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Journal of the Physical Society of Japan
Vol. 79, No. 3, March, 2010, 034710#2010 The Physical Society of Japan

Simultaneous Metal–Insulator and Spin-State Transitionin (Pr1y REy )1x Cax CoO3
(RE ¼ Nd, Sm, Gd, and Y)
Tomoyuki N AITO, Hiroko S ASAKI, and Hiroyuki F UJISHIRO
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan(Received June 24, 2009; accepted December 18, 2009; published March 10, 2010)

We have studied a Pr-site substitution eﬀect using various RE ions (RE ¼ Nd, Sm, Gd, and Y) ona simultaneous metal–insulator (MI) and spin-state (SS) transition in (Pr1y REy )1x Cax CoO3 using
measurements of electrical resistivity, magnetization, and thermal dilatation. The MI–SS transition took
place at the appropriate combination of x and y for samples of RE ¼ Sm, Gd, and Y. The MI–SS
transition temperatures TMI{SS can be scaled universally by the average ionic radius hrA i of the A-sitein the perovskite ACoO3 , which is independent of x, y, and the RE ion species. The atomic randomness
2of the A-site, which is deﬁned as the mean square deviation  2 , larger than the critical value cr
is also2
necessary for the occurrence of the MI–SS transition and TMI{SS increases with increasing  . In contrast,
no MI–SS transition was observed in the RE ¼ Nd samples (x ¼ 0:2 { 0:4), which can be inferred fromthe small  2 value because of the small diﬀerence in ionic radius between Pr3þ and Nd3þ . The atomic
randomness of the A-site might be an important parameter that dominates the MI–SS transition throughthe diﬀerence in electronic energy E between the spin states of Co3þ ions.
KEYWORDS: Pr–Ca–Co–O system, metal–insulator transition, spin-state transition, tolerance factor, atomic
randomness
DOI: 10.1143/JPSJ.79.034710

1.

Introduction

In RECoO3 (RE = rare-earth element), a spin-state (SS)6 0transition of Co3þ ions from a low spin state (LS; t2geg ,5 1
S ¼ 0) to an intermediate spin state (IS; t2g eg , S ¼ 1) or
4 2
a high spin state (HS; t2geg , S ¼ 2) occurs with increasing
temperature, which indicates a small diﬀerence in electronicenergy E between the LS and IS (or HS) states.1–3) Amongcobaltites, a ﬁrst-order metal–insulator (MI) transition
accompanying the SS transition was ﬁrst reported in
Pr0:5 Ca0:5 CoO3 at ambient pressure.4) Large volume contraction, mainly caused by the tilting of the CoO6 octahedra
below the transition temperature TMI{SS , was also found.4)
The tilting of the CoO6 octahedra decreases the bond angleof Co–O–Co, which weakens the covalency and thereby
destabilizes the itinerant IS state. The ratio of Pr : Ca ¼ 1 : 1(Co3þ : Co4þ ¼ 1 : 1) was thought to be apparently indispensable: a commensurate arrangement, such as a chargeordering found in manganites,5) plays a key role in the
MI–SS transition. Later, however, the MI–SS transition was
found in Pr1x Cax CoO3 at x 6¼ 0:5 at a high pressure,6)
in which the charge-ordering was not conﬁrmed throughneutron diﬀraction studies.6,7)
A similar transition was observed in (Pr1y REy )1x Cax CoO3 with an appropriate combination of x and y atambient pressure.6,8) For x ¼ 0:5, TMI{SS increased forsamples with RE ¼ Sm, Y, and Tb, but TMI{SS for the
sample with a small amount of Nd substitution decreased
concomitantly with increasing y. For (Pr1y REy )0:7 Ca0:3 CoO3 (RE ¼ Y, Tb), TMI{SS also increased concomitantlywith increasing y. Both the large volume contraction of theunit cell and the decrease in Co–O–Co bond angle below
TMI{SS indicated that the Co–Co transfer energy t was
important for determining E. However, the relationshipE-mail: tnaito@iwate-u.ac.jp

between TMI{SS and the ionic radius of the substituting RE
ion remains controversial. To clarify the substitution eﬀect
on the MI–SS transition in (Pr1y REy )1x Cax CoO3 , further
systematic studies are necessary for various RE ions, x and y.
As described in this paper, we report the respective
temperature dependences of the electrical resistivity andsusceptibility of the polycrystalline (Pr1y REy )1x Cax CoO3
samples (RE ¼ Nd, Sm, Gd, and Y) for various x and yvalues, and discuss the relationship between the MI–SS
transition and the distortion and atomic randomness in the
crystal using various parameters, such as the tolerance factor
 t , the average ionic radius of the A-site hrA i, and the meansquare deviation  2 of the A-site in ACoO3 perovskite.
2.

Experimental Procedure

Polycrystalline samples of (Pr1y REy )1x Cax CoO3 (RE ¼
Nd, Sm, Gd, and Y) were prepared using a solid-state
reaction. Raw powders of Pr6 O11 , RE2 O3 , Co3 O4 , and CaCO3
were weighted with appropriate molar ratios and groundusing an agate mortar and pestle for 1 h. Mixed powders were
calcined at 1000  C for 24 h in air. They were pulverized andground. Then, they were pressed into pellets of 20 mm
diameter and 4 mm thickness. Pellets were sintered at 1200  C
for 24 h in 0.1 MPa ﬂowing oxygen gas. The measured
densities of each sample were greater than 90% of the ideal
density. Powder X-ray diﬀraction patterns were taken foreach sample using Cu K radiation; the samples wereconﬁrmed to have a single-phase orthorhombic (Pbmn)
structure. Electrical resistivity was measured using a fourprobe method with a parallelepiped sample cut from the pellet
with a typical current density of 0.01 A/cm2 . Susceptibility
was measured using a superconducting quantum interference device (SQUID) magnetometer (Quantum Design
MPMS-XL). Thermal dilatation, dLðTÞ=Lð300 KÞ ½¼ ðLðTÞ 
Lð300 KÞÞ=Lð300 KÞ, based on the sample length at 300 K,
was measured by a strain-gauge method.

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Fig. 2. (Color online) Temperature dependence of the susceptibility ðTÞunder the ﬁeld cooling and subsequent ﬁeld warming of the (Pr1y Gdy )0:7 Ca0:3 CoO3 samples for various y values.
Fig. 1. (Color online) Temperature dependence of the resistivity ðTÞ ofthe (Pr1y Gdy )0:7 Ca0:3 CoO3 samples for various y values. The inset shows
the x dependence of ðTÞ for the (Pr0:8 Gd0:2 )1x Cax CoO3 samples.

3.

Results

Figure 1 shows the temperature dependence of theresistivity ðTÞ of (Pr1y Gdy )0:7 Ca0:3 CoO3 for various yvalues. For y ¼ 0 and 0.1, ðTÞ increases moderately withdecreasing temperature. We deﬁne ðTÞ as a ‘‘metallic’’
behavior, as indicated in the previous report.4) For y ¼
0:125, ðTÞ shows a jump with two orders of magnitude
at TMI{SS ¼ 60 K on the cooling run. In fact, TMI{SS wasdetermined as the temperature at which the temperature
derivative of the resistivity d=dT was maximum. On theheating run, ðTÞ showed a sharp drop at TMI{SS ¼ 70 K.
TMI{SS increases and the width of the transition broadenswith increasing y. Consequently, the nature of the phasetransition changes from ﬁrst-order to second-order withdecreasing ionic radius of the (Pr1y Gdy ) site; the ionicradius of Gd3þ (0.1107 nm) is smaller than that of Pr3þ
(0.1179 nm).9) Such a diﬀerence in the ionic radius causes
the local lattice distortion that results in the MI–SS transition
through the energy balance between Hund coupling andcrystal ﬁeld splitting.4,6) For y ¼ 0:125, the absolute value ofðTÞ on the heating run was larger than that on the coolingrun above TMI{SS . The irreversibility in the ðTÞ values on
the cooling and heating runs cannot be explained by thenature of the ﬁrst-order phase transition. The discrepancyin  disappears for y ¼ 0:2; however, it appears again for
y ¼ 0:3, which might come from the microcracks created by
the large volume contraction and expansion passing throughthe transition temperature.4) The microcracks might increasethe ðTÞ value on the heating run.
The inset of Fig. 1 shows the x dependence of ðTÞ for(Pr0:8 Gd0:2 )1x Cax CoO3 . The ðTÞ curve of x ¼ 0:3 is thesame as that in the main panel in Fig. 1. For x ¼ 0:2, theMI–SS transition is second-order-like. With increasing x, theabsolute value of ðTÞ decreases slightly, TMI{SS decreases,
and the transition becomes sharper. In this manner, theðTÞ behavior depends not only on the ionic radius of the(Pr1y Gdy ) site but also on the hole concentration x. The

TMI{SS transition takes place at an appropriate combinationof x and y values in (Pr1y Gdy )1x Cax CoO3 .
Figure 2 shows the temperature dependence of thesusceptibility ðTÞ at H ¼ 1000 Oe under ﬁeld cooling,in addition to the subsequent ﬁeld warming of the(Pr1y Gdy )0:7 Ca0:3 CoO3 samples presented in Fig. 1. For
y ¼ 0:1, ðTÞ monotonically increases with decreasing
temperature, depending on the Curie law. For y ¼ 0:125,ðTÞ shows a sharp drop on cooling and a sharp jump on
warming at TMI{SS , which are the same as those of the ðTÞshown in Fig. 1. The hysteretic ðTÞ behavior shows the SS
transition of Co3þ ions between the LS and IS (or HS) states
at TMI{SS . The hysteretic MI transition in ðTÞ takes place
simultaneously.4,6) The anomalies in the ðTÞ curve become
small and broad with increasing y, which are similar to they dependence of ðTÞ. In contrast to the ðTÞ behavior, theðTÞ values above TMI{SS coincide exactly on cooling andheating runs. Although microcracks are created in thesample at the transition, ðTÞ might not be aﬀected because
susceptibility has a microscopic origin. The result suggeststhat the discrepancy in ðTÞ above TMI{SS arises frommicrocracks in the sample.
Figure 3 shows the temperature dependence of thethermal dilatation dLðTÞ=Lð300 KÞ of the (Pr1y Gdy )0:7 Ca0:3 CoO3 samples. dLðTÞ=L can detect the lattice anomalies. For y ¼ 0:1, dLðTÞ=Lð300 KÞ decreases monotonicallywith decreasing temperature and no anomaly appears down
to 20 K. For y ¼ 0:125 { 0:3, dLðTÞ=Lð300 KÞ shows a large
drop below TMI{SS ; for example, dLð20 KÞ=Lð300 KÞ for the
y ¼ 0:15 sample is 0:008, which is twice as large as thatfor the y ¼ 0:10 sample. In general, a sharp drop in dLðTÞ=Lð300 KÞ originates from the decrease in CoO6 volume (Vo ),Co–O–Co bond angle (), or unit cell volume (Vu ). In
the previous studies,4,6) abrupt decreases in Vu and  wereobserved below TMI{SS . However, the Vo value increasedslightly below TMI{SS . In the present case, we consider thatthe sharp drop in dLðTÞ=Lð300 KÞ comes from the decreasein  and/or the decrease in Vu . The abrupt dilatation
broadens with increasing y similarly to the transition in ðTÞand ðTÞ. A large dilatation is the origin of the irreversibilityin ðTÞ above TMI{SS shown in Fig. 1.

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Fig. 3. (Color online) Temperature dependence of the thermal dilatationdLðTÞ=Lð300 KÞ of the (Pr1y Gdy )0:7 Ca0:3 CoO3 samples for various yvalues.

Fig. 5. (Color online) Temperature dependence of the resistivity ðTÞ ofthe (Pr1y Ndy )1x Cax CoO3 samples (x ¼ 0:2, 0.3, and 0.4) for various yvalues.

Fig. 4. (Color online) Temperature dependence of the resistivity (mainpanel) ðTÞ and susceptibility (inset) ðTÞ of the (a) (Pr1y Smy )0:7 Ca0:3 CoO3 and (b) (Pr1y Yy )0:7 Ca0:3 CoO3 samples for various y values.

We measured the ðTÞ and ðTÞ of both (Pr1y Smy )0:7 Ca0:3 CoO3 and (Pr1y Yy )0:7 Ca0:3 CoO3 series for various yvalues, as presented in Figs. 4(a) and 4(b). The insets
show ðTÞ. The ionic radii of Sm3þ (0.1132 nm) and Y3þ
(0.1075 nm) are smaller than that of Pr3þ (0.1179 nm).9)Actually, ðTÞ and ðTÞ in both series are similar to those in(Pr1y Gdy )0:7 Ca0:3 CoO3 ; the MI–SS transition is observed in
y ¼ 0:2 { 0:6 for (Pr1y Smy )0:7 Ca0:3 CoO3 and in y ¼ 0:075 {
0:15 for (Pr1y Yy )0:7 Ca0:3 CoO3 . Furthermore, TMI{SS increas-es, and the width of the transition broadens with increasingy. The critical substitution concentration ycr , at which the
MI–SS transition emerges, decreases concomitantly withdecreasing ionic radius of the substituting RE ion.
Figure 5 shows the temperature dependence of the ðTÞof (Pr1y Ndy )1x Cax CoO3 samples (x ¼ 0:2, 0.3, and 0.4)
for various y values. In fact, the absolute value of ðTÞdecreased with increasing x. The ðTÞ for x ¼ 0:3 and 0.4
was independent of temperature or increased slightly withdecreasing temperature, similarly to a metallic behavior.
No discontinuous transition was observed in all the Ndsubstituted samples studied. The absolute value of ðTÞseems to be independent of the y value up to y ¼ 0:6. The
absence of the MI–SS transition arises from the small
diﬀerence in ionic radius between Nd3þ (0.1163 nm) andPr3þ (0.1179 nm);9) the physical properties of (Pr1y Ndy )1x Cax CoO3 are similar to those of Pr1x Cax CoO3 andNd1x Cax CoO3 , neither of which shows the MI–SS transition, even at high pressures of up to 10 GPa.8,10) Fujita
et al. reported that the MI–SS transition occurred in(Pr1y Ndy )0:5 Ca0:5 CoO3 for 0  y  0:1 at ambient pressure
and TMI{SS decreased concomitantly with increasing y.6)
In the next section, we discuss the relationship between
the MI–SS transition and various parameters, such as the
species of the substituting RE ion, the concentration of thesubstituted RE ion y, and the Ca concentration x in the(Pr1y REy )1x Cax CoO3 system.
4.

Discussion

As described in the preceding section, the MI–SS
transition was not observed in (Pr1y Ndy )1x Cax CoO3 for
0  y  0:6 and 0:2  x  0:4; however, it was observedin (Pr1y Smy )0:7 Ca0:3 CoO3 for 0:2  y  0:6, although

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hrB i ¼ rCo was estimated as hrB i ¼ x  rCo4þ þ ð1  xÞrCo3þ
using rCo3þ (0.061 nm) and rCo4þ (0.053 nm).9) For the sample
showing no transition, TMI{SS is deﬁned as zero. In Fig. 6(a),for each x, TMI{SS decreases monotonically with increasing
 t , i.e., with increasing relaxation of the local lattice
distortion. The TMI{SS vs  t plot is independent of both the yvalue and the species of substituting RE ions (RE ¼ Sm, Gd,
and Y), and shifts to the right with increasing x. This result
mainly arises from the large diﬀerence in ionic radiusbetween Co3þ and Co4þ ; the  t value increases concomitantly with decreasing x because of rCo4þ < rCo3þ .
Figure 6(b) shows the relationship between TMI{SS andhrA i for the same samples presented in Fig. 6(a). All plots
except for RE ¼ Nd can be represented roughly on auniversal line that is independent of x and y values, and the
RE ion species. These results indicate that TMI{SS depends
strongly on the hrA i value. For example, for (Pr1y Ndy )0:7 Ca0:3 CoO3 (y ¼ 0:4) without MI–SS transition, the  t valueof 0.916 is the same as that of (Pr1y Smy )0:7 Ca0:3 CoO3
(y ¼ 0:2), which shows the MI–SS transition at 42 K. Fromthe viewpoint of the  t value, (Pr0:6 Nd0:4 )0:7 Ca0:3 CoO3
should show the MI–SS transition. Even if TMI{SS isuniversally scaled as a function of hrA i for the REsubstituted system (RE ¼ Sm, Gd, and Y), the absence ofthe MI–SS transition in the Nd-substituted system cannot be
explained. To clarify the absence of the transition in Ndsubstituted samples, we must introduce another parameter.
The substitution of the RE and/or Ca ions for the Pr ionswould introduce atomic randomness in the A-site in addition
to the local distortion in the lattice. The atomic randomnessof the A-site is deﬁned as the mean square deviationX2 ¼
yi ri2  hrA i2 ;Fig. 6. (Color online) MI–SS transition temperature TMI{SS as a functionof (a) the tolerance factor  t , (b) the average ionic radius of A-site hrA i,and (c) the mean square deviation  2 .

the diﬀerence in ionic radius between Sm3þ (0.1132 nm)
and Nd3þ (0.1163 nm) is only about 3%. Furthermore, the(Pr1y REy )0:7 Ca0:3 CoO3 samples (RE ¼ Sm, Gd, and Y)
showed no MI–SS transition for y < ycr . We discuss why the
MI–SS transition does not occur in these cases. First, weconsider the relationship between the MI–SS transition andthe tolerance factor  t , which deﬁnes the lattice distortion as
follows:
hrA i þ rO;
 t ¼ pﬃﬃﬃ
2ðhrB i þ rO Þ

ð1Þ

where hrA i, hrB i, and rO respectively denote the average
ionic radii of the A-site [(Pr1y REy )1x Cax ], B-site (Co), andO in the ABO3 perovskite oxide.
Figure 6(a) shows the relationship between TMI{SS determined in the cooling run and  t for all samples measured inthis study. hrA i in eq. (1) was calculated using the relation
hrA i ¼ ½ð1  xÞð1  yÞ  rPr þ ½ð1  xÞy  rRE þ x  rCa :where yi and ri respectively stand for the concentration andionic radius of each element in the A-site. Figure 6(c) shows
plots of TMI{SS vs  2 for all samples in this study. For each x
and each substituted RE ion (RE ¼ Sm, Gd, and Y), TMI{SSmonotonically decreases concomitantly with decreasing  2
2and reaches zero for  2 lower than the critical value cr. It is2
noteworthy that the TMI{SS vs  plots are scaled for each
substituted RE ion and are independent of x and y. The  2values of the (Pr1y Ndy )1x Cax CoO3 samples (0:2  x  0:4
and 0  y  0:6) are estimated to be ð0:5 { 0:7Þ  106 nm2 ,2which are smaller than the critical crvalue. An atomic
2
randomness in the A-site larger than cr is necessary for theoccurrence of the MI–SS transition, although the lattice
distortion deﬁned by the tolerance factor  t is satisﬁed. A
possible origin of the MI–SS transition related to  2 is the
structural inhomogeneity due to the local atomic randomness
that introduces the ﬂuctuation in energy balance between
Hund coupling and crystal ﬁeld splitting.
Recently, Tong et al.7) have suggested the importanceof distortion in the CoO6 octahedra in causing the MI–SS
transition by comparing Pr0:5 Ca0:5 CoO3 and Pr0:5 Ca0:5 CoO3 (  0:045); the oxygen deﬁciency relaxed the
distortion in the CoO6 octahedra, and then, the transition
vanished. The local distortion in the CoO6 octahedra
enhances electron–phonon coupling, which suppresses theitinerant nature of the eg electrons. Wang et al.11) reported
the oxygen isotope eﬀect on the MI–SS transition in(Pr0:7 Sm0:3 )0:7 Ca0:3 CoO3 . Actually, the TMI{SS of the sample

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with 18 O was higher than that of the sample with 16 O. This
result is explained by the increase in the electron mass mof the sample with 18 O because of the enhanced electron–
phonon coupling, which increased E and decreased the
Co–Co transfer energy t. Fujita et al. studied the MI–SS
transition of the (Pr1y REy )0:5 Ca0:5 CoO3 samples at ambientpressure.6) Actually, the TMI{SS of the sample with RE ¼ Sm,
Y, and Tb was higher, but that of the sample with RE ¼ Nd
was lower than that of Pr0:5 Ca0:5 CoO3 . Because all the ionicradii of the above-described RE ions are smaller than that ofPr3þ , the substitution eﬀect on the shift in TMI{SS should beapparently similar. However, the results obtained in thisstudy contradicted those obtained by Fujita et al. for the Ndsubstituted samples. From the results of this study, we inferthat the ionic radius of Nd3þ ions is similar to that of Pr3þions and that the atomic randomness in the A-site is necessary
for the occurrence of the MI–SS transition. The samples usedin this study were fabricated at ambient pressure in theﬂowing gas. Our samples were diﬀerent from the samples
prepared by Fujita et al., which were annealed in highpressure oxygen atmosphere. The diﬀerence in oxygen
content between the samples is one of the reasons for thediﬀerent results of the Nd-substituted samples. The reason
why both the Pr and Ca ions are necessary for the occurrenceof the MI–SS transition has not yet been understood in the
Pr–Ca–Co–O system.
5.

Conclusions

To study the origin of the simultaneous metal–insulator(MI) and spin-state (SS) transition in a Pr–Ca–Co–O
system, we measured the temperature dependences of theelectrical resistivity and susceptibility of polycrystalline(Pr1y REy )1x Cax CoO3 samples (RE ¼ Nd, Sm, Gd, and Y)
for x ¼ 0:2, 0.3, and 0.4. Important experimental results andconclusions are summarized as follows.
(1) The MI–SS transition was observed in samples withRE ¼ Sm, Gd, and Y at an appropriate combination of x and y. The MI–SS transition temperature
TMI{SS increases concomitantly with increasing yfor each x. However, the MI–SS transition was notrealized for (Pr1y Ndy )1x Cax CoO3 (0:2  x  0:4;
0  y  0:6).
(2) Actually, TMI{SS can be scaled by the tolerance factor
 t for each x, which is independent of the speciesof RE ions (RE ¼ Sm, Gd, and Y). The relationshipbetween TMI{SS and the average ionic radius hrA i ofthe [(Pr1y REy )1x Cax ] site can be scaled universally,

which is independent of the species of RE ions and theconcentrations of x and y. These results suggest thatTMI{SS strongly depends on the local distortion in thelattice. However, the absence of the MI–SS transitionin the Nd-substituted sample cannot be explained fromthe viewpoints of  t and hrA i.
(3) In fact, TMI{SS can be scaled by the atomic randomnessof the A-site, which is deﬁned as the mean squaredeviation  2 for each RE ion (RE ¼ Sm, Gd, and Y),
which is independent of x and y. An atomic random2
ness larger than the critical value of cr
is expected tobe necessary in the A-site for the occurrence of the
MI–SS transition by the introduction of the ﬂuctuationin energy balance. Because the ionic radius of Pr3þ issimilar to that of Nd3þ , the  2 value of (Pr1y Ndy )1x Cax CoO3 is smaller than those of other RE-substituted
2
samples. A  2 smaller than cr
is a possible explanation
for the absence of the MI–SS transition in the Ndsubstituted sample.
Acknowledgments
The authors acknowledge Dr. J. Hejtmanek of Czech
Republic for valuable discussions and Ms. M. Ishida of
Iwate University for performing part of the experiments.
We are grateful to Dr. S. Kobayashi for his cooperation inmagnetization measurements, which were performed at the
Non-Destructive Evaluation and Science Research Center,
Faculty of Engineering, Iwate University.
1) P. M. Raccah and J. B. Goodenough: Phys. Rev. 155 (1967) 932.
2) M. A. Korotin, S. Yu. Ezhov, I. V. Solovyev, V. I. Anisimov, D. I.
Khomskii, and G. A. Sawatzky: Phys. Rev. B 54 (1996) 5309.
3) J.-Q. Yan, J.-S. Zhou, and J. B. Goodenough: Phys. Rev. B 69 (2004)
134409.
4) S. Tsubouchi, T. Kyomen, M. Itoh, P. Ganguly, M. Oguni, Y. Shimojo,
Y. Morii, and Y. Ishii: Phys. Rev. B 66 (2002) 052418.
5) Y. Tomioka, A. Asamitsu, Y. Moritomo, H. Kuwahara, and Y. Tokura:Phys. Rev. Lett. 74 (1995) 5108.
6) T. Fujita, T. Miyashita, Y. Yasui, Y. Kobayashi, M. Sato, E. Nishibori,
M. Sakata, Y. Shimojo, N. Igawa, Y. Ishii, K. Kakurai, T. Adachi, Y.
Ohishi, and M. Takata: J. Phys. Soc. Jpn. 73 (2004) 1987.
7) P. Tong, Y. Wu, B. Kim, D. Kwon, J. M. S. Park, and B. G. Kim:
J. Phys. Soc. Jpn. 78 (2009) 034702.
8) T. Fujita, S. Kawabata, M. Sato, N. Kurita, M. Hedo, and Y. Uwatoko:
J. Phys. Soc. Jpn. 74 (2005) 2294.
9) R. D. Shanon: Acta Crystallogr., Sect. A 32 (1976) 751.
10) S. Tsubouchi, T. Kyomen, M. Itoh, and M. Oguni: Phys. Rev. B 69
(2004) 144406.
11) G. Y. Wang, T. Wu, X. G. Luo, W. Wang, and X. H. Chen: Phys. Rev.
B 73 (2006) 052404.

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