Physica C: Superconductivity and its applications 521–522 (2016) 13–17

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Physica C: Superconductivity and its applications
journal homepage: www.elsevier.com/locate/physc

Thermodynamic properties of superconducting andnon-superconducting Pr2 Ba4 Cu7 O15-δ compounds with metallic double
chainsTakahisa Konno a, Michiaki Matsukawa a,∗, Keisuke Sugawara a, Haruka Taniguchi a,
Junichi Echigoya a, Akiyuki Matsushita b, Makoto Hagiwara c, Kazuhiro Sano d,
Yoshiaki Ohno e, Yuh Yamada e, Takahiko Sasaki f, Yuichiro Hayasaka faDepartment of Materials Science and Engineering, Iwate University, Morioka 020-8551, Japan
National Institute for Materials Science, Ibaraki 305-0047, Japan
Kyoto Institute of Technology, Kyoto 606-8585, Japand
Department of Physics Engineering, Mie University, Tsu 514-8507, Japane
Department of Physics, Niigata University, Niigata 950-2181, Japanf
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japanbca r t i c l e

i n f oArticle history:
Received 28 September 2015
Revised 5 December 2015
Accepted 15 December 2015
Available online 25 December 2015
Keywords:
Pr2 Ba4 Cu7 O15
Superconductivity
CuO double chains
Speciﬁc heata b s t r a c t
To examine the thermodynamic properties of Pr2 Ba4 Cu7 O15-δ compounds with metallic CuO double
chains, we measured the speciﬁc heats of superconducting and non-superconducting polycrystalline samples at low temperatures (1.8–40 K) under various magnetic ﬁelds (up to 9 T). In the as-sintered nonsuperconducting sample, a λ-like enhancement in the speciﬁc heat measurement appeared near the antiferromagnetic transition temperature TN = 17 K. In contrast, the reduced superconducting sample withTcon = 26.5 K exhibited no obvious superconducting anomaly in its speciﬁc heat data, but a Schottky-likebroad maximum appeared at low temperatures. The Schottky-like anomaly was attributed to low-lying
quasi-triplet splitting of Pr3+ ions under the crystal ﬁeld effect.

1. Introduction
Since the discovery of high-Tc copper-oxide superconductors,
strongly correlated electron systems have been extensively investigated. Besides the physical properties of two-dimensional CuO2
planes, researches have focused on the physical role of onedimensional (1D) CuO chains in some families of high-Tc copperoxides.
Structurally, the Pr-based cuprates, PrBa2 Cu3 O7-δ (Pr123) and
PrBa2 Cu4 O8 (Pr124), are identical to their corresponding Y-based
high-Tc superconductors, YBa2 Cu3 O7-δ (Y123) and YBa2 Cu4 O8(Y124). Pr123 and Pr124 compounds have insulating CuO2 planes
and are non-superconductive [1,2]. The suppression of superconductivity in the Pr substitutes has been explained by the hybridization of Pr-4f and O-2p orbitals [3]. The crystal structure of Pr124
with CuO double chains differs from that of Pr123 with CuO single chains. It is well known that CuO single chains in Pr123 and∗Corresponding author. Tel.: 81 19 621 6358.
E-mail address: matsukawa@iwate-u.ac.jp (M. Matsukawa).

http://dx.doi.org/10.1016/j.physc.2015.12.004
0921-4534/© 2015 Elsevier B.V. All rights reserved.

© 2015 Elsevier B.V. All rights reserved.

CuO double chains in Pr124 show semiconducting and metallic behaviors, respectively [4]. The carrier concentration of doped double
chains of Pr124 is diﬃcult to vary, because it is thermally stable up
to high temperatures. In addition, Pr ions in both Pr123 and Pr124
become antiferromagnetic ordered at the antiferromagnetic transition temperature TN = 17 K [5,6].
The compound Pr2 Ba4 Cu7 O15-δ (Pr247) is an intermediate between Pr123 and Pr124. In this compound, CuO single-chain anddouble-chain blocks are alternately stacked along the c-axis [7,8](see Fig. 1). The physical properties of the metallic CuO double
chains can be examined by controlling the oxygen content along
the semiconducting CuO single chains. Anisotropic resistivity measurements of single-crystal Pr124 have revealed that metallic transport arises by the conduction along the CuO double chains [9].
In oxygen removed polycrystalline Pr2 Ba4 Cu7 O15-δ , superconductivity appears at an onset temperature Tcon of ∼ 15 K [10]. Hall
coeﬃcient measurements of superconducting Pr247 with Tcon = 15
K have revealed that at intermediate temperatures below 120 K,
the main carriers change from holes to electrons, as the temperature decreases. Accordingly, this compound is an electron-doped
superconductor [11]. In our previous study, we examined the14

T. Konno et al. / Physica C: Superconductivity and its applications 521–522 (2016) 13–17

Fig. 1. (a) Typical crystal structure of Pr2 Ba4 Cu7 O15-δ compound. Blocks of CuO single chains (denoted S) and CuO double chains (D) are alternately stacked along caxis. (b) TEM image of superconducting Pr2 Ba4 Cu7 O15-δ compound with a superconducting onset temperature Tcon of 26.5 K.

effect of magnetic ﬁelds on the superconducting phase of Pr247[12]. Despite of the resistive drop associated with the superconducting transition, we found that the diamagnetic signal wasstrongly suppressed as expected in the 1D superconductivity of
CuO double chains. We also reported the temperature dependenceof the Hall coeﬃcient in superconducting Pr247 with a higher
Tcon ∼ 27 K [13]. Our ﬁndings indicated that the superconducting transition temperature increased because the density of doped
electron carriers became denser under the reduction treatment,
consistent with a theoretical prediction [14].
In this paper, we demonstrate the thermodynamic properties of the electron-doped metallic double-chain compound
Pr2 Ba4 Cu7 O15-δ , which has a higher Tcon (26.5 K), under different magnetic ﬁelds. Fig. 1 displays the typical crystal structure of Pr2 Ba4 Cu7 O15-δ , in which the CuO metallic double
chains and semiconducting single chains are alternately stacked
along the c-axis. Section 2 outlines the experimental methods,
and Section 3 presents the magneto-transport and magnetothermodynamic properties of polycrystalline Pr247 samples. Alongwith the magneto-transport data, we report the temperature dependences of the speciﬁc heats in the as-sintered and reduced
Pr247. These results are discussed in terms of a three-level system (quasi triplet), in which the ground-state of the Pr3+ ions is
split by the crystal ﬁeld effect. The ﬁnal section is devoted to asummary.
2. Experiment
Polycrystalline samples of Pr2 Ba4 Cu7 O15-δ (Pr247) were synthesized by the citrate pyrolysis method [15]. After several annealing

processes, the resulting precursors were pressed into a pellet andcalcined at 875–887°C for an extended period over 120–180 h under ambient oxygen pressure. The oxygen in the as-sintered sample was removed by reduction treatment in a vacuum at 500°C for
48 h, yielding a superconducting material. Typical dimensions of
the pelletized rectangular sample were 9.9 × 2.4 × 1.7 mm3 . The
Pr247 sample with Tcon = 26.5 K was observed by high-resolution
transmission electron microscopy using a JEOL3010 microscope operated at 300 kV at Tohoku University. The local crystal structure was analyzed from images obtained by the high-angle annulardark-ﬁeld scanning transmission electron microscope method [16].
The oxygen deﬁciency in the sample with Tcon = 26.5 K preparedby the citrate method was estimated to be δ = 0.56 from gravimetric analysis. As a function of the oxygen deﬁciency, the Tcon rises
rapidly at δ ≥ ∼0.2, then monotonically increases with increasing
δ , and ﬁnally saturates around 26–27 K at δ ≥ ∼0.6 [17]. Accordingly, the carriers in the present sample are concentrated aroundthe optimally doped region.
The electric resistivity in zero magnetic ﬁeld was measured by
the dc four-terminal method. The magneto-transport up to 9 T was
measured by the ac four-probe method using a physical property
measuring system (PPMS, Quantum Design) , increasing the zeroﬁeld-cooling (ZFC) temperatures from 2 K to 40 K. The high ﬁeld
resistivity (up to 14 T) was measured in a superconducting magnet at the High Field Laboratory for Superconducting Materials, Institute for Materials Research, Tohoku University. The electric current I was applied longitudinally to the sample ; consequently, theapplied magnetic ﬁeld H was transverse to the sample (because
H ⊥ I). The speciﬁc heats in the ZFC mode were measured to be
between 2 K and 40 K by the PPMS. For comparison, the temperature dependence of the speciﬁc heat of the superconducting
Y2 Ba4 Cu7 O15-δ (Y247) compound prepared by the high-pressure
oxygen method [8] was separately measured in zero ﬁeld at NIMS.
The dc magnetization was performed under ZFC in a commercial superconducting quantum interference device magnetometer(Quantum Design, MPMS). Magnetic ﬁelds of 0.002 T, 0.01 T, 1 T, 3
T, and 5 T were applied.
3. Results and discussion
Fig. 1 shows the typical crystal structure and a TEM image ofthe superconducting Pr2 Ba4 Cu7 O15-δ compound with Tcon = 26.5 K.
S and D denote CuO single-chain and double-chain blocks, respectively. We observe a regular stacking structure of {-D-S-D-S-D}. In
the X-ray diffraction pattern of polycrystalline Pr2 Ba4 Cu7 O15-δ synthesized by the citrate pyrolysis method, a clear peak corresponding to the Miller index (004) of Pr247 was observed, but peaks of
Pr123 or Pr124 phases were absent (data not shown) [12].
Fig. 2 plots the temperature dependences of the magnetic susceptibilities of the non-superconducting and superconducting samples under various magnetic ﬁelds (up to 5 T). In the as-sinteredsample, a typical anomaly in χ occurs near 17 K. This anomaly
is associated with an antiferromagnetic transition of the Pr sublattice, as previously reported in Pr123 and Pr124 systems [5,6].
On the contrary, the 48-h-reduced sample becomes superconductive below Tcon = 26.5 K. The superconducting volume fraction f
was estimated from the magnetic data taken at 10 mT by f =χ · ρ /4π × 100, where χ and ρ denote the magnetic susceptibility
per unit weight and the sample density (5.3 g/cm3 ), respectively.
As displayed in the inset of Fig. 2(b), the volume fraction reaches∼ 30 % at 4 K, indicating bulk superconductivity.
However, under high ﬁelds, the magnetic data of the superconducting sample monotonically increases as the temperature decreases to below 17 K and saturate at low temperatures. This
trend reﬂects the ferromagnetic character of the sample. As highlighted in our previous paper [12], the diamagnetic signal is

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15

Fig. 2. Low-temperature dependences of magnetic susceptibilities χ ofPr2 Ba4 Cu7 O15-δ compounds under various magnetic ﬁelds (1 T, 3 T, and 5 T).
(a) Non-superconducting as-sintered sample and (b) superconducting 48-h-reduced
sample with Tcon = 26.5 K. Inset plots are magnetic data recorded at 10 mT, fromwhich we estimated Tcon = 26.5 K. Superconducting volume fractions estimatedfrom present data are also plotted (right vertical axis in inset).

Fig. 3. Low-temperature dependences of electric resistivities of Pr2 Ba4 Cu7 O15-δ
compounds measured under various magnetic ﬁelds. (a) As-sintered nonsuperconducting sample, measured at 0 T, 3 T, 6 T, and 9 T, and (b) 48-h-reduced
superconducting sample with Tcon = 26.5 K, measured at 0 T, 3 T, 6 T, 9 T, 12 T, and
14 T. For comparison, inset plots resistivity data of both samples versus T (between
2 K and 300 K).

suppressed despite the resistive drop associated with the superconducting transition. This observation is closely related to the 1D
superconductivity of CuO double-chains. In contrast to the positive
magnetization data at higher ﬁeld, the resistivity data of the 48h-reduced sample substantially drop as the transport currents becomes superconducting (see Fig. 3(b)). The clear difference in themagnetic behavior between the as-sintered and reduced samples
reﬂects the different magnetic interactions among the Pr magnetic
ions. The Pr atoms in Pr124, are well separated, so their antiferromagnetic ordering is not dominated by the superexchange interaction. Instead, we consider that the antiferromagnetic couplingof the Pr sublattice occurs due to the Rudermann–Kittel–Kasuya–
Yoshida (RKKY) interaction and is mediated by itinerant carriers
as noted by Xu et al. [19]. In Pr247, the vacuum reduction treatment varies the distance between the Pr ions, and the ferromagnetic property of the reduced sample occurs through the RKKY
interaction.
From the magnetic susceptibility measurements over a wide
range of temperatures range (20–200 K), we estimate the effective magnetic moment μeff of the Pr ions by the Curie–Weiss law.
Performing the calculation, we obtained that μeff = 3.02 and 3.26
μB for the non-superconducting and superconducting samples, respectively. These values are almost consistent with the effective
moment of Pr124 (μeff = 3.11μB ) [6]. In particular, the μeff of thesuperconducting sample is close to that of Pr3+ (3.54 μB ).
The magnetoresistance of the as-sintered and 48-h-reduced
samples also differ at high temperatures (above Tcon = 26.5 K). In
our next paper, concerning the effects of external pressure on themagneto-transport of superconducting and non-superconducting

Pr247, we will link this difference to the electronic phase diagramof the 1D zigzag CuO chain model.
Fig. 4 plots the temperature dependences of the speciﬁc heats
C/T of the non-superconducting and superconducting Pr247 compounds under several magnetic ﬁelds (up to 9 T). The C/T of thenon-superconducting as-sintered sample exhibits a λ-like enhancement associated with the antiferromagnetic transition of Pr ions, as
previously reported in non-superconducting Pr123 and Pr124 systems [6,18]. As the external magnetic ﬁeld increases, this sharp
increase is suppressed and peaks at lower temperatures. At 9 T,
the thermodynamic peak is considerably depressed and is locatedaround 15 K. At low temperatures (below 5 K), the speciﬁc heatalso exhibits a strong ﬁeld dependence, for reasons which have
not yet been clariﬁed. On the other hand, the C/T of the superconducting sample is not enhanced at temperatures above 15 K,
regardless of the applied magnetic ﬁeld. The absence of λ− likeenhancement in reduced Pr247 appears to be consistent with thecorresponding magnetic behavior, which shows no clear AFM transition. At temperatures below 15 K, the C/T of the superconducting
sample shows a broad peak around 8.5 K. This broad anomaly isstrongly suppressed under a magnetic ﬁeld. For comparison, Fig. 4
also plots the temperature dependence of the speciﬁc heat of superconducting Y247 in the absence of magnetic ﬁeld, which was
prepared by the high pressure oxygen method. Oxygen removed
Y2 Ba4 Cu7 O14 , with no superconductivity down to 2 K, exhibits a
C/T magnitude and temperature dependence similar to those of thesuperconductor Y247 [20]. Accordingly, because Y247 and Pr247
share the same crystal structure, we roughly assumed the lowtemperature speciﬁc heat of superconducting Y247 to be the lattice component of the Pr247 sample. We further assumed that

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T. Konno et al. / Physica C: Superconductivity and its applications 521–522 (2016) 13–17

low-temperature speciﬁc heat data of PrBa2 Cu3 O7 and PrBa2 Cu3 O6
follow temperature trends, similar to those of as-sintered andvacuum-reduced Pr247, respectively. The common features include
the λ-like enhancement in the former compounds and the broad
C/T maximum in the latter. To analyze the low-temperature peakin the speciﬁc heat trends of PrBa2 Cu3 O6 , Hilscher et al. [21] introduced a Schottky type speciﬁc heat contributed by a thermal population of electrons. In this study, we followed Hilscher’s approachto understand the broad maximum in the C/T of the corresponding
superconducting Pr247 [22]. In the Pr123 system, the crystal ﬁeld
ground state of the Pr ion is a quasitriplet and is separated by several tens of meV from the group of remaining crystal ﬁeld levels[21,23]. Accordingly, we assumed that at temperatures below 30 K,
the energy levels of the Pr ion are split into three by the crystal
ﬁeld effect.
Assuming that for three energy levels Ei (i = 0, 1, and 2 ) E0 =0 K and E1 < E2 , we then get a partition function for the threeenergy level system, Z = 1 + e−β E1 + e−β E2 (β = 1/kT ). Substituting
the above formula into a general expression for a speciﬁc heat, C =1 d2 log Z, a Schottky-type speciﬁc heat with three energy levels is
kT 2 dβ 2

given byCSch = kB

Fig. 4. Temperature dependences of speciﬁc heats of Pr2 Ba4 Cu7 O15-δ compounds
under various magnetic ﬁelds (up to 9 T). (a) The non-superconducting as-sinteredsample and (b) the superconducting 48-h-reduced sample with Tcon = 26.5 K. For
comparison, zero-ﬁeld speciﬁc heat data of superconducting Y2 Ba4 Cu7 O15-δ (Y247)
prepared in high-pressure oxygen are also plotted.

x2 e−x + y2 e−y + (x − y )2 e−x−y(e−x + e−y + 1 )2

where x = E1 /T and y = E2 /T denote the temperature reduced energy levels.
As shown in Fig. 5, the zero ﬁeld data below 30 K are roughly
ﬁtted by the Schottky expression with E1 = 23.2K and E2 = 46.4K.
The energy levels ﬁtted to the curves of the superconducting Pr247
compound are similar to the experimental and calculated crystal ﬁeld levels of the 3 H4 multiplet in PrBa2 Cu3 O6 , which has
orthorhombic crystal ﬁeld parameters. For example, as predictedfrom inelastic neutron scattering measurements of PrBa2 Cu3 O6 , thecrystal ﬁeld splitting of this compound is E1 = 19.7K and E2 =39.4K [21]. The low-temperature peak in the speciﬁc heat of theoxygen-removed superconducting sample is reasonably describedby the Schottky anomaly (see Fig. 5). The small discrepancy between the calculated curve and the experiment data is probably
attributed to magnetic interactions among the Pr ions. The reduced superconducting sample shows no obvious anomaly associated with the superconducting transition, inconsistent with theexperimentally observed resistive drop and diamagnetic signal as
the temperature decreases. As shown in the inset of Fig. 2, thesuperconducting volume fraction is several percent around 15 K,
and rapidly increases as the temperature falls below 10 K. Thus,
we infer that the superconducting anomaly of metallic CuO double
chains is masked by the Schottky like broad enhancement in C/T
caused by the crystal ﬁeld effect of the Pr ions.
4. SummaryFig. 5. Temperature dependences of speciﬁc heat differences C/T observed in
Pr247 and Y247 (CPr247 /T and CY247 /T, respectively). Dashed curves are calculated
Schottky heat anomalies due to crystal ﬁeld splitting of Pr3+ . Parameters under zeroﬁeld were ﬁtted as E1 = 23.2 K and E2 = 46.4 K.

the low-temperature dependences of the electronic components ofboth Y247 and Pr247 were signiﬁcantly smaller than those of thelattice parts.
Fig. 5 plots the speciﬁc heat differences dC/T between the superconducting Pr247 and Y247 data (CPr247 /T and CY247 /T, respectively) versus temperature. Comparing our results with the previous data obtained using Pr-based 123 [21], it is evident that the

We demonstrated the thermodynamic properties of superconducting and non-superconducting Pr2 Ba4 Cu7 O15-δ compounds withmetallic CuO double chains. For this purpose, we measured thespeciﬁc heats of the polycrystalline samples at low temperatures
under varying magnetic ﬁelds (up to 9 T). The speciﬁc heat of theas-sintered non-superconducting sample displayed the λ-like enhancement near the antiferromagnetic transition temperature TN =17 K. This anomaly around the superconducting transition was absent in the reduced superconducting sample for reasons related tothe small superconducting volume fraction at temperatures above
15 K. As the temperature decreased below 15 K, the C/T of the superconducting sample broadly peaked around 8.5 K. This Schottkylike broad maximum was attributed to low-lying quasi-triplet splitting of Pr3+ ions under the crystal ﬁeld effect.

T. Konno et al. / Physica C: Superconductivity and its applications 521–522 (2016) 13–17

Acknowledgments
The authors are grateful for M. Nakamura for his assistance in
PPMS experiments at Center for Regional Collaboration in Researchand Education, Iwate University.
References[1] L. Soderholm, K. Zhang, D.G. Hinks, M.A. Beno, J.D. Jorgensen, C.U. Segre,
I.K. Schuller, Nature 328 (1987) 604.
[2] S. Horii, Y. Yamada, H. Ikuta, N. Yamada, Y. Kodama, S. Katano, Y. Funahashi,
S. Morii, A. Matsushita, T. Matsumoto, I. Hirabayashi, U. Mizutani, Physica C
302 (1998) 10.
[3] R. Fehrenbacher, T.M. Rice, Phys. Rev. Lett. 70 (1993) 3471.
[4] T. Mizokawa, C. Kim, Z.X. Shen, A. Ino, T. Yoshida, A. Fujimori, M. Goto,
H. Eisaki, S. Uchida, M. Tagami, K. Yoshida, A.I. Rykov, Y. Siohara, K. Tomimoto,S. Tajima, Y. Yamada, S. Horii, N. Yamada, Y. Yamada, I. Hirabayashi, Phys. Rev.
Lett. 85 (20 0 0) 4779.
[5] W.-H. Li, J.W. Lynn, S. Skanthankumar, T.W. Clinton, A. Kebede, C.S. Jee,
J.E. Crow, T. Mihalisin, Phys. Rev. B 40 (1989) 5300.
[6] H.D. Yang, J.-Y. Lin, S.S. Weng, C.W. Lin, H.L. Tsay, Y.C. Chen, T.H. Meen, T.I. Hsu,
H.C. Ku, Phys. Rev. B 56 (1997) 14180.
[7] P. Bordet, C. Chaillout, J. Chenavas, J.L. Hodeau, M. Marezio, J. Karpinski,
E. Kaldis, Nature 334 (1988) 596.
[8] Y. Yamada, S. Horii, N. Yamada, Z. Guo, Y. Kodama, K. Kawamoto, U. Mizutani,
I. Hirabayashi, Physica C 231 (1994) 131.

17

[9] S. Horii, U. Mizutani, H. Ikuta, Y. Yamada, J.H. Ye, A. Matsushita, N.E. Hussey,
H. Takagi, I. Hirabayashi, Phys. Rev. B 61 (20 0 0) 6327.
[10] M. Matsukawa, Y. Yamada, M. Chiba, H. Ogasawara, T. Shibata, A. Matsushita,
Y. Takano, Physica C 411 (2004) 101.
[11] A. Matsushita, K. Fukuda, Y. Yamada, F. Ishikawa, S. Sekiya, M. Hedo, T. Naka,
Sci. Technol. Adv. Mater. 8 (2007) 477.
[12] T. Chiba, M. Matsukawa, J. Tada, S. Kobayashi, M. Hagiwara, T. Miyazaki,
K. Sano, T. Sasaki, J. Echigoya, J. Phys. Soc. Jpn. 82 (2013) 074706.
[13] J. Tada, M. Matsukawa, T. Konno, S. Kobayashi, M. Hagiwara, T. Miyazaki,
K. Sano, A. Matsushita, J. Phys. Soc. Jpn. 82 (2013) 105003.
[14] K. Sano, Y. Ono, Y. Yamada, J. Phys. Soc. Jpn. 74 (2005) 2885.
[15] M. Hagiwara, T. Shima, T. Sugano, K. Koyama, M. Matsuura, Physica C 445–448(2006) 111.
[16] S.J. Pennycook, D.E. Jesson, Phys. Rev. Lett. 64 (1990) 938.
[17] M. Hagiwara, S. Tanaka, T. Shima, K. Gotoh, S. Kanda, T. Saito, K. Koyama, Physica C 468 (2008) 1217.
[18] A. Kebede, C.S. Jee, J. Schwegler, J.E. Crow, T. Mihalisin, G.H. Myer, R.E. Salomon, P. Schlottmann, M.V. Kuric, S.H. Bloom, R.P. Guertin, Phys. Rev. B 40
(1989) 4453.
[19] X. Xu, A. Carrington, A.I. Coldea, A. Enayati-Rad, A. Narduzzo, S. Horii,
N.E. Hussey, Phys. Rev. B 81 (2010) 224435.
[20] A. Irizawa, T. Ohmura, T. Shibata, M. Kato, K. Yoshimura, K. Kosuge, Y. Ito,
H. Michor, G. Hilscher, J. Phys. Soc. Jpn. 71 (2002) 574.
[21] G. Hilscher, E. Holland-Moritz, T. Holubar, H.D. Jostarndt, V. Nekvasil,
G. Schaudy, U. Walter, G. Fillion, Phys. Rev. B 49 (1994) 535.
[22] C. Kittel, Introduction to the Solid State Physics, ﬁfth ed., Wiley, New York,1976.
[23] L. Soderholm, C.K. Loong, G.L. Goodman, B.D. Dabrowski, Phys. Rev. B 43 (1991)
7923.