PHYSICAL REVIEW B

VOLUME 60, NUMBER 7

15 AUGUST 1999-I

Pressure effect on large magnetoresistance in the lower charge-density-wave transition of NbSe3
Syuma Yasuzuka, Yoshitoshi Okajima, Satoshi Tanda, and Kazuhiko Yamaya
Department of Applied Physics, Hokkaido University, Kita-ku, Sapporo 060-8628, Japan

Nao Takeshita and Nobuo Môri
The Institute for Solid State Physics, The University of Tokyo, Roppongi, Minato-ku, Tokyo 106-8666, Japan
共Received 18 December 1998兲
A large magnetoresistance appearing below the T c2 -CDW 共charge-density wave兲 transition temperature inNbSe3 has been studied under various pressures including pressure above the critical pressure where theT c2 -CDW phase is suppressed totally. The large magnetoresistance appears as long as the T c2 -CDW phase
exists. However, when the phase is suppressed totally by high pressure, neither large magnetoresistance nor
any anomalies are induced by the magnetic field up to 12 T, suggesting that it is negative for the formation ofa magnetic-field-induced CDW. The origin of the large magnetoresistance is discussed in terms of normal
carriers on the ungapped Fermi surface created on the CDW transition compared with the pressure-induced
magnetoresistance observed newly above T c2 . 关S0163-1829共99兲13227-2兴

I. INTRODUCTION

Niobium triselenide, NbSe3, which is known as a typicalquasi-one-dimensional 共Q1D兲 metal, exhibits two incommensurate charge-density-wave 共CDW兲 transitions at T c1
⫽142 K and T c2 ⫽58 K. 1–3 In most CDW materials, the formation of a CDW gap results in a complete destruction of theFermi surface, ending in a semiconducting ground state attemperatures below the transition. However, NbSe3 exhibitsa metallic or rather a semimetallic behavior at the lowtemperature regime. This has been understood by the existence of normal carriers in small pockets created by the two
CDW phase transitions. Band calculations4,5 of NbSe3 by
Shima and Kamimura demonstrate that the T c1 -CDW transition is attributable to a nearly perfect nesting between two
quasiparallel sheets of the Fermi surface, while theT c2 -CDW transition is due to an imperfect nesting of theremaining part of the Fermi surface. In fact, largeShubnikov–de Haas oscillations due to electron and hole ellipsoidal pockets have been observed at low temperatures
well below T c2 . 6 So it is accepted that the ground state of
NbSe3 is a semimetallic CDW state at low temperatures.
The study of the magnetic-field dependence of CDW in
NbSe3 has received considerable attention since the discovery of a large magnetoresistance below the T c2 -CDW transition by Coleman et al.6,7 They observed that when a magnetic field is applied perpendicular to the high conductivity
axis, the large magnetoresistance appears just below theT c2 -CDW transition and increases rapidly with decreasing
temperature, and its value is above 400% at low temperatures around 10 K. It was also found that the large magnetoresistance is very anisotropic to the direction of the appliedmagnetic field, suggesting that the orbital response of theelectrons to the magnetic field plays an important role.6
Balseiro and Falicov8,9 proposed a theory in which themagnetic field constrained the electronic motion to improve
the nesting condition of a Q1D Fermi surface and resulted inthe enhancement of the CDW gap. Similar models have been
accepted as a standard model for a formation mechanism of0163-1829/99/60共7兲/4406共4兲/$15.00

PRB 60the field-induced spin-density-wave 共SDW兲 observed in Q1D
organic conductors.10 Many transport experiments such as
narrow-band noise,11,12 Hall effect,13 and the thermopower14
have been tried in the transverse magnetic fields to investigate whether the CDW order parameter of NbSe3 is enhanced by the magnetic field. However, these results werenegative for the change in the CDW order parameter withmagnetic field.
In addition to the transport data, recently Kiryukhin
et al.15 have performed an x-ray-scattering study in magnetic
fields up to 10 T to investigate a magnetic-field-induced shiftof the nesting vector and the T c2 -CDW order parameter in
NbSe3. They found that there was ⌬q b /q b ⭐2.5⫻10⫺3 on
the magnetic-field-induced shift of the nesting vector of theT c2 -CDW, and the magnetic-field dependence of theT c2 -CDW order parameter was independent on the magnetic
field to within 10%. These results may also be negative forthe change in the CDW order parameter with magnetic field.
Both the results of the magnetotransport and the x-ray scattering lead us to the prediction in which the large magnetoresistance appearing below T c2 could be simply explained byconsidering light carriers in small ungapped pockets of theFermi surface generated by the imperfect nesting on the formation of the T c2 -CDW state, as pointed out by Trittet al.11,12 However, quantitative estimates of such effects
have not yet been reported.
As shown in the P-T-H phase diagram of SDW in Q1D
organic conductors,10 the field-induced SDW phase appears
in the high magnetic field near the critical pressure where theSDW phase is suppressed totally in zero magnetic field. On
the other hand, although the P-T-H phase diagram of CDW
in NbSe3 is not yet settled, it is well known that in zeromagnetic field the T c2 -CDW phase of NbSe3 is suppressed
totally by pressure above the critical pressure of 7.5 kbar.16 It
is important to investigate magnetic-field effects on CDW ofNbSe3 in the region near the critical pressure in order to see
whether the CDW order parameter is changed by the magnetic field.
In this paper, we report on the experimental results on the4406©1999 The American Physical Society

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PRB 604407

FIG. 1. Temperature dependence of the resistance in the range
2–80 K at ambient pressure at H⫽0, 7, and 12 T.

FIG. 2. Temperature dependence of the resistance in the range
2–80 K at P⫽7.3⫾0.2 kbar at H⫽0, 7, and 12 T.

large magnetoresistance appearing at the T c2 -CDW transition as a function of temperature under various pressures
including pressure above the critical pressure, which suppresses totally the T c2 -CDW phase. It is found that neither
large magnetoresistance nor any anomalies appear in a highmagnetic field when the T c2 -CDW phase is totally suppressed. This is contrary to the case of the field-induced
SDW, supporting the idea that the origin of the large magnetoresistance may be due to light carriers in small pockets
created at T c2 rather than the enhancement of the CDW gap
with magnetic field. Furthermore, we find newly a pressureinduced magnetoresistance which appears from a temperature well above T c2 , although the value is two orders smaller
than that of the large magnetoresistance below T c2 . The origin is discussed with comparing behaviors of the large magnetoresistance.

The magnetic fields enhance the resistance anomaly associated with the formation of the lower CDW state. It is notedthat the large magnetoresistance appears as soon as theT c2 -CDW phase is formed, and it is negligibly small above
T c2 . These results agree well with previous results.6,7 T c2 isindependent of the magnetic fields within our experimental
error of ⫾0.5 K. This is not inconsistent with previous results by Coleman et al., in which the T c2 increases only by
0.5 K, or less, in a field in excess of 20 T.6,7 Thus, T c2
remains essentially unchanged by magnetic fields.
Figure 2 shows the temperature dependence of the resistance in the magnetic fields under pressure at P⫽7.3⫾0.2 kbar. The lower CDW transition is observed at T c2
⫽25 K under zero magnetic field. The large magnetoresistance is also observed below T c2 under pressure. We findthat the temperature where the large magnetoresistance appears runs after T c2 , which decreases with increasing pressure. The value of T c2 under various pressures is found to bealmost constant to the magnetic field up to 12 T. This result
is contrary to the case of the field-induced SDW, whose transition temperature strongly depends on magnetic fields.10
Moreover, it is found under pressure that a small enhancement of the resistance with the magnetic fields is observed
even above T c2 . The small magnetoresistance above T c2tends to increase with increasing pressure. So we call it thepressure-induced magnetoresistance.
Figure 3 shows the temperature dependence of the resistance R and its temperature derivative dR/dT for 共a兲 H⫽0 T and 共b兲 H⫽12 T under applied pressure at P⫽8.3⫾0.8 kbar, which is larger than the critical pressure 共7.5kbar兲 of the T c2 -CDW phase.16 In zero magnetic field 关Fig.
3共a兲兴, there is no anomaly associated with the T c2 -CDW
phase in both curves of R versus T and dR/dT versus T. At
the same time, the superconductivity occurs at T s ⫽2.5 K.
Here, the superconducting transition temperature T s is defined as the temperature where the resistance becomes onehalf of the resistance in the normal state. The value of T s isslightly smaller than that of the earlier result,16 which may be
due to pressure inhomogeneity in a pressure cell. In the highmagnetic field 关Fig. 3共b兲兴, we also find no sign for the superconductivity and no anomaly associated with the formation

II. EXPERIMENTThe NbSe3 crystals were grown by vapor transport insealed evacuated quartz tubes using Nb wire of 99.9% purity
and Se shots of 99.999% and heated to 740 °C for two weeks
at a temperature gradient of approximately 1 °C/cm. Thepurecrystalgave
residualresistanceratiosR(300 K)/R(4.2 K) in the range 50–60. The resistance ofNbSe3 was measured by a usual four-probe dc method,where a current is parallel to the b axis and a magnetic field
is parallel to the c axis. The samples were attached to fourgold wires with Dupont silver paint 共No. 4929兲. A superconducting magnet was used for magnetic fields in the range
0–12 T. Pressures were generated by use of a WC piston anda beryllium-copper clamp type cylinder with the internal diameter of 6 mm ␾. Transmitting liquid was a 1:1 mixture ofFluorinert FC70 and FC77. Pressures were estimated fromthe pressure dependence of T c1 and T c2 in NbSe3 based on aprevious result.16
III. RESULTS AND DISCUSSION

Figure 1 shows the temperature dependence of the resistance of NbSe3 in the magnetic fields at ambient pressure.

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FIG. 3. Temperature dependence of the resistance R and its
temperature derivative dR/dT at 共a兲 H⫽0 T and 共b兲 H⫽12 T at
P⫽8.3⫾0.8 kbar. The superconductivity appears at T s ⫽2.5 K at
H⫽0 T.

of the CDW gap induced by the magnetic field 共the fieldinduced CDW兲 over the whole temperature range measured.
This is contrary to the case of the field-induced SDW, whichappears in the region near the critical pressure,10 suggestingthat it is negative for the formation of the field-inducedCDW, at least within the magnetic field measured up to 12 T.
Figure 4 shows the temperature dependence of the magnetoresistance ⌬ ␳ / ␳ 0 under various pressures in the magnetic field of H⫽12 T. In the case of the presence of theT c2 -CDW phase, the large magnetoresistances rapidly appear just below T c2 for the applied pressure from 0 to 7.3⫾0.2 kbar. These values are very large and are from 400%

PRB 60to 700% at low temperatures. At ambient pressure, ⌬ ␳ / ␳ 0 isvery small above T c2 , which is consistent with previous
reports.6,7 Under the pressures, however, the pressureinduced magnetoresistance is observed above T c2 and its appearance temperature increases with increasing pressure. Onthe other hand, in the case of the absence of the T c2 -CDWphase, the large magnetoresistance disappears totally under
the high pressure of P⫽8.3⫾0.8 kbar even in the strong fieldof H⫽12 T, while the pressure-induced magnetoresistance isobserved below 77 K. The temperature dependence of thepressure-induced magnetoresistance at P⫽8.3⫾0.8 kbar increases gradually as temperature decreases. The value at thelow-temperature range is below 200%, quite a bit smaller
than that of the large magnetoresistance, namely, the behavior of the pressure-induced magnetoresistance is found to beclearly different from that of the large magnetoresistance appearing below T c2 .
As shown by Shima and Kamimura,4,5 the T c2 -CDW transition is attributable to an imperfect nesting. As a result,small ungapped pockets of the Fermi surface are created below T c2 , while there are few pockets above T c2 because of anearly perfect nesting of the T c1 -CDW phase. It is natural toassume that carriers with light mass are generated at the ungapped Fermi surface below T c2 . If the large magnetoresistance is caused by these carriers, we can easily understandthe appearance of the large magnetoresistance below T c2 andthe absence of that above T c2 . Moreover, when theT c2 -CDW phase is suppressed totally under high pressure,the pockets will also disappear at the same time, leading to
the absence of the large magnetoresistance. Thus, we canexplain consistently our results by assuming the existence ofcarriers generated at the ungapped Fermi surface.
We discover the pressure-induced magnetoresistanceabove T c2 . The pressure-induced magnetoresistance is observed in spite of an absence of the T c2 -CDW phase and adisappearance of the large magnetoresistance. The pressureinduced magnetoresistance always appears above T c2 and its
temperature dependence is independent of the value of T c2 .
Band-structure calculations4,5 demonstrate that theT c1 -CDW transition corresponds to a nearly perfect nesting
between two quasiparallel sheets of the Fermi surface, while
the T c2 -CDW transition is due to an imperfect nesting. Thismeans that above T c2 there are few electron and hole pockets
in the T c1 -CDW phase. However, applying pressure leads toa collapse of the nearly perfect nesting of the Fermi surface
in the T c1 -CDW transition, that is, the decrease in the nesting size of the Fermi surface. As a result, the number of thenormal carriers will increase with increasing pressure. Thus,
it is considered that the pressure-induced magnetoresistancemight result from carriers in pockets created by an imperfectnesting induced by pressure. Here, it should be emphasizedthat our explanation for the pressure-induced magnetoresistance is not inconsistent with changes in the Fermi surface
associated with the chain corresponding to the T c1 -CDW,
which has been pointed out in the NMR studies by Shi
et al.17 and uniaxial stress studies under magnetic fields withfermiology changes by Kuh et al.18
IV. CONCLUSIONS

FIG. 4. Temperature dependence of the magnetoresistance⌬ ␳ / ␳ 0 at various pressures in the magnetic field of 12 T.

In conclusion, we have investigated the magnetoresistance as a function of temperature under various pressures inPRB 60

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NbSe3. It is found that the large magnetoresistance always
appears as long as the T c2 -CDW phase exists, while when
the T c2 -CDW phase is suppressed totally by high pressure,neither large magnetoresistance nor any field-induced
anomalies are observed even in the high magnetic field ofH⫽12 T. This suggests that the large magnetoresistancemight not result from the change in the CDW order parameter with magnetic field but rather from light carriers in small
ungapped pockets of the Fermi surface generated by an imperfect nesting of the Fermi surface. Furthermore, we discover the pressure-induced magnetoresistance above T c2 . It
can be explained by assuming the existence of carriers insmall pockets created by a pressure-induced imperfect nesting of the T c1 -CDW. These results may be attributable to thesemimetallic CDW character of NbSe3. We believe thatwhen the T c1 -CDW phase is suppressed totally by higher
pressure,19 the pressure-induced magnetoresistance will disappear similar to the case of the large magnetoresistance.
Such a study is in progress now.

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ACKNOWLEDGMENTS

The authors thank Takeshi Nakanishi and Masashi Ohashi
for experimental assistance and technical support. The authors acknowledge Yasushi Okayama for discussing the results in this work. A part of the experimental work was carried out at the Institute for Solid State Physics, the Universityof Tokyo.

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