IOP PUBLISHING

SUPERCONDUCTOR SCIENCE AND TECHNOLOGYSupercond. Sci. Technol. 21 (2008) 085001 (4pp)

doi:10.1088/0953-2048/21/8/085001

Thermal conductivity of Er–Ba–Cu–O and
Ho–Ba–Cu–O superconducting bulks
Tomoyuki Naito1 , Hiroyuki Fujishiro1 , Kazumasa Iida2 ,Shinya Nariki3 and Masato Murakami4
1

Faculty of Engineering, Iwate University, Morioka 020-8551, Japan
IRC in Superconductivity and Department of Engineering, University of Cambridge,
Madingley Road, Cambridge CB3 0HE, UK
3
Superconductivity Research Laboratory, ISTEC, Tokyo 135-0062, Japan4
Shibaura Institute of Technology, Tokyo 108-8548, Japan2

E-mail: tnaito@iwate-u.ac.jp

Received 5 March 2008, in final form 3 April 2008
Published 15 May 2008
Online at stacks.iop.org/SUST/21/085001
Abstract
We have measured the temperature dependence of the in-plane thermal conductivity, κab (T ), forboth Er–Ba–Cu–O and Ho–Ba–Cu–O superconducting bulks. The absolute values of κab (T ) for
both bulks are smaller than that of Y–Ba–Cu–O bulk, but are larger than that of Dy–Ba–Cu–O
bulk, which is known to show an anomalous small κab . κab (T ) for Ho–Ba–Cu–O shows apositive slope (dκab /dT > 0) in the normal state, similarly to that for Dy–Ba–Cu–O. On theother hand, a slightly negative slope (dκab /dT < 0) is found for Er–Ba–Cu–O. The
out-of-plane thermal conductivity, κc , was also measured for Er–Ba–Cu–O bulk, and theanisotropy in the thermal conductivity, (κab /κc ), was estimated to be about 2.
(Some figures in this article are in colour only in the electronic version)

such temperature dependence is considered to originate
from the phonon–phonon Umklapp process, which dominates
the scattering mechanisms of the heat transport. In the
superconducting state, κab (T ) starts to increase rapidly
on cooling below Tc and has a maximum at around
50–60 K, which is well known feature for the high-Tc
cuprates [6]. In the case of SmBCO bulk [7], κab (T ) showsa temperature-independent behaviour in the normal state andthe enhancement below Tc is somewhat suppressed, which isinterpreted to come from the substitution [8] between the Sm
and Ba sites.
Recently, κab (T ) of DyBCO bulk was found to show thefollowing anomalous features [2, 9]. First, the absolute valueof κab (T ) is significantly smaller than that of other bulks: halfor one-third of that in YBCO bulk. Second, the peak structure
below Tc is strongly suppressed. Third, the slope of κab (T )in the normal state is positive, dκab /dT > 0. A possible
origin of these anomalies in DyBCO is the difference of ionicradius and/or mass of the RE. Although the ionic radius of
Dy3+ is slightly larger than that of Y3+ , it is believed that thesubstitution between Dy and Ba sites hardly occurs, unlike in
SmBCO bulk. On the other hand, the effect of the mass is notclear, and the origin of the anomalous κab (T ) of DyBCO bulk

1. Introduction
Using a melt-texture growth method [1], we can obtain a large
RE–Ba–Cu–O (REBCO; RE = rare earth elements) quasisingle crystal, which consists of a superconducting matrix
phase of REBa2 Cu3 O7−δ (RE123) and a non-superconducting
secondary phase of RE2 BaCuO5 (RE211). For designing a
superconducting application such as a current lead, the thermal
conductivity, κ , is an important physical property, because theestimation of the heat intrusion is necessary [2]. Therefore, wehave measured the thermal conductivity for various REBCO
bulk superconductors at low temperatures (below 300 K), andhave constructed a database of the results obtained [3, 4]. It
has been found that the temperature dependence of the thermal
conductivity in the ab -plane, κab (T ), of the REBCO bulk
strongly depends on the kind of RE ion, except for the heavy
RE ions such as Ho, Er, and so forth. There are few data for κ
for REBCO containing heavy RE ions; in particular, the effectof the oxygen deficiency and the anisotropic behaviour havenot been studied at all.
For YBCO bulk [5], κab (T ) increases with decreasing
temperature above the critical temperature Tc . Since themain heat carriers in the high-Tc cuprates are phonons,
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Supercond. Sci. Technol. 21 (2008) 085001

T Naito et al

Figure 1. The temperature dependence of the in-plane resistivity,ρab (T ), of RE–Ba–Cu–O (REBCO; RE = Er, Ho) bulk
superconductors for different annealing temperatures, Tan s, 400 and
500 ◦ C. The broken line shows the data for DyBCO bulk
( Tan = 400 ◦ C) as a reference.

Figure 2. The temperature dependence of the in-plane thermal
conductivity, κab (T ), of RE–Ba–Cu–O (REBCO; RE = Er, Ho) bulk
superconductors for the different annealing temperatures, Tan s, 400
and 500 ◦ C. The broken line shows the data for the DyBCO bulk
( Tan = 400 ◦ C) as a reference. The inset shows κab (T ) and thethermal conductivity along the c-axis, κc (T ), for YBCO bulk
annealed at 400 ◦ C [2].

Table 1. Specification of samples.

Tc (K)◦

SampleRE123:RE211

Tan = 400 C

450 ◦ C500 ◦ C

Er–Ba–Cu–O
Ho–Ba–Cu–O
Dy–Ba–Cu–O

1:0.33
1:0.4
1:0.4

88.8
91.5
87.8

88.8
—
—

89.4
88.9
—

for 7 days in 0.1 MPa flowing oxygen gas. As shownin table 1, the superconducting transition temperatures, Tc s,of all samples were about 90 K, obtained by electricalresistivity measurement.
The thermal conductivity wasmeasured by a conventional steady-state heat flow method [5].
The temperature gradient of the sample was estimated bymeasuring the temperature difference along the sample using
chromel–constantan thermocouples. The electrical resistivity
was measured by a conventional four-probe method with atypical current density of about 0.1 A cm−2 . The temperatureof the sample stage was controlled from 6 to 300 K usinga Gifford–McMahon cycle helium refrigerator. To eliminate
radiation loss, the thermal conductivity was measured below
250 K.

remains an unsolved problem. However, DyBCO has alreadybeen used for the current lead, utilizing its low κ [2]. Therefore
it is interesting to examine the nature of κ(T ) of REBCO bulks
containing the heavier RE elements in terms of the physics andpractical applications.
In this paper, we study mainly the temperature dependenceof the in-plane thermal conductivity, κab (T ), as a function of
annealing temperature, which is known to affect the oxygen
deficiency, for both ErBCO and HoBCO bulks; Er and Ho areboth heavier than Dy. We found that the absolute values ofκab (T ) of both bulks are larger than that of DyBCO bulk, andthat the broad peak below Tc is also more visible. However,both the absolute value and peak height in κab (T ) were still
somewhat smaller than those of YBCO bulk. In addition,
we estimated the anisotropy in the thermal conductivity for
ErBCO bulk.

3. Results and discussion
3.1. Thermal conductivity in the ab -plane for Er–Ba–Cu–O
and Ho–Ba–Cu–O bulks
Figure 1 shows the temperature dependence of the in-plane
resistivity, ρab (T ), for the ErBCO and HoBCO bulks withdifferent annealing temperatures [12], Tan s, of 400 and 500 ◦ C.
The data of DyBCO bulk (Tan = 400 ◦ C) are also shown
as a reference. All samples show the sharp superconducting
transition at around 90 K. The value of Tc for ErBCO is almost
independent of Tan . On the other hand, Tc for HoBCO changes
with Tan : Tc for the sample annealed at Tan = 400 ◦ C is slightly
higher than that for Tan = 500 ◦ C. Although the Tc value does
not systematically change with Tan , the absolute ρab values
increase with increasing Tan , meaning that the amount of theoxygen vacancies for the Tan = 400 ◦ C sample is smaller thanthat for the Tan = 500 ◦ C sample in both bulks.
Figure 2 shows the temperature dependence of the inplane thermal conductivity, κab (T ), for both ErBCO and2. Experimental details
ErBCO and HoBCO bulks were grown by a melt-texture
technique [10, 11]. For comparison, a DyBCO bulk wasalso prepared. The molar ratios of RE123 with RE211
powders were 1:0.33 (RE = Er), 1:0.4 (RE = Ho), and 1:0.4(RE = Dy), respectively. 0.5 wt% Pt powder was added inall samples. The rectangular shaped sample was prepared by
cutting an as-grown bulk near the seed crystal. The amountof oxygen deficiency, δ , in the RE123 phase of the sample
was varied by controlling the annealing temperature [12].
In this study, the samples were annealed at 400–500 ◦ C
2Supercond. Sci. Technol. 21 (2008) 085001

T Naito et al

HoBCO bulks. The data for DyBCO bulk (Tan = 400 ◦ C) arealso shown as a reference. In the ErBCO bulk, κab slightly
increases with decreasing temperature in the normal state forsamples annealed at both 400 and 500 ◦ C. Note that the slopeof the latter sample is somewhat small. In the superconducting
state, a broad peak can be observed, and the κab values at thepeak temperature are almost the same in both samples. For
HoBCO bulks, κab (T ) of the sample annealed at 400 ◦ C showsa slight positive slope (dκab /dT > 0) in the normal state whichbecomes more discernible in the sample annealed at 500 ◦ C.
The κab enhancement below Tc for HoBCO bulks is relatively
smaller than that for ErBCO bulks.
The magnitude of κab (T ) of ErBCO bulk is larger than thatof HoBCO bulk. This result does not come from the different
composition ratio between RE123 and RE211, because we
previously found that the κab values for the SmBCO andGdBCO bulks are almost independent of the composition ratio
in the case of high RE211 content, RE211/RE123  0.3 [4, 7].
The absolute κab values for both ErBCO and HoBCO
bulks studied here are larger than that for DyBCO bulk.
However, they are still smaller than that of YBCO bulk.
For comparison, the κab (T ) data for YBCO bulk [2] areshown in the inset of figure 2. It is well known that asimilar small magnitude of κab was observed in SmBCO andNdBCO bulks [4, 7]. The origin of the reduction in κab wasinterpreted as follows. With larger ionic radius of the RE, thesubstitution between the RE3+ and Ba2+ ions tends to occur
more easily [8]. This substitution gives rise to the formationof a RE1−x Ba2+x Cu3 O y -type solid solution, which works as aphonon scattering centre. As a result, the thermal conductivity
is strongly suppressed. However, this scenario cannot beapplicable to the results observed here. The ionic radii of Er3+
and Ho3+ are 0.1004 nm and 0.1015 nm, respectively, which
are smaller than that of Y3+ (0.1019 nm); thus we conclude thatthe substitution-induced reduction of κ does not occur in both
ErBCO and HoBCO bulks. Consequently, we can point out
only that the REBCO bulk containing heavy RE tends to showa small magnitude of the thermal conductivity, which mightcome from the low phonon frequency due to the heavy massof RE.
Let us discuss the change in the κab (T ) slope owing to
the different Tan in the normal state for HoBCO bulks. Notethat the slope change is negligibly small for ErBCO bulk, so
we do not discuss it here. In general, the thermal conductivity
in a conducting solid is composed of the phonon and charge
contributions, κ ph and κ ch . The latter contribution can be
estimated from the resistivity data using the Wiedemann–chFranz law, κab= LT /ρab , where L is the Lorenz number.
ch
The obtained κabvalues are constant values of roughly 6−1 −1
and 4 mW cm K above 90 K for Tan = 400 ◦ C and500 ◦ C samples, respectively. For REBCO bulk, the oxygen
deficiency, δ , in the RE123 phase, which increases withincreasing Tan , is related to the amount of charge carrier andacts as a point defect itself at the same time. Therefore theslope change due to the different Tan is not brought about
by the charge contribution but the phonon scattering due tothe point defects. Similar behaviour was observed in Y123
polycrystals [13].

Figure 3. (a) The temperature dependence of the in-plane andout-of-plane electrical resistivity, ρab (T ) and ρc (T ), respectively,
for Er–Ba–Cu–O (ErBCO) bulks with Tan = 450 ◦ C. (b) The
temperature dependence of the in-plane and out-of-plane thermal
conductivity, κab (T ) and κc (T ), respectively, for the same sample asin the resistivity measurements.

Considering the different temperature dependence of κabin the normal state between ErBCO and HoBCO bulks, thephonon scattering mechanism must differ considerably. Sinceκ ph is generally described by the T −1 -dependence in the casethat the phonon–phonon Umklapp process dominates the heattransport, the deviation from such behaviour for both bulks
indicates the existence of a powerful phonon scattering centre
in addition to the Umklapp process and point defects. To
get a deeper understanding of the possible phonon scattering
mechanism, we would need to measure the thermal diffusivity,
α , and sound velocity, v , which would give the phonon mean
free path ph from the relation α = 13 vph .
3.2. Anisotropic thermal conductivity of Er–Ba–Cu–O bulks
Figure 3(a) shows the temperature dependence of the electricalresistivity in the ab -plane, ρab (T ), and along the c-axis, ρc (T ),for ErBCO bulks annealed at Tan = 450 ◦ C. The anisotropy
parameter, γ , which is generally defined as the ratio of the inplane and out-of-plane
coherence length, is estimated to be of√about 5.3 from ρc /ρab at 100 K.
Figure 3(b) shows the temperature dependence of thethermal conductivity in the ab -plane, κab (T ), and along
the c-axis, κc (T ), for the same sample as in the resistivity
measurements. The behaviours of κab (T ) are quite similar
to those demonstrated in figure 2. On the other hand, κcincreases monotonically with decreasing temperature from 250
to around 50 K, with a rather broad peak at around 50 K,
and decreases toward zero. The anisotropy of the thermal
conductivity, γk (=κab /κc ), is estimated to be about 2 at around
100 K, which is somewhat smaller than γ = 5.3 described3Supercond. Sci. Technol. 21 (2008) 085001

T Naito et al

above or γk = 5.7 estimated from the data for Y123 single
crystals [14]. Considering the reported values of γk = 3–5 ataround 100 K for other REBCO bulks [3, 4], γk for ErBCO
bulk is not so anomalous. As shown in our previous report [5],
κ due to the Y211 phase is larger than κc of the Y123 phase.
Moreover, the temperature dependence and absolute values ofκc for ErBCO bulk are very similar to those for YBCO as
shown in the inset of figure 2, although the former κab (T ) is
half of the latter. Therefore, the relatively small γk for ErBCO
does not come from the content and/or distribution of the Er211
part, but the small magnitude of κab (T ). The results obtained
indicate that we have to use values of κab and κc that haveactually been measured for designing a practical application.

Acknowledgments
This work was supported in part by the JGC-S Scholarshipfoundation (No. 1907) and a Grant-in-Aid for Scientific
Research (No. 19560003) from JSPS, Japan.

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4. Summary
We have measured the temperature dependence of the in-plane
thermal conductivity, κab (T ), for both Er–Ba–Cu–O and Ho–
Ba–Cu–O superconducting bulks as a function of the annealing
temperature. To our knowledge, this is the first report of results
for both bulks. We found that the absolute values of κab (T ) of
both bulks are larger than that of Dy–Ba–Cu–O bulk, which iswell known to show an anomalous small κab , and that the broad
peak below Tc is also more visible. However their κab (T )values are still rather smaller than that of Y–Ba–Cu–O bulk.
The behaviours of κab (T ) in the normal state deviate from theT −1 -dependence for both bulks, which indicates the existenceof powerful phonon scattering centres in addition to the crystal
defects, unlike Y–Ba–Cu–O. As a result, both Er–Ba–Cu–O
and Ho–Ba–Cu–O bulks show the relatively small magnitudeof κab . To understand this, we pointed out that only a RE–
Ba–Cu–O bulk containing a heavy RE (rare earth elements)
tends to show small κab . The c-axis thermal conductivity was
also measured for Er–Ba–Cu–O bulk, and the anisotropy of thethermal conductivity, (κab /κc ), was estimated to be about 2.

4