Physica C 468 (2008) 1428–1430

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Physica C
journal homepage: www.elsevier.com/locate/physc

Anisotropic thermal conductivity of Er–Ba–Cu–O bulk superconductors
T. Naito a,*, H. Fujishiro a, K. Iida b, M. Murakami cabc

Faculty of Engineering, Iwate University, Morioka 020-8551, Japan
IRC in Superconductivity and Department of Engineering, University of Cambridge, Madingley Road, Cambridge CB3 0HE, United Kingdom
Shibaura Institute of Technology, Tokyo 108-8548, Japana r t i c l ei n f oArticle history:
Available online 12 June 2008PACS:
74.25.Fy
74.72.Jt
Keywords:
Thermal conductivity
Er–Ba–Cu–O bulk superconductors
Anisotropya b s t r a c t
We have measured the temperature dependences of the thermal conductivity in the ab-plane, jab(T), andalong the c-axis, jc(T), respectively, for the Er–Ba–Cu–O bulk superconductors, which were fabricated bya method of the melt texture growth. Above the critical temperature Tc, the jab decreases quite moderately as increasing temperature or is almost independent of the temperature. Below the Tc, the wellknown enhancement is observed but is relatively small. The jc(T) shows the small absolute values andwe found that the anisotropy of the thermal conductivity (jab/jc) for Er–Ba–Cu–O bulks is of about 2–6.
Ó 2008 Elsevier B.V. All rights reserved.

1. Introduction
Thermal conductivity, j, is one of the important physical properties for designing the superconducting applications; for instance,
it is used for estimating the heat intrusion through the superconducting current lead. Since the high temperature superconducting
bulks have high potential for various practical applications, wehave measured the thermal conductivity, j, at wide temperatures(4–300 K) on various RE–Ba–Cu–O bulk superconductors (RE = rareearth elements) and found that the behaviors of the temperaturedependence of the thermal conductivity, j(T), depend strongly
on the kind of RE [1,2]. The j for RE = Y, Gd increases with decreasing temperature with a negative curvature above the critical temperature Tc. Since the main heat carriers are phonons, it isinterpreted that such temperature dependence originates fromthe fact that the phonon–phonon Umklapp scattering dominates
the heat transfer. In the superconducting state, the j(T) shows abroad peak, which is well-known feature in high temperature
superconductors [3]. For RE = Sm, Nd, the j is almost independentof the temperature in the normal state and the enhancement below
the Tc is somewhat suppressed, which is interpreted to come fromthe substitution between the RE and Ba sites. Recently, we foundrather anomalous behaviors in j(T) of the Dy–Ba–Cu–O bulks [4].
The magnitude is a half or one-third of that of the Y–Ba–Cu–O* Corresponding author. Tel./fax: +81 19 621 6362.
E-mail address: tnaito@iwate-u.ac.jp (T. Naito).
0921-4534/$ - see front matter Ó 2008 Elsevier B.V. All rights reserved.
doi:10.1016/j.physc.2008.05.262

bulks and the enhancement is also pretty small; furthermore, thej(T) has a positive slope in the normal state.
We measured the temperature dependences of thermal conductivity in the ab-plane, jab(T), and along the c-axis, jc(T), for Er–Ba–Cu–O bulk superconductors. We found that the jab(T) shows aquite moderate negative slope or almost T-independent behavior
in the normal state. The absolute values of the jab are larger thanthose of the Dy–Ba–Cu–O bulks in the whole measuring temperatures, but are smaller than those of other RE–Ba–Cu–O bulks. Thejc shows small values and we found that the anisotropy of jab(T)and jc(T) for Er–Ba–Cu–O bulks is estimated to be of about 2–6.
2. Experimental
Er–Ba–Cu–O bulks, which consist of the superconducting matrix phase ErBa2Cu3O7 d (Er123) and the nonsuperconducting secondary phase Er2BaCuO5 (Er211), were fabricated by a method of
the melt texture growth [5]. Two types of Er–Ba–Cu–O bulks werefabricated; the Er211 powders were ball-milled and not ballmilled. The former composition ratio of the Er123 to the Er211
was 1:0.33 and the latter one was 1:0.5. We added 0.5 wt% Pt powders in both samples. We prepared the rectangular shaped samples
by cutting the as-grown bulk crystals; note that we used the region
at around the seed crystal. To control the amount of the oxygendeﬁciency d in the Er123 phase, the rectangular samples were annealed at Tan = 400–500 °C for 168–240 h in 1 bar ﬂowing oxygengas. The superconducting transition temperature of samples wereof about 89 K, which was deﬁned at the temperature where the1429

T. Naito et al. / Physica C 468 (2008) 1428–1430

electrical resistivity becomes to the zero. The thermal conductivity was measured by a conventional steady-state heat ﬂow
method; the temperature gradient of the sample was estimatedby measuring the two temperatures of the sample using chromel–constantan thermocouples. The temperature of the sample
stage was controlled from 10 to 250 K using a Gifford–McMahon
cycle helium refrigerator. The electrical resistivity was measured
by a conventional four-terminal method with a typical current
density of about 0.1 A/cm2.
3. Results and discussion
Fig. 1 shows the temperature dependence of the ab-plane and caxis thermal conductivity for the Er–Ba–Cu–O bulk superconductors (Tan = 450 °C) with the ball-milled (BM) and the non ballmilled (nonBM) Er211 particles, respectively. The jab for the Er–Ba–Cu–O (BM) increases quite moderately with decreasing temperature in the normal state, on the other hand that for the Er–Ba–Cu–O (nonBM) seems to be almost temperature independent.
Both show the broad peak below the Tc, but the peak is very smallin comparison with that observed in other RE–Ba–Cu–O bulks except for RE = Dy. The absolute jab values of the Er–Ba–Cu–O(BM)are smaller than those for Er–Ba–Cu–O(nonBM), which is explained qualitatively by the fact that the size of Er211 particles issmaller, the effective cross section for the heat carrier scattering
becomes larger. Note that the composition ratio (Er123:Er211)
cannot give the discrepancy between the jab values of both Er–Ba–Cu–O bulks, because it was shown that the jab values of both
Sm–Ba–Cu–O and Gd–Ba–Cu–O bulks hardly depend on the composition ratio in the case of the high RE211 content (RE211/RE123 P 0.3) [2]. We also found that the absolute jab values forboth Er–Ba–Cu–O bulks are rather smaller than those of other
RE–Ba–Cu–O bulks except for Dy–Ba–Cu–O. It is well-known thatthe similar small j values were observed in RE–Ba–Cu–O bulks(RE = Sm, Nd) grown in air [1]. In this case, a part of the RE ionsis substituted for a Ba site, which gives rise to form the RE1+xBa2 xCu3O7 d-type solid solution, because both ionic radii arecomparable. This migration enhances the weak superconducting
regions which work as the phonon scattering centers, thus thethermal conductivity should be suppressed strongly. Such reduction in j has not been observed in bulks for RE = Y [1], meaningthat the substitution between the Y and Ba sites does not occur.
Since the ionic radius of Er3+ is smaller than that of Y3+, the similar

substitution between the Er and Ba sites does not occur and thisscenario cannot be applicable for Er–Ba–Cu–O bulks; the originof the small jab remains an unsolved question.
The jc for the Er–Ba–Cu–O(BM) increases with decreasing temperature and takes a very broad peak at around 50 K. The anisotropy of the thermal conductivity Ck(=jab/jc) for the Er–Ba–Cu–O(BM) is of about 2, which is comparable to that of other RE–Ba–Cu–O bulks (Ck = 2 3) [1]. On the other hand, we ﬁnd no anomaly
in the jc(T) for the Er–Ba–Cu–O(nonBM) and the Ck is estimated tobe of about 6. As reported in Ref. [6], the j(T) of Y211 polycrystals
is larger than jc(T) of Y–Ba–Cu–O bulk, so that the small magnitude of the jc of nonBM sample is anomalous. Therefore, it is obvious that the discrepancy in the jc(T) between both Er–Ba–Cu–O
bulks cannot be explained by the size of the Er211 particles orthe composition ratio (Er123/Er211); we speculate that the stacking faults at the CuO2 planes brings about the small jc(T) for nonBM sample.
Fig. 2 shows the jab(T) curves of Er–Ba–Cu–O(BM) bulk for different annealing temperature Tan = 400 °C and 500 °C, respectively.
It is noticed that the slope in the normal state becomes somewhat
large in sample with Tan = 400 °C. The oxygen vacancies decrease
monotonically with lowering Tan, meaning that the heat transfer
tends to be dominated by phonon-phonon interaction in the lower
Tan sample. Thus, Tan dependence of the jab(T) is consistent withthis picture.
Fig. 3 shows the temperature dependence of the ab-plane electrical resistivity, qab, for the same bulks shown in Fig. 2. The Tc forthe sample with Tan = 400 °C and 500 °C are of 88.7 K and 89.4 K,respectively. The magnitude of the resistivity for the sample with
Tan = 400 °C is smaller than that for Tan = 500 °C, which is consistent with the amount of the oxygen vacancies. Since both qab(T)curves show the good T-linear behavior, we can estimate the thermal conductivity due to the charge carriers, jch( = LT/qab), using
the Wiedemann–Franz law, where L is the Lorenz number. As a result, the former jch and the latter jch, respectively, are estimated tobe of about 5.7 and 4.2 mW/cm K above 100 K; which are quantitatively consistent with the difference in the total j(=jph + jch) for
both samples, where jph is the phonon thermal conductivity. Consequently, it is found that the nature of the jab, especially in thenormal state, is affected sensitively by the oxygen deﬁciencies.

Er-Ba-Cu-O

100

100

κab(nonBM)

80

8060

κab(BM)40

κc(BM)

κab (mW/cmK)Thermal Conductivity(mW/cmK)1206040κc(nonBM)

20Tan20Er-Ba-Cu-O(BM)00100500 ºC
400 ºC

200Temperature(K)Fig. 1. The temperature dependence of the ab-plane and c-axis thermal conductivity, jab(T) and jc(T), for Er–Ba–Cu–O bulk superconductors (Tan = 450 °C). The
closed and open symbols, respectively, represent the Er–Ba–Cu–O bulk with theball-milled (BM) and nonBM Er211.

00100

200T(K)
Fig. 2. The temperature dependence of the ab-plane thermal conductivity of Er–Ba–Cu–O bulk superconductors for Tan = 400 °C and 500 °C.

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T. Naito et al. / Physica C 468 (2008) 1428–1430

Er–Ba–Cu–O bulk superconductors. We found that the jab(T)shows a quite moderate negative slope or T-independent behavior
in the normal state. The absolute values of the jab are larger thanthose of the Dy–Ba–Cu–O bulks in the whole measuring temperatures, but are smaller than those of other RE–Ba–Cu–O bulks. The
anisotropy of the thermal conductivity (jab/jc) for Er–Ba–Cu–Obulks is estimated to be of about 2–6.

T =500°C
an1Resistivity ρab(mΩcm)

1.5

Acknowledgements

0.5This work was supported in part by the JGC-S Scholarship foundation (No. 1907) and a Grant-in-Aid for Scientiﬁc Research fromthe Ministry of Education, Culture, Sports, Science and Technology,
Japan (No. 19560003) from JSPS, Japan.

T =400°C
an

Er-Ba-Cu-O(BM)050100150200250300Temperature(K)Fig. 3. The temperature dependence of the ab-plane electrical resistivity, qab(T), ofEr–Ba–Cu–O bulk superconductors for Tan = 400 °C and 500 °C.

4. SummaryWe have measured the temperature dependences of thermal
conductivity in the ab-planes jab(T) and along the c-axis jc(T) forReferences[1] H. Fujishiro, K. Katagiri, A. Murakami, Y. Yoshino, K. Noto, Physica C 426–431(2005) 699.
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