Journal of Low Temperature Physics, VoL 105, Nos. 3/4, 1996

Thermal Conductivity and Phonon Scattering
Mechanisms in La2.xMxCuO 4
Hiroyuki Fujishiro, Manabu Ikebe, Masayuki Yagi,
Kiminari Nakasato,Yuzo Shibazaki and Tetsuo Fukase*
Faculty of Engb~eering, Iwate University, Morioka 020, Janan*Institutefor Materials Research, Tohoku University, Sendal 980, JapanThe thermal conductivity x of high densityLa2.xMxCu04 (M=Ba, Sr) sinteredmaterials was measured between 15K and 150K for the various
concentrations of Ba and the phonon thermal conductivity was analyzed
comparing with that of Nd2.xCexCu04 . The pretty large ~ value for pure
La2CuO 4 was drastically diminished by substituting La by a small amount ofBa atoms especially at low temperatures. It was found that a new type of thephonon scattering center such as a two-level tunneling must be taken accountof in order to explain the observed tc reduction.
PACS number: 74. 25 Fy, 74. 72.Jt, 74. 62.Dh.

1. INTRODUCTION
In several high-Tc cuprates such as YBCO, Bi2223 etc., the temperaturedependence of the thermal conductivity K(T) shows a characteristic enhancement below the transition temperature T c. In contrast, so-called (214) familysuch as La2.xMxCuO 4 (M=Ba, Sr) with T-type and Ln2.xCexCuO 4 (Ln=Nd, Pr)with T'-type crystal structure do not clearly show the characteristic K(T) enhancement. There is much argument about the origin of the ~;(T) enhancement, whether it is electronic or phononic. We have measured the thermal
conductivity K of YBa2Cu3071,(BiPb)2Sr2CazCu3Ox2, Nd2.xCexCuO43 etc. andhave systematically analyzed the phonon thermal conductivity ~ph based on
the Tewordt and Wolkhausen (TW) theory 4. We fabricated high density
sintered La2_xBaxCuO4 and La1.85Sr0.15CuO4 crystals and the thermal conductivity ~: and the thermal diffusivity c~ were investigated as a function of Ba
concentration X. In this paper, the phonon scattering mechanisms in La214
system are analyzed.
981
0022-2291/96/1100-0981509.50/0 9 1996 Plenum Publishing Corporation

982

H. Fujishiro et al.

2. E X P E R I M E N T A L
La>xBaxCuO4 sintered materials (0 -< X -< 0.2) and Lal.ssSro.15CuO 4 wereprepared from stoichiometric mixtures of La203, BaCO 3 (SrCO3) and CuO
raw powders. The mixtures were calcined twice at 880~ for 12h in air. They
were pressed into pellets and sintered at 1100~ for 18h in air and thenfurnace-cooled. Finally, the samples were heat-treated at 800~ for 24h inflowing oxygen. The X-ray diffraction analyses confirmed a single T-phasestructure for all the samples. The density of each sample was higher than 90%of the ideal density. The K measurement was made between 10 - 150K by acontinuous heat flow method and (x was measured simultaneously with K by
an arbitrary heating method under an identical experimental setup 2.

3. R E S U L T S
Figure I shows the temperature dependence of the electrical resistivity p of
La2_xBaxCuO4 (0 < X ~ 0.2) and La1.ssSr0.15CuO4 samples. The p values ofBa-substituted samples decreased with increasing Ba concentration X. T c increased with increasing X and reached a maximum of To=28K (X=0.15) andthen decreased with further increase of X. Lal,ssSr0asCuO4 showed Tc=38K,
the highest To among the samples in this report. Figure 2 shows the thermal
conductivity ~: as a function of temperature T. The pretty large K values for

--•-o

6

M=Ba,X=0.02

M=Ba,X=0.05 I--m5

M=Ba,X=0A5 If[ ] - - M=Ba,X=0.20 I

AoEO

1

M=Ba, X=0.10

M=Sr,X=O.lS I J

J-xSf~.~A./.
-J~"II43,m=.

2
1~-.~'J,

00-,----2.•215 - v 4 ,,I,,,,

100
200
Temperature(K)

300Fig. 1. The temperature dependence of the electrical resistivity 9 of La2.xBaxCuO4(0 < X < 0.2) and Lal.shSro.15CuO4 samples.

Thermal Conductivity of La2.xMxCuO4983

the pure La2CuO4 sample with the maximum value about 80mW/cmK at about
37K were drastically diminished by substituting La by Ba atoms. This
remarkable reduction in K makes a marked contrast to Nd substitution by Cein Nd2.xCexCuO4, in which case n was enhanced with X as shown in Fig. 33.
The specific heat C(T) was estimated from the relation C=K/e and the Debye
temperature OD=400K was found to be roughly appropriate for all thepresent samples from Debye specific heat lines.
~'100-,,,,I'. . . . . . . .
[9 M=Ba,X=0]o
M=Ba,X=0.02~f"809%e~,._.

=e 99960.~

9[]

M=Ba,M=Ba,M=Ba,
M=Ba,

[

9M=Sr, X=0.15

X=O.05
X=0.10
X=0.15
X=0.20940oooooooO~176 o o ~ 1 7 6 o o o ~ o O O % o " 9ooOO*E~too___~~"9a]I....,,,....

,

9m"a="%[[. ~. 9__~ 9A9,La~.xMxCUO,lM=Ba,Sr)

050
Temperature

100(K)

150

Fig. 2. The temperature dependenceof the thermal conductivity ~: of La2.xBaxCuO4(0 ~; X ~ 0.2) and LaLssSro.lsCuO4 samples.
~.400Ilnr

iill,l,if

E0~300

&A

9l

=

X=OoA

X=0.10
X=0.15
X=0.2

9 oo~ =AOoA~iii

9 oo>~.= 2 0 0~

AA0Nd2.xCexCuO~

O aZ~Oo0 i Ao.~e%...

0 100

94O &&k9~~176 o ..Ae - 9 A. A el, 9 9 ~ ~"~"~AO~O^O^~- -~Ou@0000000~O~

&.

,F-0=

0ii~

I~

I~

50
Temperature

eI100(K)iI

I50

Fig. 3. The temperature dependenceof the thermal conductivity ~: of Nd2.xCexCuO4(0 < X < 0.2) samples of our previous study3.

984

H. Fujishiro et al.

4. DISCUSSION
The heat transport in conductors is due to both electrons (~) and phonons(~:ph)' We assume that the electron contribution in the superconducting state,K~sfollows the theory proposed by Kadanoff and Martin 5 with the d-wave en 5
ergy gap 5=2ABcsCOS2~b6. Taking account of the phonon scattering by vari~
ous crystal defects and electrons, the phonon thermal conductivity ~:p~=~-~:~ isgiven by 7%/r
3dnRT 3v2 ( X4C(1)

where n(=7) is the number of atoms composing these compounds, R the gas
constant, v(=5000m/s) the average phonon velocity and x is the reduced
phonon frequency, respectively. The phonon relaxation time "cph is given byT h-l-T-1 + T - ~ + T1T-1 + ' g -1 +-gV-1
P-- b~' 4~e..

='t( 1 + p T :g~ + Uxexp(-Or~T ) +ETXg(X, y) +KTX.

(2)

H e r e , T b is the phonon relaxation time due to grain boundaries and p and E
refer to the strength of the phonon scattering by point defects and electrons,respectively. The function Uexp(-|(a=1.8) is a standard form ofphonon Umklapp processes at relatively low temperatures 8. Let us notice that
KTX term, which usually corresponds to the phonon scattering by strain
fields of dislocation, may also be regarded as standing for the scattering by
two-level tunneling states familiar in amorphous solids. The KTX term resultsin T 2 dependence of K(T) at very low temperatures and gives much the same
results as K'Txtanh(X/2) term which explicitly corresponds to the tunnelinglevel scattering. The function g(X, y)='tp~/tp~ which depends on the energy
gap through the parameter B=A(T)/kBT stands for the ratio of the phononelectron relaxation time in the normal and superconducting state 11. ~%=ldv
was determined by the grain size of each sintered material lb, which wasmeasured by a scanning electron microscope (SEM).
Figure 4(a) shows the fitting curves for the phonon thermal conductivity~:p~ of the La2_xBaxCuO4 samples. The parameters used and determined in thefitting process are summarized in Table I. The calculated l<ph(T) could fully
reproduce the experimental data. Kph was remarkably reduced even for Ba
concentration of only x=0.02. The phonon scattering by point defects
increased presumably by substituted Ba ions and the strength of Umklapp
processes Udecreased. The reduction in K is not due to only the increase of

Thermal Conductivity of La2.xMxCuO4985

the point defect and the boundary scatterings. The strength of the phonon
scattering represented by the KTx term increased with increasing X. This
increase of the K term is mainly responsible for the peculiar K depression atlow temperatures. We propose that the enhancement of the K term comesfrom local structural instability probably connected with the instability of thelow temperature orthorhombic (LTO) lattice against the high temperature
tetragonal (HTT) phase. The LTO phase is known to become more unstable80(a)=06O"~40P

E~~E!t-x=o05~20Oc/:,n [] u - -La2.xBaxCuO 40a.

X=0.20

00,

~

I

~

J,,50

I,~,50100

Temperature (K)

40''

I''''

I''''(b)T =38K9" ~20

M_-s/ ~ M=Ba

~Ee---I-"

coE

lO///

Lal.asMo.lsCU04

T=28K

0eItIII

50IIaII

100

Temperature (K)IIII50

Fig. 4. (a) The fitting curves for the phonon thermal conductivity ~ph of theLa2.xBaxCuO4 samples. (b) The ~:p~sfitting curves f o r Lal.85Ba0.15CuO4 andLal.ssSro.15CuO4 superconductingsamples.

986

H. Fujishiro et al.

Table I. Fitting parameters determinedby Kph analyses.
LBCO LBCO LBCO
LBCO LBCO LBCO LSCO
(X=0) (x=0.02) ( X = 0 . 0 5 ~ 0 . ~ 5 )(X=0.2)___~--0.15)x(l(s a) 1.6x108 2.9xllf 5.7x108 8.1xl08 8.1xlOs 1.0xl09 6,7x108
57tb(~m)
3117966U(K-2s1) 1.8x1012 1.3x1011
00000p(K-4s"1) 1.1xl03 4.8x103 6.8x103 7.3x103 8.1x103 9.3x103 1.1x104
E(Kls -1)
00008.1x107
01.9x108
L0000
0.02
00.05
K(Kqs-1) 2.7x10s 3.7x108 6.8x108 8.9x10s 8.9xi0s 1.0xl09 3.2xt08
T(K)1026282538

by substitution of La by Ba and Sr atoms. The tunneling states related toapical oxygens may be the origin of the K term, because the apical oxygen
plays a key role at LTO to HTT transition.
Figure 4(b) shows the Kpb~ fitting curves for Lal.ssBao.lsCuO4 andLa1.gsSr0.15CuQ superconducting samples. The characteristic enhancement
associated with the onset of superconductivity is confirmed, though very
weak, in this figure, which means that the electron-phonon coupling cannot
be neglected in La214 system. The enhancement of K of Laj.gsSro.~sCuO4 isclearer than that of La1.gsBa0nsCuO4 and the electron phonon coupling
constant ~. of La1.8sSr0.asCuO4 (=2a< t >.E/a~o,a is the lattice constant, < t >the effective hopping matrix element of electrons9) is three-times larger thanthat of Lal.85Ba0.~sCuO4, both of which, however~ were about one order ofmagnitude smaller than that of the 90K-phase YBCO1.
REFERENCES

1. H.Fujishiro, M.Ikebe, T.Naito and K.Noto, Physica C 235-240,825 (1994).
2. M.Ikebe, H.Fujishiro, T.Naito and K.Noto, J.Phys. Soc.Jpn. 63,3107 (1994).
3. H. Fujishiro, M. Ikebe, M. Yagi, M. Matsukawa, H. Ogasawara and K. Noto,
Physica B 219-220, 163 (1996).
4. L. Tewordt and T. Wolkhausen, Solid State Commun. 70,839 (1989) .
5. L.P. Kadanoff and P.C. Martin: Phys. Rev. 124, 670 (1962).
6. M. Ikebe, H. Fujishiro and K. Nakasato, to be published in J. Low Temp.
Phys. (1996).
7. L. Tewordt and T. Wolkhausen, Solid State Commun. 75, 515 (1990).
8. P.G.Klemens, in Solid State Physics, l (Academic Press, New York, I958)~
9. J. Bardeen, G. Rickayzen and L. Tewordt, Phys. Rev. 113~ 982 (1959).