Anomalous Dispersion of Longitudinal Optical Phonons in $\mathrm{\mathbf{Nd_{1.86}Ce_{0.14}CuO_{4+\bmδ}}}$ Determined by Inelastic X-ray Scattering

4 Pages·0.2 MB·English

by  M. d'Astuto

Anomalous Dispersion of Longitudinal Optical Phonons in Nd Ce CuO
1.86 0.14 4+δ
Determined by Inelastic X-ray Scattering
M. d’Astuto,1 P. K. Mang,2 P. Giura,1 A. Shukla,1 P. Ghigna,3
A. Mirone,1 M. Braden,4 M. Greven,2,5 M. Krisch,1 and F. Sette1
2 1European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble Cedex, France
0 2Department of Applied Physics, Stanford University, Stanford, California 94305
0 3Dipartimento di Chimica Fisica “M. Rolla”, Un. Pavia, V.le Taramelli 16, I-27100, Pavia, Italy
2 4II. Physikalisches Inst., Univ. zu K¨oln, Zu¨lpicher Str. 77, 50397 K¨oln, Germany
n 5Stanford Synchrotron Radiation Laboratory, Stanford, California 94305
a (Dated: February 1, 2008)
J
8 ThephonondispersionsofNd1.86Ce0.14CuO4+δ alongthe[ξ,0,0]directionhavebeendetermined
byinelasticx-rayscattering. Comparedtotheundopedparentcompound,thetwohighestlongitudi-
2
nalphononbranches,associated withtheCu-Obond-stretchingandout-of-planeoxygenvibration,

are shifted to lower energies. Moreover, an anomalous softening of the bond-stretching band is ob-
]
n servedaroundq=(0.2,0,0). Thesesignaturesprovideevidenceforstrongelectron-phononcoupling
o in this electron-doped high-temperaturesuperconductor.
c
-
r
p While the coupling between electrons and phonons to a coupling between charge fluctuations and phonons,
u is known to be the driving mechanism for Cooper-pair charges with different character may induce quite differ-
s
formation in conventional superconductors, its role in ent electron-phonon interactions.
.
at the high-critical-temperature superconductors (HTcS) In this Letter, we present an inelastic x-ray scatter-
m is the subject of intense research efforts. Recently, ing (IXS) study of the phonon dispersion in the n-type
evidence for electron-phonon coupling has been in- cuprates Nd Ce CuO (NCCO). Inelastic x-ray
- 1.86 0.14 4+δ
d voked in the interpretation of inelastic neutron scat- scattering can overcome the main limitation of inelas-
n
tering (INS) and angle-resolved photoemission spec- tic neutron scattering, i.e. the need for sufficiently large
o
troscopy (ARPES) experiments. The INS studies, car- single crystals of high chemical and structural quality
c
[ ried out on La1.85Sr0.15CuO4+δ [1, 2, 3, 4], oxygen- [2]. Lateral x-ray beam sizes of few tens of µm are rou-

1 dopedLa2CuO4+δ [5]andYBa2Cu3O6+δ [2, 6]revealan tinely obtained. Moreover, at photon energies around
anomalous softening with doping of the highest longitu- 10-20 keV and Z > 3, the total cross section is domi-
v
1 dinaloptical(LO)phononbranch,inparticularalongthe natedbyphotoelectricabsorption,andthereforethetyp-
0 q =[ξ,0,0]direction. This branchis assignedto the Cu- ical x-ray penetration depths for high-Z materials is of
5 O bond-stretching mode [2, 7]. The observed softening the order of 10 - 100 µm. Consequently, very small
1 has been interpreted as a signature of a strong electron- samples (down to less than 10−4 mm3) can be studied
0
phononcoupling[2,3],whichhasbeendiscussedsincethe with signal rates comparable to typical INS experiments
2
0 discoveryofHTcS[8,9]. Furthermore,inanenergyrange on cm3-sized samples. Despite these advantages, little
/ similarto theLObond-stretchingphononband,ARPES work has been done using IXS on the HTcS compounds
t
a studies on three different families of hole-doped HTcS [13]. We choose Nd2−xCexCuO4+δ for our IXS study,
m
revealadistinct“kink”anomalyinthe quasiparticledis- since its crystallographicstructure is one of the simplest
- persion [10]. The scenario emerging from the above INS among the HTcS, and because extensive INS studies ex-
d
and ARPES works suggests a strong coupling between istforitsundopedparentcompoundNd CuO (NCO)
n 2 4+δ
o thechargecarriersandtheCu-Obond-stretchingphonon [1, 2]. Our interest is focused on the [ξ,0,0] direction,
c modes to be ubiquitous in HTcS materials, at least for where the LO branch displays its strongest anomaly for
v: hole-doped compounds. However, its role in the pair- hole-doped HTcS [3, 4]. The present results reveal that,
i ing mechanism remains completely unclear [4]. At the nearthezonecenter,thetwohighestlongitudinaloptical
X
moment, it may not even be excluded that the electron- branches,assignedtotheCu-Obond-stretchingandO(2)
r phonon interaction is pair-breaking for the d-wave su- vibrationmodes,areshiftedtolowerfrequencieswithre-
a
perconducting order parameter. Therefore, it appears spect to the undoped parent compound. The interpre-
very important to analyze the strength of the phonon tation of our data is supported by lattice dynamics cal-
anomaliesin as many cuprate families as possible and to culations,takingintoaccountaThomas-Fermi screening
comparethem with their superconducting properties. In mechanism. Furthermore,weobserveananomaloussoft-
this context, the electron-doped cuprates are of central ening of the highest branch around q = (0.2,0,0). Our
importance due to the distinct character of the doped results demonstrate that this anomalous behavior of the
charges in this material: Cu 3dx2−y2 (O 2p) for n(p)- high-energyLOphononbranchisauniversalpropertyof
type cuprates [11], leading to a very different electronic both hole- and electron-doped HTcS compounds, there-
structure [12]. Since the phonon anomalies are related fore providing further evidence that electron-phonon in-
2
teractions may play an important role in high-Tc super- 80
conductivity. Furthermore, the present results are an Q=(6.8,1,0)
important demonstration of IXS as a powerful tool for Q=(7,0.8,0)
60 4
the study of the lattice dynamics in small, high-quality s)
crystals of complex transition metal oxides. unit
b.
The experiment was carried out at the very-high- ar 40 2
energy-resolution IXS beam-line ID16 at the European y (
sit
Synchrotron Radiation Facility (ESRF). X-rays from n
e
an undulator source were monochromated using a Si Int 20 0
10 12 14 16 18
(111)double-crystalmonochromator,followedbyahigh-
energy-resolution backscattering monochromator [14],
operating at 15816 eV (Si (888) reflection order). A 0
−10 0 10 20 30
toroidal gold-coated mirror refocused the x-ray beam ν(THz)
onto the sample, where a beam size of 250×250 µm2
full-width-half-maximum (FWHM) was obtained. The FIG. 1: Experimental IXS phonon spectra of
scattered photons were energy-analyzed by a spherical Nd1.86Ce0.14CuO4+δ at T = 15 K and corresponding har-
silicon crystal analyzer 3 m in radius, operating at the monicoscillatormodelbestfits(solidanddottedlines). Both
same Bragg reflection as the monochromator [15]. The scanswereperformedintheτ =(7,1,0)Brillouinzoneswith
a propagation vector of ξ =0.2 in an almost longitudinal ge-
total energy resolution was 1.6 THz (6.6 meV) FWHM.
ometry along the a∗ direction (diamonds) and in an almost
The momentum transfer Q was selected by rotating the transverse geometry along b∗ (open circles).
3 mspectrometer armin the scatteringplane perpendic-
ulartothelinearx-raypolarizationvectoroftheincident
beam. Themomentumresolutionwassetto≈0.087˚A−1
Fig. 1showsatypicalenergyscaninalmostlongitudi-
in both the horizontal and the vertical direction by an
aperture of 20×20 mm2 in front of the analyzer. Fur- nalgeometryatQ=(6.8,1,0),correspondingtoξ =0.2.
The data are shown together with the results of a fit,
ther experimental details are given elsewhere ([14, 15]
where the excitations where modeled by harmonic oscil-
and references therein). The sample is a single crystal
lators,convolutedwith the instrumentalresolutionfunc-
grownby the traveling-solventfloating-zonemethod in 4
tion. Three features can be clearly distinguished: (i) an
atm of O at Stanford University. It has been reduced
2
◦ elasticpeakat0THz,duetochemicaldisorderand,pos-
under pure Ar atmosphere at 920 C for 20 h, followed
◦ sibly,strainduetothedifferentthermalexpansioncoeffi-
by a further 20 h of exposure at 500 C to a pure O
2
cientsbetweenthesampleandthesamplesupportduring
atmosphere. Such a procedure is necessary to produce a
cooling, (ii) the longitudinal acoustic phonon, centered
superconductingphaseinNd Ce CuO ,although
1.86 0.14 4+δ
near 2.7 THz and (iii) a weaker feature around 13 THz.
its exact effect is not understood. Following this treat-
In the intermediate energy region (from about 4 to 10
ment the sample had a narrow superconducting transi-
THz), no distinct phonon peaks are resolved due to the
tionwithanonsettemperatureofT =24K.Thesample
c
dominating contributionfrom the tails of the elastic and
is of very good crystalline quality, with a rocking curve
◦ acoustic phonon signals. The inset of Fig. 1 emphasizes
width of 0.02 (FWHM) around the [h,0,0] direction.
the high-energy region of the spectrum. One can clearly
It was mounted on the cold finger of a closed-loop he-
distinguish two phonons, centered around 12 and 13.5
lium cryostat, and cooled to 15 K. The experiment was
THz, respectively. The weak shoulder at around 16 THz
performed in reflection geometry, and the probed scat-
tering volume corresponded to about 1.5×10−3 mm3. can be attributed to an admixture of the transverse op-
tical (TO) mode, as indicated by the comparison (after
IXS scans were performed in the -2< ν <24 THz range,
in the τ =(6,0,0) and τ =(7,1,0) Brillouin zones [18]. normalizationto the same intensity at 20 THz) with the
equivalent scan in transverse geometry Q = (7,0.8,0).
The data were collected along the following three lines:
I) Q = (6 + ξ,0,0), in longitudinal configuration (i.e. Consequently,thetwostrongerpeaksareunambiguously
with q=(ξ,0,0) kQ), assigned to longitudinal optical (LO) modes. From the
II) Q=(7±ξ,1,0) in almost longitudinal configuration absence of other higher frequency modes up to 23 THz,
(i.e. with q=(ξ,0,0) and (Q·q)/Q≈q), we conclude that the two modes at 12 and 13.5THz can
III) Q = (7,1−ξ,0) in almost transverse configuration be identified with the O(2) vibration and Cu-O bond-
(q=(0,ξ,0) and (Q·q)/Q≈0). stretching modes, respectively (see Refs. 2, 7).
The low temperature and high momentum transfer were Inordertodeterminethedispersionofthetwohighest
chosen so as to optimize the count rate on the high- LObranches,IXSspectrawererecordedfor0<ξ ≤1. In
frequencyopticalmodewhilelimitingthelossofcontrast Fig. 2we show three spectratakenalongthe (7−ξ,1,0)
due to the contribution from the tails of the intense low direction. Close to the zone center, at q = (0.1,0,0),
frequency acoustic modes. the highestfrequencymode is observedslightly above15
3
0.8 18
18
ξ=0.1
16
c) 0.6
e
s/s 16 14
sity (count 0.4 ξ=0.2 ν (THZ) 14 12
n
nte 0.2 10
I 12
ξ=0.4
8 Hz)
T
08 12 16 20 24 10 ν (
0 1 6
ν(THz) [ξ,0,0]
FIG. 2: IXS spectra in the τ =(7,1,0) Brillouin zone with 4
propagationvectorqalonga∗,asindicatedinthefigure. The INS data on pure
NCO (from Ref. [2])
experimentaldata(circles)areshowntogetherwiththeircor- 2
shell model
responding harmonic oscillator model best fits (solid lines), (no screening)
as discussed in thetext. Cu-O BS mode
other long. modes 0
shell model
(with screening) 0 1
[ξ, 0, 0]
THz. At q = (0.2,0,0) the highest mode is found at
the much lower energy of 13.5 THz. Finally, for q = FIG. 3: Right hand side: (◦, •) experimental longitudinal
(0.4,0,0), we again find a high-frequency mode around phonon frequencies determined from IXS spectra in NCCO
15.5 THz. at T = 15 K along the [ξ,0,0] direction. Solid circles (•)
emphasize the highest energy frequencies measured. Solid
The peak positions extracted from these and many
(dot-dashed) lines indicate lattice dynamics calculation with
other scans are summarized in Fig. 3. The highest
a screened (unscreened) Coulomb interaction.
branch exhibits a sharp dip around q = (0.2,0,0) and
Left hand side: magnification of the high energy portion of
recovers for larger q-values. This behavior is most likely the right hand side graph showing the dispersion of the top
due to an anti-crossing with the second highest branch two phonon branches. The highest frequency branch (△),
which is mainly associated with vibrations of the O(2) as measured by INS (from Ref. 1) in the insulating parent
position in the ξ-direction. Therefore, within a standard compound Nd2CuO4+δ is shown for comparison. The exper-
imental data are in agreement with calculations, except for
anti-crossing framework, one should interpret the high-
the anomalous softening at q = (0.2,0,0) of the two higher
est longitudinal intensities for q = (0.3,0,0) and above
energy branches (see text).
as being mainly due to O(2) vibration. Within that sce-
nario, this second-highest branch increases its frequency
in the middle of the zone as in the undoped compound,
and, except for the fact that the Lyddane-Sachs-Teller tential V (q) by V (q)/ǫ(q), and for the dielectric func-
c c
(LO-TO) gap closes, seems to be insensitive to doping. tion we take the semi-classical Thomas-Fermi limit of
The LO bond-stretching mode just above q = (0.2,0,0) ǫ(q) = 1+κ2/q2, where κ2 indicates the screening vec-
s s
is then found at quite low energies, ∼ 12 THz, but can tor. The results of the calculation (without screening:
notbeunambiguouslyfollowedtolargerq-values. Never- dot-dashedlines;withscreening: solidlines)areshownas
theless, our data document that the LO bond-stretching wellinFig. 3. Thelatticedynamicscalculationswithout
branch in NCCO is strongly renormalized compared to screening have been included, since they reproduce very
undoped NCO, in particular it bends down anomalously well the experimental dispersion of the undoped parent
from the zone center to q=(0.2,0,0). compound [1]. The shift at the zone center of the high-
In order to further validate the correctness of our as- energy phonon branches of NCCO with respect to NCO
signments, we performed a lattice dynamical calculation is due to the closing of a large LO-TO splitting. Indeed,
[16] based on a shell model. We used a common poten- the corresponding ∆1 and ∆3 branches in Nd2CuO4+δ
tial model for cuprates, in which the interatomic poten- areseparatedbyalmost3THz atthe zonecenter,asob-
tials have been derivedfroma comparisonof INS results servedbyINS[1]. Wepointoutthatinourcaseastrong
for different HTcS compounds by Chaplot et al. [17], softeningduetoThomas-Fermi screeningdoesnotimply
using a screened Coulomb potential, in order to simu- a higher Thomas-Fermi parameter κs: actually, we find
late the effect of the free carriers introduced by doping. a screening vector κ of about 0.39 ˚A−1, which is com-
s
Following Ref. [17] for metallic La Sr CuO and parabletothat forLa Sr CuO [17]. Thoughour
1.85 0.15 4+δ 1.85 0.15 4+δ
YBa Cu O , we replaced the long-range Coulomb po- modified calculation reproduces the closing of the LO-
2 3 7
4
0.04 of Ref. 12.
a) b) In conclusion, the present results reveal that the
s) anomalous softening previously observed in hole-doped
n
ar compounds[1,2,3,4,5,6],isalsopresentintheelectron-
b
2 doped cuprates. This is evidenced by the comparison of
-0
1 0.02 the present results on doped NCCO with the previously
sity ( reportedonesonpureNCO[1]. Thisimpliesthat: (i)the
en anomalyalsoexistsinn-typecuprates,givingstrengthto
Int thehypothesis[1,2,3,4,5,6]ofanelectron-phononcou-
pling origin of this feature; (ii) this is a generic feature
of the high-temperature superconductors, as expected,
0
0 0.25 0.5 0.75 0.25 0.5 0.75 1 if phonons are relevant to high temperature supercon-
[ξ,0,0]
ductivity. Moreover,this Letter demonstratesthat high-
energyresolutioninelasticx-rayscatteringhasdeveloped
FIG. 4: Comparison between experimental (diamonds) and
intoaninvaluabletoolforthestudyofthelatticedynam-
calculated (line) phonon intensities for the two highest opti-
cal phonon branches along (7−ξ,1,0). a) bond-stretching icsofcomplextransitionmetaloxides,allowingmeasure-
ments on small high-quality single crystals which are in-
LO mode starting around 15 THz and b) O(2) vibration LO
branch starting around 10.5 THz. accessible to the traditional method of inelastic neutron
scattering.
WeacknowledgeL.PaolasiniandG.Monacoforuseful
TO splitting, we still observe an anomalous additional
discussions and H. Casalta for precious help during pre-
softening of the highest bond-stretching LO branchnear
liminary tests. The authorsare gratefulto D. Gambetti,
q = (0.2,0,0), which is not reproduced by our calcu-
C. Henriquet and R. Verbeni for technical help, to J.-L.
lations (see Fig. 3). This branch softens in frequency
HodeauforhelpinthecrystalorientationandJ.-P.Vas-
from q = (0.1,0,0) to q = (0.2,0,0) by about ∆ν ≈
salli for crystal cutting. P.K.M. and M.G. are supported
1.5 THz, which is a shift comparable to the anomalous
by the U.S. Department of Energy under Contracts No.
shift observed in La Sr CuO at slightly larger q
1.85 0.15 4+δ DE-FG03-99ER45773and No. DE-AC03-76SF00515,by
[1, 3, 4]. Therefore, we believe that this anomalous soft-
NSF CAREER Award No. DMR-9985067, and by the
eningisofthe samenatureastheoneobservedinp-type
A.P. Sloan Foundation.
La Sr CuO .
1.85 0.15 4+δ
Acomparisonbetweentheexperimentalandcalculated
intensities for the two highest phonon branches is shown
in Fig. 4. The good agreement of the observed inte-
grated intensities with the calculated ones for the upper [1] L. Pintschovius et al., Physica B 174, 323 (1991).
branches validates the correctness of our phonon branch [2] L.PintschoviusandW.Reichardt,inPhysicalProperties
assignment, at least for ξ ≤ 0.2. For ξ > 0.2 we would ofHighTemperatureSuperconductors,editedbyD.Gins-
berg (World Scientific, Singapore, 1995), p.295.
have expected an intensity exchange between the two
[3] R. McQueeney et al., Phys.Rev.Lett. 82, 628 (1999).
highest branches, which seems to be not observed.
[4] L.PintschoviusandM.Braden,Phys.Rev.B60,R15039
The main difference between La Sr CuO and
1.85 0.15 4+δ (1999).
Nd1.86Ce0.14CuO4+δ is,besides the screeningeffect, that [5] L.PintschoviusandM.Braden,J.LowTemp.Phys.105,
in NCCO the Cu-O bond-stretching branch is closer in 813 (1996).
energy to the out-of-plane oxygen vibration one, hav- [6] W. Reichardt, J. Low Temp.Phys. 105, 807 (1996).
ing almost the same energy at ξ = 0.2. These two [7] J.-G. Zhang et al., Phys. Rev.B 43, 5389 (1991).
[8] J. G. Bednorz and K. A. Mu¨ller, Z. Phys. B 64, 189
branches belong to the same symmetry and therefore
(1986).
cannot cross, so that for ξ > 0.2 softening implies in-
[9] W. Weber, Phys.Rev. Lett. 58, 1371 (1987).
teraction with the out-of-plane oxygen vibration mode [10] A. Lanzara et al., Nature412, 510 (2001).
with the same symmetry. In the region between q = [11] Y.Tokura et al., Nature337, 345 (1989).
(0.25,0,0) and (0.3,0,0), the two modes are poorly de- [12] N.P.Armitageetal.,Phys.Rev.Lett.87,147003(2001).
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in La Sr CuO by Pintschovius and Braden [4] Energy Resolution (SpringerVerlag,1991),p65,Fig.6.9.
1.85 0.15 4+δ
[14] R. Verbeniet al., J. Synch.Rad. 3, 62 (1996).
and McQueeney et al. [3] for ξ ∼ 0.25−0.3. The corre-
[15] C. Masciovecchio et al., Nucl. Inst. Methods B 111, 181
sponding real space periodicity of 3 to 4 unit cells may
(1996).
therefore be linked to the proximity to some charge in- [16] A.Mirone,OpenPhonon code source (2001),availableon
stability. Weremarkthatareducedvectorξ ∼0.25−0.3 http://www.esrf.fr/computing/scientific/.
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[ξ00] direction, as can be inferred from the ARPES data [18] All reciprocal lattice vectors are expressed in r.l.u.