phys. stat. sol. (b) 225, No. 1, 135–143 (2001)

Characteristic Phonon Scattering Enhancement Correlatedwith Magnetic and Charge Ordersin La1XSrXMnO3 (X  0.50)
M. Ikebe1), H. Fujishiro, S. Kanoh, and T. Mikami*)
Department of Materials Science and Technology, Faculty of Engineering,
Iwate University, 4-3-5 Ueda, Morioka 020-8551, Japan(Received September 11, 2000; in revised form December 8, 2000;
accepted December 8, 2000)
Subject classification: 63.20.Dj; 66.70.+f; 72.15.Eb; 75.30.Kz; S10.15
The thermal conductivity j(T) and the thermal diffusivity a(T) of La1––XSrXMnO3 (X  0.50) havebeen measured and phonon scattering mechanisms have been analyzed in terms of the power of dependence on phonon frequency wph. For 0.50  X < 0.55, where the high temperature ferromagnetic phasebecomes unstable against the A-type antiferromagnetic (AF) order, the phonon scattering mechanism
proportional to w1ph is enhanced in the low temperature AF phase. In contrast, in the charge ordered4
is enhanced. The enhancephase for X  0.67, the phonon scattering mechanism proportional to wph
ment in the phonon scattering mechanisms reflects the types of the order in this manganese system.

1. Introduction
A series of carrier doped manganites with the formula RE1––XAEXMnO3 (RE: lanthanide, AE: alkaline earth ions) show a variety of dramatic physical properties on thestage of the Mott metal–insulator transition. The dramatic properties result from competition or cooperation of various interactions such as the ferromagnetic double exchange, antiferromagnetic superexchange, charge ordering, orbital ordering, static anddynamic Jahn-Teller effect and structural instability etc. From theoretical [1] and experimental [2–7] investigations, it has been widely recognized that, besides the double exchange interaction, the electron-lattice coupling is important to determine the transport
properties. The electrical transport has been extensively and intensively studied, while
the thermal transport has not been so systematically investigated [8–11]. Because theelectrical resistivity r(T) of La1––XSrXMnO3 is pretty large even in the ferromagnetic
metallic phase, the heat conduction is overwhelmingly due to phonons. The phonon
scattering in the manganite compound is expected to show uncommon features because
the lattice system is also under a strong influence of the various interactions whichcause uncommon properties of the electron system.
La1––XSrXMnO3 (LSMO) exhibits various magnetic and charge order phenomena for
X  0.50. Our previous studies for the electrical resistivity r(T) [12], the magnetization
M(T) [13] and the sound velocity anomaly [12] have clarified the following characteristics of the phase diagram of LSMO. LSMO (X ¼ 0.48) is a ferromagnet with Tc ¼ 320 K.
For X ¼ 0.50 and 0.55, the high temperature ferromagnetic (FM) phase becomes
unstable against the layer-type (A-type) antiferromagnetic (AF) order. The A-type AF
1) Tel.: +81-19-621-6362; FAX: +81-19-621-6373; e-mail address: ikebe@iwate-u.ac.jp*) Present address: Nippon System Ware Co. Ltd., Sakuragaoka, Shibuya-ku, Tokyo 150-0031,
Japan.

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M. Ikebe et al.: Phonon Scattering Enhancement Correlated with Magnetic Order

order is stabilized below TN for 0.50  X  0.60 in the LSMO system [12–14]. It is tobe noticed that the A-type AF order is not compatible with the charge order (CO)phase [15]. The CO transition takes place for X ¼ 0.67 and X ¼ 0.75, possibly concomitant with the C-type AF order [16]. We have already reported an anomalous phonon
scattering mechanism operating in LSMO (X  0.17) compounds around the ferromagnetic ordering temperature Tc [11]. For these compounds, the strong phonon scattering
around Tc was pointed out to originate from dynamical structural fluctuations correlated with critical spin fluctuations. We have also pointed out a two-level-like dynamical
scattering mechanism which may operate in LSMO for X  0.125, where the chargeorder related to the polaron localization occurs [17]. In the present paper, we reportenhanced phonon scattering mechanisms characteristic of the type of ordering in
La1––XSrXMnO3 system for X  0.50.

2. Experimental
La1––XSrXMnO3 samples were prepared from stoichiometric mixtures of La2O3, SrCO3and Mn3O4 powders. The mixtures were calcined twice at 1000  C for 24 h in air,pressed into pellets and sintered at 1500  C for 8 h in air. The pellets were heat-treatedat 1500  C for 24 h in O2 gas flow. The densities of the samples, which were determinedby measuring the volume and weight, were higher than 80% of ideal ones. All thesamples were confirmed to be in a single phase by X-ray diffraction at room temperature. The thermal conductivity j(T) was automatically measured by a steady state heatflow method between 10 and 300 K, using a Gifford-McMahon cycle helium refrigerator as a cryostat [18]. The thermal diffusivity a(T) was measured by an arbitrary heating method under the same experimental setup as the j(T) measurement.

3. Experimental Results
Figures 1 to 4 show the temperature dependence of the phonon thermal conductivity
jph and the phonon thermal diffusivity aph (¼ jph/C, C specific heat) of LSMO for
X ¼ 0.48, 0.50, 0.60 and 0.67 as typical samples. The electronic contribution, je and ae,estimated from the Wiedemann-Franz law is negligibly small except for X ¼ 0.48. In
Fig. 1, for ferromagnetic LSMO (X ¼ 0.48), je (which is at most 2% of the total j) isFig. 1. The thermal conductivity
j(T) and the diffusivity a(T) as afunction of T for La1––XSrXMnO3(X ¼ 0.48). The solid line (10 K T  90 K) is the calculated fitting curve for j(T) (see text)

phys. stat. sol. (b) 225, No. 1 (2001)

137
Fig. 2. j(T) and a(T) of LSMO for
X ¼ 0.50, which are sharply depressed at the onset of the A-type
antiferromagnetic order at TN . The
solid line is the fitting curve

subtracted from the measured j to obtain jph. In Figs. 2 and 3, the arrow indicates theNéel temperature TN and in Fig. 4, the arrow represents the CO temperature TCO (¼ TN)
determined from r(T), M(T) or the sound velocity vs(T) [13].
With decreasing temperature, jph(T) of LSMO (X ¼ 0.50) in Fig. 2 shows a clear andsharp reduction around TN. This sample shows the FM order at Tc  290 K, which
gives place to the A-type AF order below TN  160 K [12, 13]. jph of LSMO (X ¼ 0.52)
shows the similar behavior, though the reduction at TN is considerably smaller (notshown in the figure). It is to be noticed that the FM to AF transition is of first orderwith hysteresis. The reduction of jph suggests an enhancement in the phonon scatteringor the appearance of a new scattering mechanism. The corresponding decrease in jph(¼ vs2htphi/3, htphi average phonon scattering time) around TN can also be seen in Fig. 2,
which more directly demonstrates the phonon scattering enhancement. jph(T) andaph(T) of LSMO (X ¼ 0.67) in Fig. 4, also show a reduction around TCO . In contrast,
jph(T) of LSMO (X ¼ 0.60) in Fig. 3 shows a broad shallow dip around TN . This dip injph(T) is indicative of the phonon scattering enhancement through some dynamical mechanism related to the critical spin fluctuations around the second order magnetic phasetransition in this compound.

Fig. 3. j(T) and a(T) of LSMO
for X ¼ 0.60. The phonon scattering enhancement is noticeablearound TN. The solid line is thefitting curve

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M. Ikebe et al.: Phonon Scattering Enhancement Correlated with Magnetic Order
Fig. 4. j(T) and a(T) of LSMO
for X ¼ 0.67. The phonon scattering is strongly enhanced below
and above the charge order temperature TCO. The solid line is thefitting curve

As we have seen, the AF transition and the CO transition accompany the scatteringenhancement in LSMO. Including the data on other samples not presented in the figures, the effects of AF order and CO for X  0.50 are summarized as follows: (i) For
0.50  X < 0.55, where the FM order becomes unstable against the low temperature
A-type AF phase, the phonon scattering enhancement appears rather sharply at T N andthe enhancement occurs over the whole temperature range below TN . (ii) For 0.55  X
 0.60, where the A-type AF phase is dominant and the FM order is absent or not
influential, the phonon scattering enhancement occurs only in the critical region aroundT N and is not so significant at low temperatures. (iii) For 0.67  X  0.75, the chargeorder accompanied by the C-type AF order strongly enhances the phonon scattering
again over the whole temperature range below TCO . The enhancement appears rather
gradually at a temperature somewhat higher than TCO . In the following section, we
analyze the phonon scattering mechanisms operative in each ordered phase.

4. Discussion
On the basis of the relaxation time method [19], the phonon thermal conductivity isgiven by
3dnRT 3 2
vs
jph ¼
MQ3D

QDð=T
0

x4 ex
ðex  1Þ2

tph dx ;ð1Þ

where d is the mass density, M the weight of one mole, n the number of atoms in thechemical formula of the compound (n ¼ 5 for La1––XSrXMnO3), R the gas constant, QD
the Debye temperature and x (¼ wph/T) is the reduced phonon frequency. Assuming akind of Matthiessen’s rule for the phonon scattering rate, the phonon relaxation time
tph is given by (see, e.g., [19])
1
2 2
4 4
t1
ph ¼ t b þ KTx þ sT x þ pT x :ð2ÞHere, tb is the scattering time due to grain boundaries and the K, s and p terms represent the phonon scattering strength proportional to w1ph , w2ph and w4ph , respectively. It is
to be noticed that, with increasing power of wph, the corresponding scattering becomes

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phys. stat. sol. (b) 225, No. 1 (2001)

Fig. 5. The estimated specific heat C by
use of the relation C ¼ j/a. The solidline represents the Debye specific heat
for the Debye temperature QD ¼ 370 K

relatively more efficient in a higher
temperature region. The standard
theory of the phonon scattering [20]refers to the K term as the phonon
scattering by the strain fields
around dislocations and to the s andp term as the phonon Rayleigh scattering by sheet-like faults and point
defects, respectively. In order toanalyze the phonon scattering on the basis of eqs. (1) and (2), we need the QD value of
La1––XSrXMnO3. Since we have measured both j and a, the specific heat C (per unit
volume) can be estimated by the relation C ¼ j/a. Figure 5 shows the estimated specific heat of LSMO for X ¼ 0.50 and 0.67. As can be seen, the magnitudes of the specificheat of both specimens (and of other samples not shown in the figure) are roughly
consistent with the Debye specific heat line with QD ¼ 370 K. So we set the QD value
to be 370 K for all the present La1––XSrXMnO3 compounds. In the estimation of QD, theelectronic contribution to the specific heat was neglected because the carrier density is
low and the fitting with the Debye curve was performed in a rather high temperature
range (30 K < T < 90 K). The phonon scattering time by boundaries tb is set to satisfy
the relation lb ¼ tbvph, where lb is the average size of the grains. The size of lb wasdetermined to be 5 mm  lb  40 mm by a scanning electron microscope and vph was
determined by the ultrasonic pulse superposition method [12]. Actually, the grainboundary scattering is almost neglectable in the temperature range of the present work
(T > 10 K) because other scattering mechanisms are by far dominant. By using eqs. (1)and (2), jph was calculated to best fit the experimental data with K, s and p values asadjustable parameters. The fitting temperature region was selected between 10 and
90 K. It is to be noticed that the wph power law of tph given by eq. (2) is valid only fortemperatures well below QD and the fitting temperature region satisfies the condition,
Ta b l e 1
Summary of the parameters determined in the jph fitting processes in La1––XSrXMnO3
samples on the basis of eqs. (1) and (2)sampletb ––1
lb
s
p
K
d
vs
(g/cm3) (105 cm/s) (108 s ––1) (mm) (108 K ––2s ––1) (104 K ––4s ––1) (109 K ––1s ––1)

X ¼ 0.48
X ¼ 0.50
X ¼ 0.60
X ¼ 0.67

5.67
5.50
5.45
5.49

4.15
5.16
5.23
5.72

2.6
2.6
7.2
7.0

37
30
14
14

0.41
1.0
1.5
1.5

0.28
0.29
0.29
1.3

0.11
1.7
1.1
0.41

X ¼ 0.17

5.28

4.30

2.2

45

0.5

0.76

1.1

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M. Ikebe et al.: Phonon Scattering Enhancement Correlated with Magnetic Order

T < QD/4 [20]. The results of the fitting for jph are given in Figs. 1 to 4 by solid lines
and the parameter values determined are summarized in Table 1, together with theresults for another concentration X not shown in the figures.
In order to clearly see the contributions of each scattering mechanism, the total phonon scattering rate and the scattering rates of each scattering term were calculated as
an average over the Debye phonon spectrum. The results are given in Figs. 6a–d for
X ¼ 0.48, 0.50, 0.60 and 0.67. The total scattering rate htphit ––1 was calculated by use of
the following equation and the parameter values in Table 1:
QDð=T

tph
 1
tph ¼

0
QDð=T
0

x4 ex
ðex  1Þ2

dx
:

ð3Þ

4 x

x e

ðex  1Þ2

dx

Fig. 6. Calculated phonon scattering rate htphi ––1 and contributions of the scattering terms proportional to wph1 (K term), wph2 (s term), and wph4 (p term) for LSMO samples with a) X ¼ 0.48, b)
X ¼ 0.50, c) X ¼ 0.60 and d) X ¼ 0.67. The contributions of each scattering term were estimatedassuming that the every scattering term was completely removed (see text). Open circles are experimental points corresponding to the observed thermal conductivity j(T)phys. stat. sol. (b) 225, No. 1 (2001)

141

It is to be noticed that the total scattering rate is inversely proportional to the measured phonon thermal diffusivity aph (¼ vs2 htphi/3) if the sound velocity vs is assumed––1, weretemperature independent. The contributions of the K, s and p terms, htphiK,s,pobtained by calculating htphi on the assumption that the corresponding term is removed
and subtracting htphi ––1 from the total htphit––1 . On the basis of a number of trials, eachparameter value was reproducible within 5% of the total scattering rate htphi ––1.
Comparing Figs. 6a and b, we notice that the K-term (w1ph) contribution is appreciable for LSMO (X ¼ 0.50), in contrast to the very small, almost negligible K-term
contribution for ferromagnetic LSMO (X ¼ 0.48). As we have previously mentioned, astandard origin of K-term scattering is due to the strain fields around dislocations. In
the present LSMO (X ¼ 0.50), however, it is unlikely that the A-type AF order causes
a drastic increase of dislocations and the other phonon scattering mechanism must be
operative below TN. Another scattering mechanism which has approximately the same
w1ph dependence is due to tunneling states. The thermal dilatation dL/L of LSMO(X ¼ 0.50) displays a sharp contraction at TN with decreasing temperature [12]. This
result suggests an appreciable lattice change associated with the FM to AF transition inthis compound. In the previous paper [17] we pointed out a possibility of strong phonon tunneling scattering associated with the polaron order in LSMO for X  0.18. The
lattice site tunneling of oxygen, the most light atom composing LSMO, was considered
to be important for the phonon scattering. Because the FM and AF orders in
La0.50Sr0.50MnO3 accompany different lattice states through the strong spin–lattice interaction, a kind of two-level phonon scattering associated with spin fluctuation may bepossible in this compound. The scattering rate due to the two-level tunneling states isexpressed as ATx tanh (x/2) [21]. On the basis of the Debye phonon spectrum, thedominant phonon frequency wd at temperature T is given by hwd ¼ 1.6kBT and theterm ATx tanh (x/2) is approximately equal to ATx tanh (0.8) ¼ 0.67 ATx, thus giving
the same w1ph dependence as the K term in eq. (2). We propose that the appearance of
K-term scattering in LSMO (X ¼ 0.50) is due to the phonon scattering by lattice tunneling states which originates from the oxygen site tunneling correlated with FM and
AF order fluctuations.
Comparing the scattering strength of LSMO (X ¼ 0.67) in Fig. 6d to LSMO(X ¼ 0.50), we notice that the K-term scattering is weakened and the p-term component
is enhanced in this CO phase sample. Contrary to the A-type antiferromagnet LSMO(X ¼ 0.50), the lattice of LSMO (X ¼ 0.67) shows expansion around TCO with decreasing temperature [12] and there is a difference between the lattice states of the A-type
AF and the CO with C-type AF phases. Several recent investigations reported an enhancement of the Jahn-Teller distortion below the charge order onset temperature TCO.
4
is usually ascribed to the scattering by pointThe p-term scattering proportional to wph
type defects. If we literally follow this rule, the charge ordering should enhance thepoint defect scattering. This may be possible if CO enhances the local incoherent JahnTeller distortion around Mn3+ ions, though we cannot point out the exact origin of theenhancement at the present stage. The strong p-term scattering at low temperatures, is
one of the characteristic features of the phonon scattering in the CO phase samples.
Another characteristic feature of the phonon scattering enhancement in the COphase sample can be seen at high temperatures. In Fig. 4, both the conductivity j(T)and the diffusivity a(T) of LSMO (X ¼ 0.67) clearly decrease at higher temperatures
than its TCO . The similar behavior was observed also for LSMO (X ¼ 0.75). Recent

142

M. Ikebe et al.: Phonon Scattering Enhancement Correlated with Magnetic Orderextensive studies [21, 22] have shown that dynamic charge correlation is important inthese Mott insulators above TCO . The enhanced phonon scattering above TCO is indicative of the importance of a dynamical phonon scattering mechanism related to thecharge order fluctuation.
Although the enhanced K-term scattering provides a peculiarity of the A-type AF
state and the enhanced p-term scattering makes a peculiarity of the CO state accompanied with the C-type AF order, the s-term component is always dominant in Figs. 6a–d.
Especially in Fig. 6c, the scattering strength of both K and p term is weak for LSMO(X ¼ 0.60) and the s term is overwhelmingly dominant. This compound directly enters
into (possibly the A-type) AF order not showing the intermediate FM order. The dilatation dL/L displays very slight contraction at TN [12]. Then the lattice effect may not
be influential in this compound, which is possibly consistent with relatively small
2
K-term and p-term scattering. The s-term scattering, which is proportional to wph, usually comes from two-dimensional-like lattice defects such as stacking faults, twin boundaries, etc. The microscopic origin for the s-term scattering is not clear either, but thedominant s-term scattering provides another peculiarity of the phonon scattering in the
La1––XSrXMnO3 system as a whole.

5. Summary
The phonon thermal conductivity jph and the thermal diffusivity aph of La1––XSrXMnO3
were measured for the nonmetallic region of the Sr concentration X ( 0.50) and thephonon scattering mechanisms were analyzed in terms of the power of dependence onphonon frequency wph. The A-type antiferromagnetic order and the charge order accompanied with the C-type AF order resulted in an enhancement of the characteristic
phonon-scattering mechanisms. The phonon scattering proportional to w1ph was enhanced in La0.50Sr0.50MnO3 (A-type AF) and we proposed that the phonon scattering
due to tunneling states related to lattice instability might be important in4
was enhanced
La0.50Sr0.50MnO3. In contrast, the phonon scattering proportional to wph
in the charge ordered C-type AF phase of La0.33Sr0.67MnO3. The enhanced local Jahn4
phonon scatterTeller distortion might be responsible for the enhancement in the wph
ing. Thus, in the La1––XSrXMnO3 system the different type of ordering brings about aphonon scattering enhancement characterized by different power dependence on phonon frequency wph.

References[1] A.J. Millis, B.I. Shraiman, and R. Mueller, Phys. Rev. Lett. 77, 175 (1996).
[2] A. Asamitsu, Y. Moritomo, Y. Tomioka, T. Arima, and Y. Tokura, Nature 373, 407 (1995).
[3] H.Y. Huang, S-W. Cheong, P.G. Radaelli, M. Marezio, and B. Batlogg, Phys. Rev. Lett. 75,
914 (1995).
[4] P. Dai, J. Zhang, H.A. Mook, S-J. Liou, P.A. Dowben, and E.W. Plummer, Phys. Rev. B 54,
3694 (1996).
[5] S.J.L. Billinge, R.G.DiFrancesco, G.H. Kwei, J.J. Neumeir, and J.D. Thompson, Phys. Rev. Lett.
77, 715 (1995).
[6] G. Zhao, K. Conder, H. Keller, and K.A. Müller, Nature 381, 676 (1996).
[7] H. Kawano, R. Kajimoto, M. Kubota, and H. Yoshizawa, Phys. Rev. B 53, R14709 (1996).
[8] D.W. Visser, A.P. Ramirez, and M.A. Subramanian, Phys. Rev. Lett. 78, 3947 (1997).
[9] J.L. Cohn, J.J. Neumeier, C.P. Popoviciu, K.J. McClellan, and Th. Leventouri, Phys. Rev. B 56,
R8495 (1997).

phys. stat. sol. (b) 225, No. 1 (2001)

143[10] J. Hejtmanek, Z. Jirak, Z. Arnold, M. Marysko, S. Krupicka, C. Martin, and F. Damay, J.
Appl. Phys. 83, 7204 (1998).
[11] M. Ikebe, H. Fujishiro, and Y. Konno, J. Phys. Soc. Jpn. 67, 1083 (1998).
[12] H. Fujishiro, T. Fukase, and M. Ikebe, J. Phys. Soc. Jpn. 67, 2582 (1998).
[13] H. Fujishiro, M. Ikebe, and Y. Konno, J. Phys. Soc. Jpn. 67, 1799 (1998).
[14] T. Akimoto, Y. Maruyama, Y. Moritomo, A. Nakamura, K. Hirota, K. Ohoyama, and M. Ohashi, Phys. Rev. B 57, 1 (1998).
[15] H. Kawano, R. Kajimoto, H. Yoshizawa, Y. Tomioka, H. Kuwahara, and Y. Tokura, Phys.
Rev. Lett. 78, 4235 (1997).
[16] E.O. Wollan and W.C. Koeher, Phys. Rev. 100, 545 (1955).
[17] H. Fujishiro and M. Ikebe, Physica B 263/264, 691 (1999).
[18] M. Ikebe, H. Fujishiro, T. Naito, and K. Noto, J. Phys. Soc. Jpn. 63, 3107 (1994).
[19] R. Berman, Thermal Conduction in Solids, Clarendon Press, Oxford/New York 1976.
[20] P.G. Klemens, Solid State Physics, Eds. F. Seitz and D. Turnbull, Vol. 7, Academic Press,
New York 1958.
[21] S-W. Cheong and C.H. Chen, in: Colossal Magnetoresistance, Charge Ordering and Related
Properties of Manganese Oxides, Eds. C.N.R. Rao and B. Raveau, World Scientific, Singapore
1998.
[22] J. Zaanen, Science 286, 251 (1999).