.05
I
0
I
0
I
1
quantum
2
number
n
Figure 7. Reciprocal magnetic fields 1/Bn corresponding to the maxima of the oscillations as a function of the quantum number n.T= 1.9K. 0.7
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
,
. . . .
0.6 0.5 0.4 0.3 0.2 0.1 0 10
20
30
40
50
60
70
T(K)
Figure 8. Amplitude of the n= 2 oscillation corresponding to Bn= 8.2T as a function of temperature.Solid curve is a fit to the data with A0 = 0.66, mr = 0.095, as described in the text. In summary, our results confh-m the anisotropic character of this compound. The resistivity kink and other anomalies observed previously at 26K under magnetic field could be related either to a field induced readjustment of the nesting vector of the CDW or to the onset of an additional density wave instability, possibly spin density wave.Further experiments are in progress to elucidate this point. REFERENCES 1 "Low Dimensional Elecla'onic Properties of Molybdenum Bronzes and Oxides", ed. C. Sehlenker (Kluwer Pub. , 1989). 2 M.H. Whangbo, E. Canadell, C. Schlenker, J. Am. Chem. Soc. 109 (1987) 6308. 3 M.H. Whangbo, E. Canadell, P. Foury, J.P. Pouget, Science 252 (1991) 96.
2730
4 R. Buder, J. Devenyi, J. Dumas, J. Marcus, J. Mercier, C. Schlenker, J. Phys. Lett. 43 (1982) L59. 5 E. Bervas, R.W. Cochrane, J. Dumas, C. Filippini, J. Marcus, C. Schlenker, in "Charge Density Waves in Solids", Lecture Notes in Physics, Vol.217 (Springer Verlag, 1984), p. 144. 6 C. Schlenker, J. Dumas, C. Filippini, H. Guyot, J. Marcus, G. Fourcaudot, Philos. Mag. 52 (1985) 643. 7 J. Beille, A. Rotger, J. Dumas, C. Schlenker, Philos. Mag. Lett. 64 (1991) 221. 8 C. Schlenker, J. Dumas, C. Filippini, M. Boujida, Phvsica Scriota T 29 (1989) 55. 9 M. Naito, S. Tanaka, J. Phvs.Soc.Jnn 51 (1982) 219; 228. 10 A. Rotger, J. Dumas, J. Marcus, C. Se,lalenker, J.P. Ulmet, A. Audouard, S. Askenazy, Synth. Metals 41-43 (1991) 4013. 11 J.P. Ulmet, A. Khmou, P. Auban, L. Bach~re, Solid State Commun. 58 (1986) 753. 12 S. Askenazy, in "New Developments in Semiconductors", Part IV, ed. P.R. Wallace, R. Harris, M.J.Zuckermann, Nooddhoff Int. Pub., Leyden (1990); A.B. Pippard,"Magnetoresistance in metals", Cambridge University Press (1989), p.36.