Recently, it has been argued that a strong electron-phonon interaction arising from the Jahn-Teller splitting of the outer Mn d level plays a crucial role in understanding the nonmetal-to-metal transition observed in the La1-xAxMnO3 (A=Ca, Sr, Ba) system. We show, by neutron powder diffraction, that La0.65Ca0.35MnO3 exhibits an anomalous volume and oxygen/manganese displacement change around Tc, in qualitative agreement with the theoretical prediction

Dai, P.

Dowben, Peter A.

Liou, Sy_Hwang

Mook, H.A.

Plummer, E. Ward

Zhang, Jiandi

English

DigitalCommons@University of Nebraska

University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Peter Dowben Publications Research Papers in Physics and Astronomy 8-1-1996 Experimental evidence for the dynamic Jahn-Teller effect in La0.65Ca0.35MnO3 P. Dai Oak Ridge National Laboratory Jiandi Zhang University of Nebraska-Lincoln, jiandiz@lsu.edu H.A. Mook Oak Ridge National Laboratory Sy_Hwang Liou University of Nebraska-Lincoln, sliou@unl.edu Peter A. Dowben University of Nebraska-Lincoln, pdowben@unl.edu See next page for additional authors Follow this and additional works at: https://digitalcommons.unl.edu/physicsdowben  Part of the Physics Commons Dai, P.; Zhang, Jiandi; Mook, H.A.; Liou, Sy_Hwang; Dowben, Peter A.; and Plummer, E. Ward, "Experimental evidence for the dynamic Jahn-Teller effect in La0.65Ca0.35MnO3" (1996). Peter Dowben Publications. 45. https://digitalcommons.unl.edu/physicsdowben/45 This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Peter Dowben Publications by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. Authors P. Dai, Jiandi Zhang, H.A. Mook, Sy_Hwang Liou, Peter A. Dowben, and E. Ward Plummer This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/physicsdowben/45 Experimental evidence for the dynamic Jahn-Teller effect in La0.65Ca0.35MnO3P. DaiSolid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831Jiandi ZhangSolid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831and Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111H. A. MookSolid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831S.-H. Liou and P. A. DowbenDepartment of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111E. W. PlummerSolid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831and Department of Physics, University of Tennessee, Knoxville, Tennessee 37996~Received 7 November 1995!Recently, it has been argued that a strong electron-phonon interaction arising from the Jahn-Teller splittingof the outer Mnd level plays a crucial role in understanding the nonmetal-to-metal transition observed in theLa12xAxMnO3 (A5Ca,Sr,Ba! system. We show, by neutron powder diffraction, that La0.65Ca0.35MnO3 ex-hibits an anomalous volume and oxygen/manganese displacement change aroundTc , in qualitative agreementwith the theoretical prediction.@S0163-1829~96!00830-2#The recent rediscovery of ‘‘colossal magnetoresistance’’~CMR! in perovskite-based La12xAxMnO3 (A 5 Ca,Sr,Ba!1has generated considerable interest in these materials. In thedoping range of 0.2<x<0.4, La12xAxMnO3 orders ferro-magnetically and the temperature (T) dependence of the re-sistivity is closely related to the magnetic ordering. The‘‘double exchange’’ model, proposed some 30 years ago,2has been used more recently3 to explain the physics of theobserved nonmetal-to-metal transition. However, Milliset al.4 argue that double exchange alone cannot account forthe large resistivity drop below the paramagnetic to ferro-magnetic phase transition temperatureTc . A strong Jahn-Teller electron-phonon coupling must also play an essentialrole.5,6 In particular, the polaron effect, due in part to local-ization of the conduction band electrons by slowly fluctuat-ing ~dynamic! local Jahn-Teller distortions, is reduced dras-tically belowTc , permitting the formation of a metallic state.For medium electron-phonon coupling, which is believed tobe relevant to the composition range (0.2<x<0.4) wherethe nonmetal-to-metal transition is observed, Milliset al.predict that the temperature dependence of the average root-mean-square~rms! oxygen displacements is linear with aslope that is different forT above and belowTc .5 The largeelastic anharmonicity, coupled with the Jahn-Teller distor-tions, induces a large volume change that might have beenobserved.7–10Although some aspects of this model such as the behaviorof the resistivity5 agree well with the existing experimentalresults, the central prediction of anomalous temperature de-pendence of the rms oxygen displacements, due directly tothe electron-phonon coupling, is yet to be observed. The lackof a direct experimental proof has sparked lively debateabout the relevance of the dynamic Jahn-Teller distortion inunderstanding the microscopic origin of the observed CMReffect.6,11 In this paper, we present neutron diffractiondata which demonstrate that the polaron effect scenariosuggested by Milliset al. may indeed be realized in theLa0.65Ca0.35MnO3 system. Specifically, the oxygen and Mnrms displacements, obtained by neutron Rietveld analysis,are found to exhibit anomalous behavior aroundTc , in quali-tative agreement with the theoretical prediction.Our neutron experiments were performed using theHB-1A triple-axis and HB-4 high-resolution powder diffrac-tometers at the High-Flux Isotope Reactor at Oak Ridge Na-tional Laboratory. The HB-1A triple-axis spectrometer, op-erated in the two-axis mode with an incident beamwavelength of 2.356 Å and collimation of 408-408-108-308 in usual notation, was used for magnetization mea-surements. The HB-4 diffractometer has an array of 32 de-tectors and available instrument scattering angle between11° and 135°. When operated using the wavelength of1.0314 Å, it allows a maximum wavevector transferQ(54p/lsinu) of ;11.25 Å 21 to be reached.The polycrystalline sample used in the experiments wassynthesized by a solid state reaction. Starting materialsLa2O3, CaCO3, and Mn were mixed in stoichiometric pro-portions and heated in O2 at 1200 °C for 24 h, at 1350 °Cfor 50 h, and then at 1400 °C for 50 h with two intermediategrindings. The bulk magnetization, resistivity, and magne-toresistance are all consistent with previous results.12 Thefine black powder was loaded in a thin wall vanadium canwhich was then mounted inside a larger aluminum can filledPHYSICAL REVIEW B 1 AUGUST 1996-IIVOLUME 54, NUMBER 6540163-1829/96/54~6!/3694~4!/$10.00 R3694 © 1996 The American Physical Societywith helium exchange gas. For measurements below roomtemperature, the aluminum can was attached to the cold fin-ger of a Displex helium refrigerator. For higher temperaturemeasurements, we have used an Institute Laue Langevin typefurnace without the aluminum can. The temperature accu-racy for the Displex is about 1 K while the high-T furnacehas an uncertainty of610 K.Figure 1 shows the full pattern of the Rietveld analysisresult at 300 K using theGSAS program.13 We find that thecompound has an orthorhombic structure at all the tempera-tures investigated with a space groupPnma~Ref. 14! that isdifferent than the cubic structure proposed originally byWollan and Koehler7 and by Yakel8 for this Ca composition.The conclusion of an orthorhombic unit cell is drawn, notfrom the the observation of line splitting, but on the basis ofsuperlattice reflections absent in the cubic structure as shownin Fig. 1. The inset in Fig. 1 shows the unit cell structure,Table I summarizes the lattice parameters, selected bond dis-tances, and angles obtained from the Rietveld analysis.Having shown that the structure of our sample is ortho-rhombic, we now focus on the temperature dependence ofthe order parameter and the lattice constants. Figure 2 sum-marizes the results. Frame~a! displays the square of thesample magnetization, measured at zero field using the inten-sity change of the sum of~0,2,0! and~1,0,1! reflections as afunction of temperature on warming. The 2u angle of thereflection, directly related to the lattice parameters, is plottedin frame ~b!. Frames~c! and ~d! show the temperature de-pendence of the lattice parameters and unit cell volume. Theanisotropic lattice contractions aroundTc are clearly evidentin the data, indicating a strong coupling between the latticeand magnetism.Although the sample structure, magnetization, and latticeparameters are important to study, such information will notFIG. 1. Rietveld refinement patterns for La0.65Ca0.35MnO3 at 300 K. Plus marks are observed neutron-diffraction intensities, and thesolid line is calculated intensities. The first and second set of vertical marks below the profile indicate the positions of Bragg reflections forthe cubic and orthorhombic structure, respectively. Major reflections are labeled with the orthorhombic indices. The curve at the bottom isthe difference between the observed and calculated intensities for the orthorhombic structure. The inset shows the schematic crystal unit cell.The La/Ca, Mn, O~1!, and O~2! atoms are represented in green, red, light blue, and dark blue, respectively.TABLE I. Refined parameters for lattice constants, selectedbond distances, and angles at 300 and 40 K. Numbers in the paren-thesis are statistical errors of the last significant digit. O~1!-Mn andO~2!-Mn are along theb axis and in thea-c plane, respectively.Parameter T5300 K T540 Ka ~Å! 5.4537~4! 5.4371~6!b ~Å! 7.7042~6! 7.6793~7!c ~Å! 5.4682~4! 5.4496~5!O~1!-Mn~Å! 1.9562~6! 1.9512~7!O~2!-Mn~Å! 1.9596~26! 1.9512~24!O~2!-Mn~Å! 1.9557~26! 1.9507~25!Mn-O~1!-Mn(°) 159.86~19! 159.42~20!Mn-O~2!-Mn(°) 160.99~11! 161.11~12!54 R3695EXPERIMENTAL EVIDENCE FOR THE DYNAMIC. . .provide a direct test of the theory of the dynamic Jahn-Tellereffect. Neutron diffraction, however, is also ideal for deter-mining the oxygen rms displacements because of its sensi-tivity to oxygen atoms. The neutron cross section for coher-ent elastic scattering is proportional toe22W where theDebye-Waller temperature factor 2W(Q)5^(Q–u)2&, andthe rms displacements (^u2&) are therefore mostly sensitiveto the Bragg intensities at large wave-vector transfers. To testthis idea, Rietveld analysis was performed forT5300 and493 K data where no magnetic intensity is present in Braggreflections. We find that all the parameters are essentially thesame using a full~11°<2u<135°) and a partial(60°<2u<135°) pattern. Consequently, we have only analyzedthe partial pattern for all the temperatures to avoid compli-cation of magnetic ordering.15The procedure for analyzing the temperature dependenceof the HB-4 powder data is as follows. First, we simulta-neously refined the scale factor, background, and peak pro-file, lattice parameters, atomic positions, and Debye-Wallerfactors for all the atoms16 for the 40 K data set. The peakprofiles were then fixed to the optimum values at 40 K andother parameters allowed to vary in subsequent refinementsfor higher temperatures. For all the refinements, weightedR factors (Rwp) of ;7% were obtained with a reducedx2,about 1.2.Figure 3 summarizes the outcome for the temperature de-pendence of the atomic rms displacements for all the atomsin the unit cell. Frames~a! and~b! show the results for oxy-gen at two different sites@see inset of Fig. 1#. For conven-tional materials such as aluminum, the atomic Debye-WallerfactorW, therefore the rms displacement, is linear as a func-tion of temperature.17 If higher order anharmonic effects areimportant,W will contain additional terms which vary asT2 andT3. Instead of being linear, the data bear great resem-blance to theT dependence of the lattice parameters. Todetermine whether the observed anomalous behavior inWcan be entirely accounted for by the lattice expansion, wenote thatW, in the simplest phenomenological model, is re-lated to volume by W(T2)/W(T1)5@V(T2)/V(T1)#2g,whereg is the Grüneisen constant, which for most materialsis between 2 and 3.17 If the observed anharmonicity inW isdue entirely to volume expansion, one would expect the ef-fectiveg, or geff , computed fromW andV to be less than 3.Instead, we find thatgeff.85 for T between 260 and 40 Kand;25 between 600 and 260 K, suggesting that the vol-ume expansion is too small to account for the change inW. In the theory of the dynamic Jahn-Teller effect,4,5 theTdependence of the rms oxygen displacements is expected tobe linear with a slope that is different for temperatures aboveand belowTc . Our data agree with the model fairly well forT aboveTc , but deviate from it at low temperatures. Thepresence of the nonlinearT dependence in the oxygen rmsdisplacements suggests a strong elastic anharmonicity in thecrystal belowTc . Such anharmonicity, although known to bepresent, is not considered explicitly in the model of Milliset al.5 Therefore, calculations that include detailed structuralinformation, and possibly quantum effects, will be requiredbefore a quantitative comparison between theory and experi-ment can be made.Finally in Figs. 3~c! and~d!, the rms displacements of Mnand La/Ca are plotted. It is clear that Mn exhibits a tempera-ture dependence similar to the oxygen atoms while La/CaFIG. 2. ~a! Reduced magnetization vs temperature on warmingup (d), obtained by subtracting the background and normalizingthe data to the intensity at 40 K.~b! 2u angle vsT for ~1,0,1! and~0,2,0! Bragg reflections.~c! Lattice parameters as a function oftemperature. The inset shows an expanded version of thea latticeconstant.~d! unit cell volume vsT. For HB-4 data, closed symbolsare measurements obtained with a Displex helium refrigerator whileopen symbols are furnace results. The errors in the lattice param-eters are less than the size of the symbol. The lattice parameterdifferences at roomT between closed and open symbols are duemostly to systematic errors in the measurements. Solid lines areguides to the eye.FIG. 3. Isotropic Debye-Waller factors vsT as obtained fromRietveld refinements for~a! O~1!, ~b! O~2!, ~c! Mn, and~d! La/Ca.Solid lines are guides to the eye.R3696 54DAI, ZHANG, MOOK, LIOU, DOWBEN, AND PLUMMERhas the normal Debye-Waller factor behavior. Although theT dependence of the rms displacements for Mn and La/Ca isnot predicted directly in the theory, this result is not surpris-ing given that the bond lengths of the La/Ca-O~2.41–3.11Å! and La/Ca-Mn~3.25–3.42 Å! atoms are much larger thanthat of the Mn-O~1.95 Å! atoms. Therefore, the influence ofthe apparent anharmonicity and dynamic Jahn-Teller distor-tions is greatly reduced for the La/Ca atoms.One of the key issues in understanding the microscopicorigin of the CMR in these perovskites is the possible cou-pling among structural, electronic, and magnetic phase tran-sitions. Recent work by Hwanget al.10 has demonstrated adirect linkage between the Curie temperatureTc andthe average ionic radius of the La sitêr A& inLa0.72xBxCa0.3MnO3 (B 5 Pr, Y!. Similarly, the size of thedoping divalent alkaline-earth ions in La12xAxMnO3 canalso significantly affect its structural and magnetic proper-ties. During the course of this work, we have learned of aneutron scattering experiment by Martinet al.18 on theLa0.7Sr0.3MnO3 metallic ferromagnet, which has a similardoping level as La0.65Ca0.35MnO3. The authors concludedthat for this Sr composition the oxygen rms displacementsare independent of the temperature being above or belowTc . We note, however, that the paramagnetic to ferromag-netic phase transition in the La0.7Sr0.3MnO3 corresponds toa metal-to-metal transition which, according to Milliset al.,5has a weaker electron-phonon coupling and hence lessanomalous behavior in the oxygen Debye-Waller factors. ForLa0.65Ca0.35MnO3, the smaller Ca ionic size may facilitate astronger electron-phonon interaction, thereby inducing thelocalization of the conduction band electrons aboveTc andcausing the observed metal-to-nonmetal transition.In conclusion, we have studied the structural and mag-netic phase transitions in perovskite La0.65Ca0.35MnO3 byneutron powder diffraction. Our results indicate that thecompound has an orthorhombic structure at all temperaturesinvestigated. An anomalous volume, oxygen, and Mn rmsdisplacement change aroundTc is discovered. These resultsare in qualitative agreement with the dynamic Jahn-Tellerdistortions theory.4,5Note added. After the submission of this paper, relateddiffraction results on La12xCaxMnO3 (x50.25,0.5) havebeen published by P.G. Radaelliet al. @Phys. Rev. Lett.75,4488 ~1995!#.We are grateful to B.C. Chakoumakos, R.M. Moon, S.E.Nagler, R.M. Nicklow, and A.J. Millis for helpful discus-sions. This research was supported by U.S. DOE under Con-tract No. DE-AC05-84OR21400 with Lockheed Martin En-ergy Systems, Inc., at ORNL, NSF Grants No. DMR 92-21655 and No. OSR-9255225 at Univ. of Nebraska.1K. Chabaraet al., Appl. Phys. Lett.63, 1990 ~1993!; R. vonHelmolt et al., Phys. Rev. Lett.71, 2331 ~1993!; S. Jinet al.,Science264, 413~1994!; Y. Tokuraet al., J. Phys. Soc. Jpn.63,3931 ~1994!.2C. Zener, Phys. Rev.82, 403 ~1951!; P.W. Anderson and H.Hasegawa,ibid. 100, 675~1955!; P.G. DeGennes,ibid. 118, 141~1960!.3C.W. Searle and S.T. Wang, Can. J. Phys.48, 2023 ~1970!; K.Kubo and N. Ohata, J. Phys. Soc. Jpn.33, 21 ~1972!; N. Fu-rukawa,ibid. 63, 3214~1994!.4A.J. Millis et al., Phys. Rev. Lett.74, 5144~1995!.5A. J. Millis et al., Phys. Rev. Lett.~to be published!.6K. Bärner et al., Phys. Status Solidi B187, K61 ~1995!; W.H.Jung and E. Iguchi, J. Phys. Condens. Matter7, 1215 ~1995!;M.I. Salkolaet al., Phys. Rev. B51, 8878~1995!; J. Zanget al.,ibid. 53, R8840~1996!.7E.O. Wollan and W.C. Koehler, Phys. Rev.100, 545 ~1955!.8H.L. Yakel, Acta Crystallogr.8, 394 ~1955!.9K. Kni z̆ek, et al., J. Solid State Chem.100, 292 ~1992!.10H.Y. Hwanget al., Phys. Rev. Lett.75, 914 ~1995!.11N. Furukawa, J. Phys. Soc. Jpn.64, 2734 ~1995!; 64, 2754~1995!.12P. Schifferet al., Phys. Rev. Lett.75, 3336~1995!.13A.C. Larson and R.B. Von Dreele, GSAS-General StructureAnalysis System~Los Alamos National Laboratory, 1986!.14J.B.A.A. Elemanset al., J. Solid State Chem.3, 238 ~1971!.15Because of the Mn magnetic form factor, magnetic contributionsto the Bragg reflections for 2u>60° (sinu/l>0.485) are essen-tially negligible. To reduce the errors for the atomic Debye-Waller factors, a slightly larger data range~40.2°<2u<135°)was used forT aboveTc .16The La/Ca and oxygen content of the sample are assumed to beideal. Previous works on similarly prepared La0.67Ba0.33MnOz@H.L. Ju et al., Phys. Rev. B 51, 6143 ~1995!# andLa12xCaxMnO3 ~Ref. 12! show the oxygen stoichiometry to bewithin ,1% of ideal. In addition, the compounds are known tobe stable below 600 K.17R.M. Nicklow and R.A. Young, Phys. Rev.152, 591 ~1966!.18M.C. Martin et al., Phys. Rev. B53, 14 285~1996!.54 R3697EXPERIMENTAL EVIDENCE FOR THE DYNAMIC. . .

Experimental evidence for the dynamic Jahn-Teller effect in La\u3csub\u3e0.65\u3c/sub\u3eCa\u3csub\u3e0.35\u3c/sub\u3eMnO\u3csub\u3e3\u3c/sub\u3e

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University of Nebraska - Lincoln 
DigitalCommons@University of Nebraska - Lincoln 
Peter Dowben Publications Research Papers in Physics and Astronomy 
8-1-1996 
Experimental evidence for the dynamic Jahn-Teller effect in 
La0.65Ca0.35MnO3 
P. Dai 
Oak Ridge National Laboratory 
Jiandi Zhang 
University of Nebraska-Lincoln, jiandiz@lsu.edu 
H.A. Mook 
Oak Ridge National Laboratory 
Sy_Hwang Liou 
University of Nebraska-Lincoln, sliou@unl.edu 
Peter A. Dowben 
University of Nebraska-Lincoln, pdowben@unl.edu 
See next page for additional authors 
Follow this and additional works at: https://digitalcommons.unl.edu/physicsdowben 
 Part of the Physics Commons 
Dai, P.; Zhang, Jiandi; Mook, H.A.; Liou, Sy_Hwang; Dowben, Peter A.; and Plummer, E. Ward, "Experimental 
evidence for the dynamic Jahn-Teller effect in La0.65Ca0.35MnO3" (1996). Peter Dowben Publications. 45. 
https://digitalcommons.unl.edu/physicsdowben/45 
This Article is brought to you for free and open access by the Research Papers in Physics and Astronomy at 
DigitalCommons@University of Nebraska - Lincoln. It has been accepted for inclusion in Peter Dowben Publications 
by an authorized administrator of DigitalCommons@University of Nebraska - Lincoln. 
Authors 
P. Dai, Jiandi Zhang, H.A. Mook, Sy_Hwang Liou, Peter A. Dowben, and E. Ward Plummer 
This article is available at DigitalCommons@University of Nebraska - Lincoln: https://digitalcommons.unl.edu/
physicsdowben/45 
Experimental evidence for the dynamic Jahn-Teller effect in La0.65Ca0.35MnO3
P. Dai
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
Jiandi Zhang
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
and Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111
H. A. Mook
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
S.-H. Liou and P. A. Dowben
Department of Physics and Astronomy, University of Nebraska, Lincoln, Nebraska 68588-0111
E. W. Plummer
Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831
and Department of Physics, University of Tennessee, Knoxville, Tennessee 37996
~Received 7 November 1995!
Recently, it has been argued that a strong electron-phonon interaction arising from the Jahn-Teller splitting
of the outer Mnd level plays a crucial role in understanding the nonmetal-to-metal transition observed in the
La12xAxMnO3 (A5Ca,Sr,Ba! system. We show, by neutron powder diffraction, that La0.65Ca0.35MnO3 ex-
hibits an anomalous volume and oxygen/manganese displacement change aroundTc , in qualitative agreement
with the theoretical prediction.@S0163-1829~96!00830-2#
The recent rediscovery of ‘‘colossal magnetoresistance’’
~CMR! in perovskite-based La12xAxMnO3 (A 5 Ca,Sr,Ba!
1
has generated considerable interest in these materials. In the
doping range of 0.2<x<0.4, La12xAxMnO3 orders ferro-
magnetically and the temperature (T) dependence of the re-
sistivity is closely related to the magnetic ordering. The
‘‘double exchange’’ model, proposed some 30 years ago,2
has been used more recently3 to explain the physics of the
observed nonmetal-to-metal transition. However, Millis
et al.4 argue that double exchange alone cannot account for
the large resistivity drop below the paramagnetic to ferro-
magnetic phase transition temperatureTc . A strong Jahn-
Teller electron-phonon coupling must also play an essential
role.5,6 In particular, the polaron effect, due in part to local-
ization of the conduction band electrons by slowly fluctuat-
ing ~dynamic! local Jahn-Teller distortions, is reduced dras-
tically belowTc , permitting the formation of a metallic state.
For medium electron-phonon coupling, which is believed to
be relevant to the composition range (0.2<x<0.4) where
the nonmetal-to-metal transition is observed, Milliset al.
predict that the temperature dependence of the average root-
mean-square~rms! oxygen displacements is linear with a
slope that is different forT above and belowTc .
5 The large
elastic anharmonicity, coupled with the Jahn-Teller distor-
tions, induces a large volume change that might have been
observed.7–10
Although some aspects of this model such as the behavior
of the resistivity5 agree well with the existing experimental
results, the central prediction of anomalous temperature de-
pendence of the rms oxygen displacements, due directly to
the electron-phonon coupling, is yet to be observed. The lack
of a direct experimental proof has sparked lively debate
about the relevance of the dynamic Jahn-Teller distortion in
understanding the microscopic origin of the observed CMR
effect.6,11 In this paper, we present neutron diffraction
data which demonstrate that the polaron effect scenario
suggested by Milliset al. may indeed be realized in the
La0.65Ca0.35MnO3 system. Specifically, the oxygen and Mn
rms displacements, obtained by neutron Rietveld analysis,
are found to exhibit anomalous behavior aroundTc , in quali-
tative agreement with the theoretical prediction.
Our neutron experiments were performed using the
HB-1A triple-axis and HB-4 high-resolution powder diffrac-
tometers at the High-Flux Isotope Reactor at Oak Ridge Na-
tional Laboratory. The HB-1A triple-axis spectrometer, op-
erated in the two-axis mode with an incident beam
wavelength of 2.356 Å and collimation of 408-408-
108-308 in usual notation, was used for magnetization mea-
surements. The HB-4 diffractometer has an array of 32 de-
tectors and available instrument scattering angle between
11° and 135°. When operated using the wavelength of
1.0314 Å, it allows a maximum wavevector transferQ
(54p/lsinu) of ;11.25 Å 21 to be reached.
The polycrystalline sample used in the experiments was
synthesized by a solid state reaction. Starting materials
La2O3, CaCO3, and Mn were mixed in stoichiometric pro-
portions and heated in O2 at 1200 °C for 24 h, at 1350 °C
for 50 h, and then at 1400 °C for 50 h with two intermediate
grindings. The bulk magnetization, resistivity, and magne-
toresistance are all consistent with previous results.12 The
fine black powder was loaded in a thin wall vanadium can
which was then mounted inside a larger aluminum can filled
PHYSICAL REVIEW B 1 AUGUST 1996-IIVOLUME 54, NUMBER 6
540163-1829/96/54~6!/3694~4!/$10.00 R3694 © 1996 The American Physical Society
with helium exchange gas. For measurements below room
temperature, the aluminum can was attached to the cold fin-
ger of a Displex helium refrigerator. For higher temperature
measurements, we have used an Institute Laue Langevin type
furnace without the aluminum can. The temperature accu-
racy for the Displex is about 1 K while the high-T furnace
has an uncertainty of610 K.
Figure 1 shows the full pattern of the Rietveld analysis
result at 300 K using theGSAS program.13 We find that the
compound has an orthorhombic structure at all the tempera-
tures investigated with a space groupPnma~Ref. 14! that is
different than the cubic structure proposed originally by
Wollan and Koehler7 and by Yakel8 for this Ca composition.
The conclusion of an orthorhombic unit cell is drawn, not
from the the observation of line splitting, but on the basis of
superlattice reflections absent in the cubic structure as shown
in Fig. 1. The inset in Fig. 1 shows the unit cell structure,
Table I summarizes the lattice parameters, selected bond dis-
tances, and angles obtained from the Rietveld analysis.
Having shown that the structure of our sample is ortho-
rhombic, we now focus on the temperature dependence of
the order parameter and the lattice constants. Figure 2 sum-
marizes the results. Frame~a! displays the square of the
sample magnetization, measured at zero field using the inten-
sity change of the sum of~0,2,0! and~1,0,1! reflections as a
function of temperature on warming. The 2u angle of the
reflection, directly related to the lattice parameters, is plotted
in frame ~b!. Frames~c! and ~d! show the temperature de-
pendence of the lattice parameters and unit cell volume. The
anisotropic lattice contractions aroundTc are clearly evident
in the data, indicating a strong coupling between the lattice
and magnetism.
Although the sample structure, magnetization, and lattice
parameters are important to study, such information will not
FIG. 1. Rietveld refinement patterns for La0.65Ca0.35MnO3 at 300 K. Plus marks are observed neutron-diffraction intensities, and the
solid line is calculated intensities. The first and second set of vertical marks below the profile indicate the positions of Bragg reflections for
the cubic and orthorhombic structure, respectively. Major reflections are labeled with the orthorhombic indices. The curve at the bottom is
the difference between the observed and calculated intensities for the orthorhombic structure. The inset shows the schematic crystal unit cell.
The La/Ca, Mn, O~1!, and O~2! atoms are represented in green, red, light blue, and dark blue, respectively.
TABLE I. Refined parameters for lattice constants, selected
bond distances, and angles at 300 and 40 K. Numbers in the paren-
thesis are statistical errors of the last significant digit. O~1!-Mn and
O~2!-Mn are along theb axis and in thea-c plane, respectively.
Parameter T5300 K T540 K
a ~Å! 5.4537~4! 5.4371~6!
b ~Å! 7.7042~6! 7.6793~7!
c ~Å! 5.4682~4! 5.4496~5!
O~1!-Mn~Å! 1.9562~6! 1.9512~7!
O~2!-Mn~Å! 1.9596~26! 1.9512~24!
O~2!-Mn~Å! 1.9557~26! 1.9507~25!
Mn-O~1!-Mn(°) 159.86~19! 159.42~20!
Mn-O~2!-Mn(°) 160.99~11! 161.11~12!
54 R3695EXPERIMENTAL EVIDENCE FOR THE DYNAMIC. . .
provide a direct test of the theory of the dynamic Jahn-Teller
effect. Neutron diffraction, however, is also ideal for deter-
mining the oxygen rms displacements because of its sensi-
tivity to oxygen atoms. The neutron cross section for coher-
ent elastic scattering is proportional toe22W where the
Debye-Waller temperature factor 2W(Q)5^(Q–u)2&, and
the rms displacements (^u2&) are therefore mostly sensitive
to the Bragg intensities at large wave-vector transfers. To test
this idea, Rietveld analysis was performed forT5300 and
493 K data where no magnetic intensity is present in Bragg
reflections. We find that all the parameters are essentially the
same using a full~11°<2u<135°) and a partial(60°
<2u<135°) pattern. Consequently, we have only analyzed
the partial pattern for all the temperatures to avoid compli-
cation of magnetic ordering.15
The procedure for analyzing the temperature dependence
of the HB-4 powder data is as follows. First, we simulta-
neously refined the scale factor, background, and peak pro-
file, lattice parameters, atomic positions, and Debye-Waller
factors for all the atoms16 for the 40 K data set. The peak
profiles were then fixed to the optimum values at 40 K and
other parameters allowed to vary in subsequent refinements
for higher temperatures. For all the refinements, weighted
R factors (Rwp) of ;7% were obtained with a reducedx
2,
about 1.2.
Figure 3 summarizes the outcome for the temperature de-
pendence of the atomic rms displacements for all the atoms
in the unit cell. Frames~a! and~b! show the results for oxy-
gen at two different sites@see inset of Fig. 1#. For conven-
tional materials such as aluminum, the atomic Debye-Waller
factorW, therefore the rms displacement, is linear as a func-
tion of temperature.17 If higher order anharmonic effects are
important,W will contain additional terms which vary as
T2 andT3. Instead of being linear, the data bear great resem-
blance to theT dependence of the lattice parameters. To
determine whether the observed anomalous behavior inW
can be entirely accounted for by the lattice expansion, we
note thatW, in the simplest phenomenological model, is re-
lated to volume by W(T2)/W(T1)5@V(T2)/V(T1)#
2g,
whereg is the Grüneisen constant, which for most materials
is between 2 and 3.17 If the observed anharmonicity inW is
due entirely to volume expansion, one would expect the ef-
fectiveg, or geff , computed fromW andV to be less than 3.
Instead, we find thatgeff.85 for T between 260 and 40 K
and;25 between 600 and 260 K, suggesting that the vol-
ume expansion is too small to account for the change in
W. In the theory of the dynamic Jahn-Teller effect,4,5 theT
dependence of the rms oxygen displacements is expected to
be linear with a slope that is different for temperatures above
and belowTc . Our data agree with the model fairly well for
T aboveTc , but deviate from it at low temperatures. The
presence of the nonlinearT dependence in the oxygen rms
displacements suggests a strong elastic anharmonicity in the
crystal belowTc . Such anharmonicity, although known to be
present, is not considered explicitly in the model of Millis
et al.5 Therefore, calculations that include detailed structural
information, and possibly quantum effects, will be required
before a quantitative comparison between theory and experi-
ment can be made.
Finally in Figs. 3~c! and~d!, the rms displacements of Mn
and La/Ca are plotted. It is clear that Mn exhibits a tempera-
ture dependence similar to the oxygen atoms while La/Ca
FIG. 2. ~a! Reduced magnetization vs temperature on warming
up (d), obtained by subtracting the background and normalizing
the data to the intensity at 40 K.~b! 2u angle vsT for ~1,0,1! and
~0,2,0! Bragg reflections.~c! Lattice parameters as a function of
temperature. The inset shows an expanded version of thea lattice
constant.~d! unit cell volume vsT. For HB-4 data, closed symbols
are measurements obtained with a Displex helium refrigerator while
open symbols are furnace results. The errors in the lattice param-
eters are less than the size of the symbol. The lattice parameter
differences at roomT between closed and open symbols are due
mostly to systematic errors in the measurements. Solid lines are
guides to the eye.
FIG. 3. Isotropic Debye-Waller factors vsT as obtained from
Rietveld refinements for~a! O~1!, ~b! O~2!, ~c! Mn, and~d! La/Ca.
Solid lines are guides to the eye.
R3696 54DAI, ZHANG, MOOK, LIOU, DOWBEN, AND PLUMMER
has the normal Debye-Waller factor behavior. Although the
T dependence of the rms displacements for Mn and La/Ca is
not predicted directly in the theory, this result is not surpris-
ing given that the bond lengths of the La/Ca-O~2.41–3.11
Å! and La/Ca-Mn~3.25–3.42 Å! atoms are much larger than
that of the Mn-O~1.95 Å! atoms. Therefore, the influence of
the apparent anharmonicity and dynamic Jahn-Teller distor-
tions is greatly reduced for the La/Ca atoms.
One of the key issues in understanding the microscopic
origin of the CMR in these perovskites is the possible cou-
pling among structural, electronic, and magnetic phase tran-
sitions. Recent work by Hwanget al.10 has demonstrated a
direct linkage between the Curie temperatureTc and
the average ionic radius of the La sitêr A& in
La0.72xBxCa0.3MnO3 (B 5 Pr, Y!. Similarly, the size of the
doping divalent alkaline-earth ions in La12xAxMnO3 can
also significantly affect its structural and magnetic proper-
ties. During the course of this work, we have learned of a
neutron scattering experiment by Martinet al.18 on the
La0.7Sr0.3MnO3 metallic ferromagnet, which has a similar
doping level as La0.65Ca0.35MnO3. The authors concluded
that for this Sr composition the oxygen rms displacements
are independent of the temperature being above or below
Tc . We note, however, that the paramagnetic to ferromag-
netic phase transition in the La0.7Sr0.3MnO3 corresponds to
a metal-to-metal transition which, according to Milliset al.,5
has a weaker electron-phonon coupling and hence less
anomalous behavior in the oxygen Debye-Waller factors. For
La0.65Ca0.35MnO3, the smaller Ca ionic size may facilitate a
stronger electron-phonon interaction, thereby inducing the
localization of the conduction band electrons aboveTc and
causing the observed metal-to-nonmetal transition.
In conclusion, we have studied the structural and mag-
netic phase transitions in perovskite La0.65Ca0.35MnO3 by
neutron powder diffraction. Our results indicate that the
compound has an orthorhombic structure at all temperatures
investigated. An anomalous volume, oxygen, and Mn rms
displacement change aroundTc is discovered. These results
are in qualitative agreement with the dynamic Jahn-Teller
distortions theory.4,5
Note added. After the submission of this paper, related
diffraction results on La12xCaxMnO3 (x50.25,0.5) have
been published by P.G. Radaelliet al. @Phys. Rev. Lett.75,
4488 ~1995!#.
We are grateful to B.C. Chakoumakos, R.M. Moon, S.E.
Nagler, R.M. Nicklow, and A.J. Millis for helpful discus-
sions. This research was supported by U.S. DOE under Con-
tract No. DE-AC05-84OR21400 with Lockheed Martin En-
ergy Systems, Inc., at ORNL, NSF Grants No. DMR 92-
21655 and No. OSR-9255225 at Univ. of Nebraska.
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15Because of the Mn magnetic form factor, magnetic contributions
to the Bragg reflections for 2u>60° (sinu/l>0.485) are essen-
tially negligible. To reduce the errors for the atomic Debye-
Waller factors, a slightly larger data range~40.2°<2u<135°)
was used forT aboveTc .
16The La/Ca and oxygen content of the sample are assumed to be
ideal. Previous works on similarly prepared La0.67Ba0.33MnOz
@H.L. Ju et al., Phys. Rev. B 51, 6143 ~1995!# and
La12xCaxMnO3 ~Ref. 12! show the oxygen stoichiometry to be
within ,1% of ideal. In addition, the compounds are known to
be stable below 600 K.
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54 R3697EXPERIMENTAL EVIDENCE FOR THE DYNAMIC. . .


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Experimental evidence for the dynamic Jahn-Teller effect in La\u3csub\u3e0.65\u3c/sub\u3eCa\u3csub\u3e0.35\u3c/sub\u3eMnO\u3csub\u3e3\u3c/sub\u3e

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