PHYSICAL REVIEW B 67, 024423 共2003兲

Appearance of the spin-Peierls phase under pressure in Cu1Àx Mgx GeO3
T. Masuda,1 D. Yano,1 R. Kuroda,1 K. Uchinokura,1 H. Kuroe,2 T. Sekine,2 Y. Katsuki,3 K. Ohwada,3,* Y. Fujii,3
H. Nakao,4,† and Y. Murakami4,†
1

Department of Advanced Materials Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan2
Department of Physics, Sophia University, 7-1 Kioi-cho, Chiyoda-ku, Tokyo 102-8854, Japan3
Neutron Scattering Laboratory, Institute for Solid State Physics, The University of Tokyo, 106-1 Shirakata,
Tokai, Ibaraki 319-1106, Japan
4
High Energy Accelerator Research Organization 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan
共Received 14 August 2002; revised manuscript received 12 November 2002; published 27 January 2003兲
The effect of pressure is studied on highly Mg-doped CuGeO3 , which at ambient pressure shows anantiferromagnetic transition but no spin-Peierls transition. The magnetic susceptibility under pressure wasmeasured; the broad maximum around 60 K shifts to lower temperatures and the spin-Peierls 共SP兲 transition
reappears. The temperature-concentration phase diagram at various pressures was constructed and it was foundthat the SP phase region enlarges with pressure. These results mean that the enhancement of frustration due tonearest-neighbor and next-nearest-neighbor exchange interactions overcomes the effect of interchain interaction, and that the spin-Peierls phase is more stabilized than the paramagnetic or antiferromagnetic phases. In
the temperature-pressure-concentration phase diagram, the compositional phase transition between the
dimerized-antiferromagnetic phase and the uniform-antiferromagnetic phase is second order at P⬎0.2 GPa,but first order at P⬍0.2 GPa. We propose that the change in order of this transition is also due to enhancementof the frustration. We show an example of frustration effects in a one-dimensional quantum spin system.
DOI: 10.1103/PhysRevB.67.024423

PACS number共s兲: 75.30.Kz, 75.10.Jm, 75.50.Ee

I. INTRODUCTION

CuGeO3 共Ref. 1兲 is one of the most interesting materials
for studying quantum spin systems. Unlike many other spinPeierls 共SP兲 materials it is an inorganic cuprate allowing the
growth of high-quality single crystals and impurity-doped
crystals. This material is well known as a spin-Peierls material, but it has further features. One is a relatively large interchain interaction compared to the intrachain interaction关 J ⬘ /J⬃0.1 共Ref. 2兲兴, and the system appears to lie near thephase boundary between the SP and Néel phases in the phase
diagram of spin-phonon coupling vs interchain interaction.3
This may be why an exotic antiferromagnetic 共AF兲 phase isobserved in Cu1⫺x M x GeO3 (M ⫽Zn, Ni, Mn) andCuGe1⫺y Siy O3 . 4,5 The novelty of this AF phase is that the SP
and AF order parameters coexist below the AF transition
temperature, a fact confirmed by inelastic neutron
scattering.6,7 The ground state of the impurity-doped SP system has been studied theoretically, and the envelopes of thestaggered moment and the lattice displacement of dimerization can be expressed by elliptic functions; they are in longrange order 共LRO兲.8 This model is consistent with ␮SRexperiments.9
By producing many high-quality single crystals and performing composition analysis, Masuda et al. recently foundthat Mg2⫹ is the best nonmagnetic impurity for homogeneous impurity-doped CuGeO3 . They obtained a temperaturevs concentration phase diagram10–13 and found that the SP
phase is suppressed drastically by impurity doping and thatSP LRO disappears at a critical concentration (x c ). At x c a
discontinuity was observed in AF temperature, suggesting acompositional first-order phase transition between the exotic
AF phase—the dimerized-antiferromagnetic 共DAF兲 phase,
which has both the SP and AF order parameters—and a con0163-1829/2003/67共2兲/024423共6兲/$20.00

ventional AF phase, the uniform-antiferromagnetic 共UAF兲
phase. A detailed study reveals that a separation of the DAF
and UAF phases exists around x c ; 0.027ⲏxⲏ0.023. 11,13,14
Another unique feature is that this material exhibits thefrustration of the interactions among spins. The angle of the
Cu-O2-Cu bond is about 100°, 15 which is close to 90°, and
it is expected that the next-nearest-neighbor 共NNN兲 interaction (J NNN) cannot be neglected. For simplicity we neglect
the interchain interaction here. If the NNN interaction is antiferromagnetic it competes with the nearest-neighbor 共NN兲interaction (J NN), and frustration of interactions exists. Frustration in CuGeO3 was proposed to explain the discrepancy
in the magnetic susceptibility between experiment and thetheoretical Bonner-Fisher curve in the high-temperature
region.16,17 The Hamiltonian of CuGeO3 above the spinPeierls transition temperature (T SP), is therefore approximated as
H⫽J兺i 共 Si •Si⫹1 ⫹ ␣ Si •Si⫹2 兲 ,共1兲

by considering only intrachain interactions. Here ␣⫽J NNN /J NN , and ␣ is reported to be 0.24 共Ref. 16兲 ⬃0.36
共Ref. 17兲. It is well known that a frustrated spin system has afinite spin gap above a critical value of ␣ ( ␣ c ). 18 For a onedimensional 共1D兲 system ␣ c is reported to be 0.24⬃0.30
共Refs. 19–21兲, and in CuGeO3 ␣ is quite close to ␣ c . The
reason that ␣ for CuGeO3 seems to exceed ␣ c is that Eq. 共1兲
neglects the interchain interaction. The values of ␣ c given in
Refs. 19–21 are for an ideal 1D system. To claim just theexistence of rather large ␣ , however, the simple model
Hamiltonian Eq. 共1兲 would not be inappropriate as Refs. 16
and 17 discussed. Some experimental results suggest that J is
suppressed and that ␣ is enhanced under hydrostatic

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T. MASUDA et al.
TABLE I. Samples of Cu1⫺x Mgx GeO3 .
Sample
A
B
C
D
E
F
G

x
0.0
0.020 (⫾0.0002)
0.026 (⫾0.0002)
0.032 (⫾0.0003)
0.035 (⫾0.0003)
0.040 (⫾0.0004)
0.045 (⫾0.0004)

x⬍x c
x⬍x c
x⬃x c
x⬎x c
x⬎x c
x⬎x c
x⬎x c

pressure.22,23 The SP transition temperature is reported to increase with the pressure (dT SP /d P⫽4.8 K/GPa). 24 References 22 and 23 therefore claim that an increase in ␣ stabilizes the SP ground state, and a numerical study shows that
T SP increases with increasing ␣ . 25
The ground state of highly doped CuGeO3 is the Néelstate, but it should be close to the phase boundary between
the SP and the Néel phases. We may control ␣ by pressure,and the SP phase should appear even in highly doped
CuGeO3 . The present paper studies the effect of pressure in
Mg-doped CuGeO3 . We observe the reappearance of the SP
phase and obtain a temperature-pressure-concentration(T-P-x) phase diagram from the magnetic-susceptibility
measurements. The reappearance of the SP phase is verified
by the synchrotron x-ray diffraction. The phase diagramshows that the compositional phase transition above a criticalpressure is a second-order transition, but first order at ambient pressure.
II. EXPERIMENTAL DETAILSSingle crystals were prepared by the floating-zone
method. Composition analysis was performed by inductively
coupled plasma atomic emission spectroscopy. The compositions of Cu1⫺x Mgx GeO3 studied are x⫽0 共sample A兲,0.020 共sample B兲, 0.026 共sample C兲, 0.032 共sample D兲, 0.035
共sample E兲, 0.040 共sample F兲, and 0.045 共sample G兲. Sample
C is on the compositional phase boundary (x c ) in Ref. 11,
and shows the SP transition and the double AF transitions.
Samples D–G are above x c and show no SP transition inmagnetic susceptibility measurements 共see Table I兲. Magnetic susceptibility was measured using a commercial superconducting quantum interference device 共SQUID兲 magnetometer ( ␹ -Mag, Conductus, Ltd.兲. All measurements were
performed with the magnetic field along the crystallographic
c axis; the field strength was 1000 Oe. We used a hydrostatic
high-pressure microcell developed by Uwatoko et al.26 in acommercial SQUID magnetometer. The pressure at low temperature 共LT兲 was calibrated by measuring the superconducting transition temperature of Pb. The relation between thepressures at LT and at room temperature 共RT兲 is reproducible( P LT⬃ P RT⫺0.2 关 GPa兴 ). From susceptibility measurementsof undoped CuGeO3 we determined the pressure dependenceof the SP transition temperature; it increases linearly withpressure, a result consistent with previous experiment.24 Thisassures us that our pressure calibration at LT works well. The

FIG. 1. 共a兲 Magnetic susceptibility of sample D at 2 K⬍T⬍200 K. Solid lines show the susceptibility calculated from Eq.
共1兲. 共b兲 Detailed behavior of the magnetic susceptibility at differingpressures in the low-temperature region for sample E. A decrease
due to SP transition is clearly observed at P⭓0.021 GPa. Data areshifted vertically for clarity.

cell is made mainly of CuBe alloy, and is slightly magnetizedin the magnetic field. We therefore tested several CuGeO3 ’sof differing volume and found that 20 mg is necessary for themeasurement, implying that about 2⫻10⫺4 emu is the lower
limit for the pressure cell. X-ray-diffraction measurements
under hydrostatic pressure were performed at facilities
BL-1B and 4C of the Photon Factory 共KEK, Tsukuba兲. The
wavelength was tuned to 0.7 Å by a Si 共111兲 double-crystal
monochromator. A cylindrically shaped imaging plate wasused as a detector, and a diamond anvil cell was used as apressure cell. We calibrated the pressure at LT by measuring
the lattice constant of NaCl powder.
III. EXPERIMENTAL RESULTS

Figure 1共a兲 shows the magnetic susceptibility ␹ (T, P) of
sample D (x⫽0.032). ␹ (T,0.1 MPa) has a broad maximum
at 60 K; the behavior at high temperature is qualitatively thesame as that of undoped CuGeO3 . Application of hydrostaticpressure shifts the maximum in ␹ (T, P) to lower temperatures. The broad maximum of the magnetic susceptibility
arises from the development of AF short-range order, so that
this shift implies the suppression of intrachain interaction or
greater frustration of the interactions among spins.
The solid lines show the magnetic susceptibility calculated from Eq. 共1兲 when ␣ ⫽0.36 and J⫽160 K for 0.1 MPa
and when ␣ ⫽0.41 and J⫽150 K for 0.80 GPa. The fitting
parameters are determined such that the absolute values ofthe broad maximum of the susceptibility and of the temperature agree with the observations. The calculation is describedin detail in Ref. 27. The temperature intervals in the susceptibility measurement are 5 K, and the interval of ␣ in thefitting is 0.01. The accuracies of the fitting parameters are
therefore ⌬J⫽5 K and ⌬ ␣ ⫽0.01. The fit of the data to the
one-dimensional model 关Eq. 共1兲兴 is good, and we conclude
that application of hydrostatic pressure suppresses the intrachain interaction and enhances the frustration between NN
and NNN spin interactions in highly doped CuGeO3 , which024423-2

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APPEARANCE OF THE SPIN-PEIERLS PHASE UNDER . . .

shows no SP transition at ambient pressure.
The parameter ␣ seems to exceed the critical value ␣ c forthe appearance of the spin gap without dimerization.19–21
The reason is that we omitted the interchain interaction in thecalculation.17 Therefore, the absolute value of ␣ in our calculation itself is not of much importance but we can safely
conclude that the increase of ␣ with the applied pressure isgenuine.
According to Fig. 2 of Ref. 28, the spin-phonon coupling
term suppresses the magnetic susceptibility over the wholetemperature range. The magnetic susceptibility is independent of the hydrostatic pressure at Tⲏ130 K. We can therefore safely assume that the spin-phonon coupling is independent of the hydrostatic pressure.
␹ (T,0.80 GPa) shows a sudden drop around 10 K, but noanomaly is observed in ␹ (T,0.1 MPa). To study this feature
we measured the magnetic susceptibility under pressure in
more detail. Figure 1共b兲 shows ␹ (T, P) of sample E (x⫽0.035) at low temperatures. The zero of the ordinate is for␹ (T,0.1 MPa), and other data are shifted every⫹10⫺6 emu/g. For ␹ (T,0.1 MPa) a sharp peak is observed
at 4.5 K due to the AF transition; the transition temperature(T N) decreases monotonically with the pressure. The suppression of the AF phase is consistent with the result of thefitting of the susceptibility at high temperature seen in Fig.
1共a兲, since the decrease in J and the increase in ␣ both suppress the AF long-range order. Above T N , no anomaly isobserved at Pⱗ0.14 GPa but a slight decrease begins to bevisible at P⬃0.21 GPa. The magnitude of the decrease, andthe temperature, at which the susceptibility begins to decrease, increase with pressure at Pⲏ0.21 GPa.
The T SP value of lightly doped CuGeO3 is about 10 K,
and the pressure-induced anomaly in sample D or E apparently represents the SP transition. We, however, have to becareful in concluding this. In this material ␣ is close to thecritical value, and we observe enhancement in ␣ in Fig. 1共b兲.
If ␣ depends on temperature and goes beyond the criticalvalue with decreasing temperature, the spin gap without lattice dimerization 共pointed out by Haldane18兲 would occur at
low temperature. To settle the issue we performed thesynchrotron x-ray diffraction on sample E at P⫽0.1 MPaand 1.0 GPa.
In the inset of Fig. 2 we observe 共1/2, 1, 3/2兲 superlatticereflection at P⫽1.0 GPa, which corresponds to SP
dimerization29 and confirms the absence of the superlattice
peak at 0.1 MPa. The ratio of the superlattice peak intensity
at 9.0 K and P⫽1.0 GPa to that of undoped CuGeO3 at thesame temperature and ambient pressure was determined as
0.15 through intensity calibration based on the fundamental
reflections. The temperature dependence of the integrated
peak intensity is shown in Fig. 2. The peak intensity increases as the temperature decreases, and we obtained T SP
⬃15.2 K, which is consistent with the magneticsusceptibility measurements. This proves that pressure genuinely causes the SP transition in sample E.
We measured ␹ (T, P) for all samples and obtained theT-P phase diagrams for samples B–G, as shown in Fig. 3.
Monotonic increase of T SP’s is observed in all Mg-doped

FIG. 2. Superlattice peak intensity at 共1/2, 1, 3/2兲 in sample E at
P⫽1.0 GPa. The inset is the peak profile of a longitudinal scan at
0.1 MPa 共circles兲 and 1.0 GPa 共squares兲.

samples. In samples D–G the SP phase appears above a critical pressure ( P c ). The vertical dotted lines in Fig. 3 show
P c . In all samples T N decreases monotonically with increasing pressure. The concentration of sample C is the critical

024423-3

FIG. 3. The T-P phase diagram in samples B–G.

PHYSICAL REVIEW B 67, 024423 共2003兲

T. MASUDA et al.

concentration for the compositional phase transition between
the previously reported DAF and the UAF phases.10 Some ofus have reported the double peaks in ␹ (T) at AF
transitions,11 and they proposed that the phase separation of
the DAF and the UAF phases exists and that the phase transition between the DAF and the UAF phases is firstorder.10,11 In sample C, the higher-temperature transition disappears at about 0.2 GPa and the two peaks do not merge. In
sample D the discontinuity is seen at P c . On the other hand,
T N decreases monotonically in sample E over the wholepressure range, and no discontinuity is observed at P c . Thismeans that the compositional phase transition between the
DAF and UAF phases at xⲏ0.035 is a second-order phasetransition.
Figure 4 shows T-x phase diagrams at various pressures.
The vertical dotted lines indicate the phase boundary at thecritical concentration x c . The region of the SP phase enlarges with pressure; T SP increases, T N decreases, and thephase boundary between DAF and UAF phases increases
with pressure. This means that pressure stabilizes the SP
phase more than the paramagnetic or antiferromagnetic
phase in Cu1⫺x Mgx GeO3 .
At ambient pressure, two T N’s are observed in sample C(x⬃x c ). This is due to the phase separation between the
DAF and the UAF phases; the compositional phase boundary
between the DAF and the UAF phases corresponds to thissample, as reported previously.10,11,13,14 At ambient pressure
two T N’s are plotted at x⬃x c due to phase separation between the DAF and the UAF phases. At 0.2 GPa, on theother hand, there is no coexistence of T N1 and T N2 , but asudden increase in T N is apparent between x⫽0.035
and 0.040.

FIG. 4. T-x phase diagrams under the pressure. Solid and broken lines are the guides to the eyes. Vertical dotted lines denote thephase boundary at the critical concentration x c . Horizontal dottedlines show the low-temperature limit of the SQUID magnetometer.

The change in T N at x⬃x c should be easier to see in Fig.
3. Discontinuity of T N is observed in the T-P phase diagram
in samples C and D but not in sample E. The schematic
T-P-x phase diagram is therefore as in Fig. 5. The composi-

FIG. 5. 共Color兲 The schematic
T-P-x phase diagram.

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APPEARANCE OF THE SPIN-PEIERLS PHASE UNDER . . .

tional phase transition between the DAF and the UAF phases
is first order at low pressure, and we propose that it becomes
second order above a critical pressure ( P ⬘c ).
IV. DISCUSSION

We now discuss why pressure stabilizes the SP phase. The
parameters that determine the phase in this system are thenearest-neighbor interaction J, the interchain interaction J ⬘ ,and the frustration factor ␣ in Eq. 共1兲. Spin-phonon couplingis also important in the SP system, but we assume that it isindependent of pressure and that its effect is negligibly small.
We found that the pressure suppresses J and enhances ␣ in
Eq. 共1兲, based on the magnetic-susceptibility measurementsin the high-temperature region 共Fig. 1兲. Nishi et al. recently
performed inelastic neutron scattering with pure CuGeO3 atambient pressure and 2 GPa.30 Dispersion of the spin excitation along the c * axis 共the 1D-chain axis兲 was suppressed,
and that along the b * axis 共perpendicular to the 1D-chain
axis兲 was unchanged by the pressure. This means that theeffective interchain interaction, J ⬘ /J, is enhanced by thepressure. Conventional SP theories of a pure system3 anddoped system31 which do not consider the frustration term,
indicate that enhancement of the interchain interaction stabilizes the Néel phase, rather than the SP phase. The experimental result, however, is different: the SP phase is morestabilized and even reappears in highly doped samples as aresult of pressure. Hence, apparently the reappearance of the
SP phase is not due to enhancement of the interchain interaction by the pressure and we must take account of the frustration factor ␣ . From the density-matrix–renormalizationgroup study on undoped CuGeO3 one can see that the SP
phase is stabilized with increasing ␣ in Fig. 3 of Ref. 25. We
therefore suppose that J ⬘ and ␣ compete with each other inthis system. At ambient pressure in highly doped CuGeO3 ,J ⬘ overcomes the effect of ␣ and the UAF phase appears.
Application of pressure enhances ␣ and the SP, and the DAF
phases appear.
The compositional phase transition between the DAF and*Present address: Synchrotron Radiation Research Center 共SPring8兲, JAERI, 1-1-1 Koto Mikazuki-cho Sayo-gun Hyogo 679-5148,
Japan.
†
Present address: Department of Physics, Tohoku University, Sendai, 980-8578, Japan.
1
M. Hase, I. Terasaki, and K. Uchinokura, Phys. Rev. Lett. 70,
3651 共1993兲.
2
M. Nishi, O. Fujita, and A. Akimitsu, Phys. Rev. B 50, 6508
共1994兲.
3
S. Inagaki and H. Fukuyama, J. Phys. Soc. Jpn. 52, 3620 共1983兲.
4
M. Hase, I. Terasaki, Y. Sasago, K. Uchinokura, and H. Obara,
Phys. Rev. Lett. 71, 4059 共1993兲.
5
S. B. Oseroff, S. W. Cheong, B. Aktas, M. F. Hundley, Z. Fisk,
and L. W. Rupp, Jr., Phys. Rev. Lett. 74, 1450 共1995兲.
6
L. P. Regnault, J. P. Renard, G. Dhalenne, and A. Revcolevschi,
Europhys. Lett. 32, 579 共1995兲.
7
Y. Sasago, N. Koide, K. Uchinokura, M. C. Martin, M. Hase, K.
Hirota, and G. Shirane, Phys. Rev. B 54, R6835 共1996兲.

the UAF phases is first order at low pressure. We proposethat it becomes second order at 0.2 GPa, as shown in Fig. 5;
the phase boundary between these two phases changes at a
critical pressure, P c⬘ , from first order to second order as thepressure increases. Saito studied the compositional phasetransition at ␣ ⫽0 using the phase Hamiltonian method,31
and asserted that the phase transition is first order when J ⬘ islarge and second order when J ⬘ is small. The experimental
result shows, however, that the phase transition changes fromfirst order to second order with J ⬘ , since neutron scattering
indicates that J ⬘ increases with pressure.30 This fact also tells
us that ␣ must be considered in order to explain the phase
diagram. We conclude that J ⬘ and ␣ compete, and ␣ dominates the effect of J ⬘ at higher pressures. The competition
between ␣ and J ⬘ plays an important role in this system.
V. SUMMARY

In summary, the application of hydrostatic pressure causes
the SP phase to reappear in highly doped CuGeO3 , whichshows no SP transition at ambient pressure. The phase of thissystem is determined by competition between the interchaininteractions and frustration between NN and NNN interactions. We have obtained the temperature-pressureconcentration phase diagram and verified that frustration
plays an important role in these features.
ACKNOWLEDGMENTS

We thank M. Nishi for informing us of the unpublisheddata on the dispersion of the spin excitation in undoped
CuGeO3 under pressure. We thank Y. Uwatoko for his valuable advice on the hydrostatic pressure cell. This work waspartly supported by a Grant-in-Aid for COE Research, andone of the authors 共T.M.兲 was also supported by a Grant-inAid for Scientific Research on Priority Areas, from the Ministry of Education, Culture, Sports, Science, and Technologyof Japan.

8

H. Fukuyama, T. Tanimoto, and M. Saito, J. Phys. Soc. Jpn. 65,3259 共1997兲.
9K. M. Kojima, Y. Fudamoto, K. Larkin, G. M. Luke, J. Merrin, B.
Nachumi, Y. J. Uemura, M. Hase, Y. Sasago, K. Uchinokura, Y.
Ajiro, A. Revcolevschi, and J.-P. Renard, Phys. Rev. Lett. 79,
503 共1997兲.
10
T. Masuda, A. Fujioka, Y. Uchiyama, I. Tsukada, and K. Uchinokura, Phys. Rev. Lett. 80, 4566 共1998兲.
11
T. Masuda, I. Tsukada, K. Uchinokura, Y. Wang, V. Kiryukhin,
and R. Birgeneau, Phys. Rev. B 61, 4103 共2000兲.
12
Y. J. Wang, V. Kiryukhin, R. Birgeneau, T. Masuda, I. Tsukada,and K. Uchinokura, Phys. Rev. Lett. 83, 1676 共1999兲.
13
H. Nakao, M. Nishi, Y. Fujii, T. Masuda, I. Tsukada, K. Uchinokura, K. Hirota, and G. Shirane, J. Phys. Soc. Jpn. 68, 3662
共1999兲.
14
M. Nishi, H. Nakao, Y. Fujii, T. Masuda, K. Uchinokura, and G.
Shirane, J. Phys. Soc. Jpn. 69, 3186 共2000兲.
15
S. Katano, O. Fujita, J. Akimitsu, and M. Nishi, Phys. Rev. B 52,
15 364 共1995兲.

024423-5

PHYSICAL REVIEW B 67, 024423 共2003兲

T. MASUDA et al.
16

G. Castilla, S. Chakravarty, and V. J. Emery, Phys. Rev. Lett. 75,
1823 共1995兲.
17
J. Riera and A. Dobry, Phys. Rev. B 51, 16098 共1995兲.
18
F. D. M. Haldane, Phys. Rev. B 25, 4925 共1982兲.
19
I. Affleck, D. Gepner, H. J. Schultz, and T. Ziman, J. Phys. A 22,
511 共1989兲.
20
T. Tonegawa and I. Harada, J. Phys. Soc. Jpn. 56, 2153 共1987兲.
21
K. Okamoto and K. Nomura, Phys. Lett. A 169, 433 共1992兲.
22
B. Büchner, U. Ammerahl, T. Lorenz, W. Brenig, G. Dhalenne,
and A. Revcolevschi, Phys. Rev. Lett. 77, 1624 共1996兲.
23
P. H. M. Loosdrecht, J. Zeman, and G. Martinez, Phys. Rev. Lett.
78, 487 共1997兲.
24
H. Takahashi, N. Môri, O. Fujita, J. Akimitsu, and T. Matsumoto,
Solid State Commun. 95, 817 共1995兲.
25
A. Klümper, R. Raupach, and F. Schönfeld, Phys. Rev. B 59,

3612 共1999兲.
Y. Uwatoko, T. Hotta, E. Matsuoka, H. Mori, J. L. Sarrao, J. D.
Thompson, N. Môri, and G. Oomi, Rev. High Pressure Sci.
Technol. 7, 1508 共1998兲.
27
H. Kuroe, J. Sasaki, T. Sekine, N. Koide, Y. Sasago, K. Uchinokura, and M. Hase, Phys. Rev. B 55, 409 共1997兲.
28
A. Kouzuki, K. Kawasaki, and K. Nakamura, Phys. Rev. B 60,
12874 共1999兲.
29
K. Hirota, D. E. Cox, J. E. Lorenzo, G. Shirane, J. M. Tranquada,
M. Hase, K. Uchinokura, H. Kojima, Y. Shibuya, and I. Tanaka,
Phys. Rev. Lett. 73, 736 共1994兲.
30
M. Nishi, N Katoh, K. Kakurai, Y. Fujii, M. Yethiraj, J. A.
Fernandez-Baca, D. A. Tennant, S. E. Nagler, O. Fujita, and J.
Akimitsu 共unpublished兲.
31
M. Saito, J. Phys. Soc. Jpn. 68, 2898 共1999兲.
26

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