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Journal of the Physical Society of Japan
Vol. 70, No. 3, March, 2001, pp. 628–631

Letters

Anomalous Lattice Softening at X = 0.19 and 0.82 in La1−X CaX MnO3
Hiroyuki Fujishiro, Tetsuo Fukase1 and Manabu Ikebe
Faculty of Engineering, Iwate University, 4-3-5 Ueda, Morioka 020-8551

1 Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Sendai 980-8577(Received December 13, 2000)

The longitudinal sound velocity vs (T ) has been measured for La1−X CaX MnO3 crystals,
and anomalous softenings of vs (T ) have been observed at the peculiar Ca concentrations of
X = 0.19 and X = 0.82. For the X = 0.19 sample, in which the ferromagnetic (FM) metallic
phase competes with the FM insulating phase with a polaron ordering, the anomalous vs (T )softening occurs immediately below the FM transition temperature Tc . For the X = 0.82
sample, in which the charge-ordered (CO) phase competes with the canted antiferromagnetic(CAF) phase, the deep local minimum of vs (T ) occurs around the CO transition temperature
TCO . These anomalous vs (T ) softenings result from the giant lattice ﬂuctuations which originate
from phase competitions and suggest strong charge-lattice and spin-lattice coupling in thissystem.
KEYWORDS: La1−X CaX MnO3 , sound velocity, electron-phonon coupling, lattice distortion, ferromagnetism,charge ordering, canted antiferromagnetism

Carrier-doped
perovskite
manganeseoxides,(RE1−X AEX )MnO3 (RE: rare-earth ion, AE: alkaline
earth ion), undergo a variety of dramatic phenomena such as colossal magnetoresistance (CMR), metalinsulator (M-I) transition and charge ordering.1, 2) The
CMR eﬀect is believed to involve strong electron-phonon
interaction in addition to a double-exchange mechanism.3) The most important origin for the strong
electron-phonon coupling is likely to be the Jahn-Teller
eﬀect due to Mn3+ spins. The local distortions of the
MnO6 octahedra play an important role in determining
the transport properties of the doped carriers, as suggested by neutron and X-ray diﬀraction studies.4, 5)
Important information on the lattice dynamics canalso be obtained from the sound velocity vs (T ) measurement. For La1−X SrX MnO3 6, 7) and La1−X CaX MnO3 ,8)
we reported the sound velocity anomalies associated withcharge ordering. For low hole concentrations, the distribution of the temperature T ∗ at which vs anomaly occurs
was centered at X = 1/8, which was consistent with thepolaron-ordered phase reported by Yamada et al.9)
In this paper, we report the very salient slowing downof vs (T ) in La1−X CaX MnO3 (LCMO) observed at thepeculiar Ca concentrations of X = 0.19 and X = 0.82.
We discuss the origin of the softenings on the basis of
the phase diagram in this system.
The La1−X CaX MnO3 (X = 0.15 ∼ 0.95) samples
were prepared from stoichiometric mixtures of La2 O3 ,CaCO3 and Mn3 O4 powders. The mixtures were calcined at 1000◦ C for 24 h in air, pressed into pellets andthen sintered at 1500◦ C for 8 h in air. The density of eachsample was determined by measuring the volume and theweight, which were conﬁrmed to be more than 85% of
the ideal values. X-ray diﬀraction analyses at room temperature conﬁrmed that all the samples showed a pureorthorhombic structure. The sound velocity vs (T ) was

measured using a pulse-superposition method from 4.2 K(or 90 K) to 300 K (or 400 K). Seven megahertz longitudinal waves used for the vs measurement were generatedby Z-cut LiNbO3 transducers. The electrical resistivity
ρ(T ) was measured by a standard four-probe method.
The thermal dilatation dL(T )/L was measured between
20 K and 300 K using a strain-gauge method. The magnetization M (T ) was measured from 10 to 300 K by asuperconducting quantum interference device (SQUID)
magnetometer.
Figure 1 shows the temperature dependence of thesound velocity vs (T ) for the 0.15 ≤ X ≤ 0.22 samples. For the X = 0.15 sample, an abrupt upturnin vs (T ) is observed below the characteristic temperature T ∗ ≈ 140 K. However, the vs (T ) anomaly ishardly discernible at the ferromagnetic Curie temperature, Tc = 175 K. The temperature T ∗ decreases to
120 K for the X = 0.18 sample. As reported in the previous paper,8) the X dependence of T ∗ is centered at
the Ca concentration X = 1/8, and the vs (T ) upturns
at T ∗ correspond to the polaron ordering. The anomaly
at T ∗ suggests the strong electron-phonon interaction inthis system. In contrast, the T ∗ anomaly disappears
for the X = 0.19 sample and the anomalous softening
in vs (T ) occurs immediately below Tc = 180 K. Then,vs (T ) takes a deep local minimum at T  = 160 K andsharply increases with further decrease in temperature.
For the X = 0.22 sample, only the vs (T ) upturn was observed immediately below Tc , which suggests the strong
coupling of the lattice to the spins.
Figure 2 presents the thermal dilatation dL(T )/L for
the same samples. As is evident, dL/L for X ≤ 0.18
shows no anomaly at Tc , while dL/L for X ≥ 0.19 showsa clear contraction at Tc with decreasing temperature.
The data of dL/L clearly demonstrate that there should
be a phase boundary between X = 0.18 and X = 0.19.
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Letters

Fig. 1. Temperature dependence of the sound velocity vs (T ) of
the La1−X CaX MnO3 samples for 0.15 ≤ X ≤ 0.22. Closed
arrows indicate the FM transition temperature Tc determinedfrom the magnetization M (T ) measurement. Open arrows for
X = 0.15 and 0.18 show the characteristic temperature T ∗ atwhich the vs (T ) upturn occurs.

Fig. 2. Temperature dependence of the thermal dilatationdL(T )/L for the same samples shown in Fig. 1. The arrows
indicate Tc determined from the M (T ) measurement. The data
demonstrate that there should be a phase boundary between
X = 0.18 and X = 0.19.

The results in Fig. 2 suggest that the lattice contraction
occurs accompanied by the transition from the paramagnetic insulator to the FM metal in this X range.
Figure 3 presents vs (T ) for X = 0.75, 0.82, 0.82 and
0.95. All the samples in this ﬁgure, except X = 0.95,
show pretty large lattice softening around the chargeordering temperature TCO (X = 0.75, 0.82) or the canted
antiferromagnetic (CAF) transition temperature TCAF
(X = 0.90)10) but the softening is the most drastic for
X = 0.82. It is worthwhile to note that the vs anomaly
is small for X = 0.95. This ﬁnding supports the ideathat the intrinsic origin of the eminent vs anomaly is
the Jahn-Teller distortion around the Mn3+ ions; thenumber density of the Mn3+ ions becomes very small at
this Ca2+ ion concentration.
Figure 4 presents dL(T )/L for the same samples as

629

Fig. 3. Sound velocity vs (T ) of the La1−X CaX MnO3 samples forfor X = 0.75, 0.82, 0.90 and 0.95. Open and closed arrows indicate the charge-ordered (CO) transition temperature TCO andthe canted antiferromagnetic (CAF) temperature TCAF determined from the M (T ) measurements.

Fig. 4. Temperature dependence of the thermal dilatationdL(T )/L for the same samples shown in Fig. 3. The data areconsistent with the existence of the phase boundary at X ≈ 0.82.

in Fig. 3. With decreasing temperature, dL/L of the
X = 0.75 shows expansion at TCO , while dL/L of the
X = 0.90 sample shows a contraction at TCAF and theanomaly is not discernible for X = 0.82. These data
again demonstrate that the phase boundary exists in thevicinity of X = 0.82. It is also to be noted that thelattice contracts at TCAF . Although the X = 0.90 sample does not show metallic conduction below TCAF , its
resistivity is far smaller10) than that of charge-ordered
LCMO samples. There seems to be a general tendency
for dL/L to show contraction at the transitions into conductive phases.
As we have seen, considerable lattice softening occurs
at the critical concentration near the phase boundaries
in La1−X CaX MnO3 . Figure 5 presents the phase diagram of the LCMO system determined by the present
authors on the basis of the magnetization M (T ) and thesound velocity vs (T ).8, 10) In La1−X CaX MnO3 at aroundJ. Phys. Soc. Jpn. Downloaded from journals.jps.jp by on 06/06/17

630

Letters

Fig. 5. The phase diagram of the La1−X CaX MnO3 system determined by the present authors. Tc is the Curie temperature which
is determined from the M (T ) [] and vs (T ) [●]. T ∗ is the CO
temperature which is determined from the vs (T ) anomaly [■].
TCO is the CO temperature which is determined from the M (T )[] and vs (T ) [▲]. TCAF is the CAF temperature determinedfrom the M (T ) [].8, 10)

X = 0.48, there is another important phase boundary
between the ferromagnetic metal and the charge-orderedinsulator.11–13) Figure 6 presents vs (T ) for X = 0.45,
0.48 and 0.50 and Fig. 7 presents dL(T )/L for the same
samples. Figure 8 shows the magnetization M (T ) under the applied ﬁeld of 0.5 T. As shown in Fig. 8, theX = 0.45 sample is ferromagnetic and X = 0.50 belongs
to the CO phase. The X = 0.48 sample shows a two-steptransition; the ferromagnetic phase below Tc = 230 K is
replaced by the charge-ordered phase at lower temperatures.14) The CO transition shows marked hysteresis between the increasing and decreasing temperature scans.
The hysteresis is also clearly observable for vs (T ) anddL(T )/L in Figs. 6 and 7. Again, dL/L of ferromagnetic
La0.55 Ca0.45 MnO3 shows a contraction at Tc and chargeordered La0.50 Ca0.50 MnO3 shows expansion at TCO withdecreasing temperature. In Fig. 6, we note that the lattice softening is very small at these concentrations X
near the FM-CO phase boundary. In order to obtain aclearer quantitative view of the vs softening, we plot in
Fig. 9 the reduced sound velocity vs /vmin vs the reduced
temperature t (= T /Tc or T /TCO ) for X = 0.19, 0.48
and 0.82.
Now let us discuss the origin of the sound velocity
softening in the LCMO system. The longitudinal soundvelocity is given by the following equation;3(1 − σ),(1)vs =
ρ(1 + σ)KT
where KT is the compressibility, σ the Poisson ratio andρ the mass density. The compressibility KT is related
to the correlation of the local volume ﬂuctuation [V (r)V (r)],15)
1KT =dr  [V (r) − V (r)] × [V (r  ) − V (r  )],kB(2)

Fig. 6. Temperature dependence of the sound velocity vs (T ) of
the La1−X CaX MnO3 samples for X = 0.45, 0.48 and 0.50.
Closed and open arrows indicate Tc and TCO , respectively, determined from the M (T ) measurements. Hysteretic behavior isobservable for X = 0.48.

Fig. 7. Thermal dilatation dL(T )/L for the same samples shownin Fig. 6. Hysteretic behavior is discernible for X = 0.48.

where kB is the Boltzmann constant and the angularbracket indicates the statistical average. Equations (1)and (2) suggest that the occurrence of very large local
ﬂuctuations is responsible for the observed giant latticesoftening for La0.81 Ca0.19 MnO3 and La0.18 Ca0.82 MnO3 .
The main origin of the large volume ﬂuctuations is considered to be the two-phase competition, i.e., the competition between the insulating and metallic phases at
X = 0.19 and that between the CO and CAF phases at
X = 0.82. If the free energy diﬀerence with regard to
the Ca concentration X is smooth and of second-orderlike across these phase boundaries, large-scale ﬂuctuations of the order parameters may occur in the vicinityof Tc and TCO , because additional freedom of the orderparameter ﬂuctuations corresponding to the competing
third phase is permitted. As the data for the thermal
dilatation dL(T )/L suggest, the ﬂuctuations of the order parameter accompany the strong lattice ﬂuctuationsin this La1−X CaX MnO3 system, resulting in the marked
sound velocity softening.

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Letters

Fig. 8. Magnetization M (T ) of the La1−X CaX MnO3 samples for
X = 0.45, 0.48 and 0.50 under the applied ﬁeld of 0.5 T. M (T )for X = 0.48 shows marked hysteresis.

Fig. 9. Normalized sound velocity vs /vmin vs the reduced temperature t (= T /Tc or T /TCO ) for the X = 0.19, 0.48 and 0.82
samples.

In contrast, vs (T ) of La0.52 Ca0.48 MnO3 does not show
any signiﬁcant softening around Tc , in spite of the competing FM-I and CO phases. As all the hysteresis behaviors of vs (T ), dL(T )/L and M (T ) clearly demonstrate,
the phase transition between the FM-M and the COphases are typically of the ﬁrst order. Thus the phaseboundary between them is not smooth in terms of thefree energy, which may preclude the occurrence of thecorrelated local volume ﬂuctuations around the phasetransition temperatures.
In summary, conspicuous slowing down of the longitudinal sound velocity vs (T ) in La1−X CaX MnO3 has been
observed for X = 0.19 and X = 0.82. Around X = 0.19,
the insulating ferromagnetic (FMI) phase competes with631

the metallic FMM phase, while around X = 0.82, thecharge-ordered phase competes with the CAF phase.
The anomalous lattice softenings result from the correlated large local lattice volume ﬂuctuations around phasetransition temperatures. The large lattice ﬂuctuation
may be possible if the free energy diﬀerence with regard to the Ca concentration X is small and smooth(second-order-like) between the competing two phasesof this strongly carrier-lattice- and spin-lattice-coupledsystem. We suggest that the free energy diﬀerences are
small and smooth across the FMI-FMM phase boundary
at X ∼ 0.19 and across the CO and CAF phase boundary at X ∼ 0.82. In contrast, vs (T ) softening was notobserved for the FMM-CO phase boundary at X ∼ 0.48.
With decreasing temperature, La0.52 Ca0.48 MnO3 showsa typical ﬁrst-order transition from FMM to CO phasewith very large hysteresis. The free energy diﬀerence is
not smooth across this phase boundary at X ∼ 0.48.
The phase diagram of La1−X CaX MnO3 over the entire
X range was proposed on the basis of the electrical resistivity ρ(T ), magnetization M (T ), thermal dilatationdL(T )/L and vs (T ) measurements.
Sound velocity measurement was performed under theinteruniversity cooperative research program of the Institute for Materials Research, Tohoku University. This
work was partially supported by a Grant-in-Aid for Scientiﬁc Research from the Ministry of Education, Science,Sports and Culture (No. 09640414).
1) Y. Tokura, A. Urushibara, Y. Moritomo, T. Arima, A.
Asamitsu, G. Kido and N. Furukawa: J. Phys. Soc. Jpn. 63(1994) 3931.
2) H. Y. Hurang, S.-W. Cheong, P. G. Radeli, M. Marezio and
B. Battlog: Phys. Rev. Lett. 75 (1995) 914.
3) A. J. Millis, P. B. Littlewood and B. I. Shaiman: Phys. Rev.
Lett. 74 (1995) 5144.
4) P. Dai, Jiandi Zhang, H. A. Mook, S.-H. Liou, P. A. Dowben
and E. W. Plummer: Phys. Rev. B 54 (1996) R3694.
5) C. H. Booth, F. Bridges, G. H. Kwei, J. M. Lawrence, A. L.
Cornelius and J. J. Neumeier: Phys. Rev. Lett. 80 (1998) 853.
6) H. Fujishiro, M. Ikebe, Y. Konno and T. Fukase: J. Phys. Soc.
Jpn. 66 (1997) 3703.
7) H. Fujishiro, T. Fukase and M. Ikebe: J. Phys. Soc. Jpn. 67(1998) 2582.
8) H. Fujishiro, T. Fukase, M. Ikebe and T. Kikuchi: J. Phys.
Soc. Jpn. 68 (1999) 1469.
9) Y. Yamada, O. Hino, S. Nohdo, R. Kanao, T. Imai and S.
Katano: Phys. Rev. Lett. 77 (1996) 904.
10) H. Fujishiro, M. Ikebe, S. Ohshiden and K. Noto: J. Phys. Soc.
Jpn. 69 (2000) 1865.
11) P. Schiﬀer, A. P. Ramirez, W. Bao and S.-W. Cheong: Phys.
Rev. Lett. 75 (1995) 3336.
12) A. Moreo, S. Yunoki and E. Dagotto: Science 283 (1999) 2034.
13) S. Mori, C. H. Chen and S.-W. Cheong: Nature 392 (1998)
473.
14) M. Roy, J. F. Mitchell, A. P. Ramirez and P. Schiﬀer: Phys.
Rev. B 58 (1998) 8185.
15) see, for example, L. E. Reichl: A Modern Course in Statistical
Physics (University of Texas Press, New York, 1980).