Superconductivity-induced changes of the phonon resonances in RBa_2Cu_3O_7 (R=rare earth)

7 Pages·0.17 MB·English

by  S. Ostertun

Superconductivity-induced changes of the phonon resonances in RBa2Cu3O7 (R =
rare earth)
∗
S. Ostertun, J. Kiltz, A. Bock , and U. Merkt
Institut fu¨r Angewandte Physik und Zentrum fu¨r Mikrostrukturforschung,
Universit¨at Hamburg, Jungiusstraße 11, D-20355 Hamburg, Germany
1
0
0 T. Wolf
2 Institut fu¨r Festk¨orperphysik, Forschungszentrum Karlsruhe, D-76021 Karlsruhe, Germany
n (February 1, 2008)
Ja Weobserveacharacteristicenergy¯hωc ≈2.1eVwhichseparatesregionsofdifferentbehaviorofthe
phonon intensities in the Raman spectra of the RBa2Cu3O7 system. A superconductivity-induced
5
drop of phonon intensities is found for the oxygen modes O(4) and O(2)-O(3) only for excitation
1
energies below ¯hωc. This intensity drop indicates an order parameter which affects energies in the
] vicinity of ¯hωc.
n
o PACS numbers: 74.25.Gz, 74.25.Jb, 74.25.Kc, 74.72.Bk, 78.30.Er
c
- I. INTRODUCTION II. EXPERIMENTAL DETAILS
r
p
u Several superconductivity-induced changes of pa- Subject of this paper are Yb-123, Er-123,Sm-123 and
s
rameters describing the phonons in the cuprate su- Nd-123 single crystals, with T = 76 K, 81 K, 94 K,
. c
t perconductors can be determined by Raman spec- and90K,respectively. Allmeasuredsinglecrystalswere
a
m troscopy. Frequency and linewidth anomalies like hard- grownwitha self-fluxmethod andannealedwith oxygen
ening and broadening have been the subject of several under high pressure.10 Due to the high oxygen content
-
d experimental1–3 and theoretical4–7 studies. While the and the different radii of the rare earth atoms Yb-123
n superconductivity-induced phonon self-energy effects al- and Er-123 are overdoped whereas Sm-123 and Nd-123
o low conclusions regarding the order parameter only for are nearly optimally doped.11 The laser beam is focused
c
energiessimilartothe phononenergies(upto 100meV), ontothesamplealongthec-direction. Theorthorhombic
[
high-energy (>1 eV) questions cannot be addressed this symmetry of the R-123 system can be treated as tetrag-

1 way. ResonantRamanscatteringisanexperimentaltech- onal. Accordingly, the Ramanactive phonons are of A
1g
v ′ ′
nique which allows one to examine the physics at high andB symmetry,whichareallowedforz(xx)¯z/z(xx)¯z
1g
7 ′ ′
energy through the resonances of phonons. In contrast and z(xx)¯z/z(xy)¯z polarizations in the Porto notation,
1
to reflectivity or transmission spectroscopy the affected respectively. All polarizations are specified with respect
2
1 phononsprovidedirectinformationonincorporatedelec- to the axes along the Cu-O bonds of the CuO2 planes,
0 tronic bands as the assignments of the phonon modes in primed polarizations are rotated by 45o. For simplicity
1 thespectratothevibratingatomsiswellknownthrough z and¯z are omitted in the following. The measurements
0 group theoretical calculations and isotope substitution were performed using several lines of Ar+, He-Ne and
/
t experiments. Thus,the dependence ofthe phononinten- Ti:Saphir lasers in quasi-backscattering geometry. The
a sities on temperature and excitation energy can provide details of the setup are described elsewhere.12 In order
m
information about the scattering mechanism and espe- toachieveahighaccuracyofintensitymeasurementsthe
- cially about the superconducting state. laserpowerwasmonitoredduringthemeasurements. All
d
n In contrast to the usually observed increase of the spectra were corrected for the response of the detector
o intensity8,9 below the criticaltemperatureTc we observe andthe opticalsystem. Also, they arenormalizedto the
c a drop of intensity in several modes when exciting with incident photon rate.
v: photons of energy h¯ωi < 2.1 eV. In the same region of For a comparisonof intensities obtained with different
i excitation energy the apical oxygen mode at 500 cm−1 excitation energies the cross-section is calculated from
X
shows a violation of the symmetry selection rule which the efficiencies using ellipsometric data of Yb-123. The
r cannot be explained in terms of an orthorhombic distor- complexdielectricfunctionofBi-2212showsonlyaslight
a
tion. Summarizing our data we conclude that the origin variation with temperature13 at our excitation energies
oftheintensityanomalyisrelatedtoamodificationofthe between1.68eVand2.71eVandtheresultingreflectivity
Cu-O chargetransfermechanismin the superconducting exhibitsmaximalvariationsbelow1%. Asthereflectivity
state in comparison to the normal state. oftheR-123systembehavessimilar,14 Ramanspectraof
all temperatures can be evaluated with the ellipsometric
data obtained at room-temperature. In Fig. 1 the com-
plex dielectric function of Yb-123 at room-temperature
is given. From the real part ε of the dielectric function
1
1
we can estimate a screened plasma frequency ω of 1.44 of the O(4) mode in Er-123, Sm-123, and Nd-123. Or-
p
eV. thorhombicdistortion,whichisusuallymentionedasthe
The low-temperature background intensity of the causeforphononintensityinforbiddensymmetries,can-
cross-sectionat ω ≈700 cm−1 is plotted versusthe exci- not explain this behavior. Though resonance effects can
tationenergy for the x’x’ andx’y’ polarizationgeometry disturbsymmetryselectionrulesinprinciple,thesymme-
in the inset of Fig. 1 in the top and bottom panel, re- try violation should appear under resonance conditions
spectively. Within experimental error no significant res- but not out of resonance.
onanceofthe cross-sectioncanbedetermined. Thescat- Subtractingthephononiccontributionwegettheelec-
teringofthedatapointsresultsfromuncertaintiesinthe tronic background of Yb-123, which is plotted in the
adjustment of the setup. Thus, the measured phonon lowerpanelsofFig.2. Thex’x’spectraarenearlyidenti-
intensities will scatter in a similar way. To obtain the calforbothexcitationenergiesandeventhe x’y’spectra
integratedphononintensitieswefittedthespectratothe are quite similar. The B pair breaking peak lies at a
1g
modelpresentedinapreviouspaper.3 AnextendedFano relativelylowenergyof320cm−1 due to the highdoping
profile is described by level15 of p ≈ 0.2, which is determined from T /T
c c,max
(see Ref. 16). There is no enhancement of the gap exci-
C
I(ω)= × tationfrom1.96eVto2.71eV.Thisisconsistentwiththe
γ(ω)[1+ǫ2(ω)] behaviorobservedfor Bi-2212whichshowsnon-resonant
R∗2(ω) −2ǫ(ω)R∗(ω)̺∗(ω) − ̺2∗(ω) (1) gaanpdeaxcgiatpatrioesnosnfaonrcdeoopninlygfloevrehlsiguhpertodoappipnrgoxleimvealtsealys0re.2-
(cid:26) C2 C2 C2 (cid:27)
ported in Ref. 17.
with the substitutions ̺∗(ω) = Cgσ2̺eσ(ω), R∗(ω) = Figure 3 depicts the results of a detailed study of the
Cg2Re(ω)+R , ǫ(ω) = ω2−ω2(ω) /2ω γ(ω), γ(ω) = integrated O(4) mode intensity. For temperatures above
σ σ 0 ν p
Γ + ̺∗(ω)/C, and ων2(ω)(cid:2) = ωp2 − 2ω(cid:3)pR∗(ω)/C. Here, Tc the x’x’ intensity increases when the temperature is
̺e(ω) and Re(ω) are the imaginary and real part of the lowered for excitation energies of 1.96 eV, 2.41 eV, and
σ σ
2.71 eV. This increase is hardly influenced by the phase
electronic response function, respectively, and g is the
σ
transitionbelowT for2.41eVand2.71eVincontrastto
lowest-orderexpansioncoefficientofthe electron-phonon c
1.96eVwheretheintensitysuddenlydrops. Thecompar-
vertex. The bare frequency and linewidth of the phonon
atively high values for intensities of the 2.71 eV data in
are ω and Γ, respectively. The constant C is a scaling
p
therangeof100Kto200Kareduetothescatteringmen-
parameterduetotheuseofarbitraryunitsinthespectra.
tioned in the introduction. Here it results from a slight
We use this extended Fano profile for the asymmetric
shift of the laser spot with respect to the entrance slit of
phonon modes and Lorentzian profiles for the remaining
the spectrometer. On the other hand the x’y’ intensity
phonons. AsdescribedinRef.3,themeasuredelectronic
shows the same behavior for all measured excitation en-
response ̺∗(ω) is described via a phenomenological for-
ergies: a slightincreasewith decreasingtemperature not
mula which containsa tanh(ω/ω ) term for the incoher-
T
or only slightly affected by T . For temperatures above
ent background and two coupled Lorentzian profiles for c
T the relation for the x’x’ intensities I :I :I is
the redistribution of the spectra below T — one for the c 2.71 2.41 1.96
c
approximately 5.0:3.1:1.0 as indicated by the solid lines
pair breaking peak and a negative one for the suppres-
intheleftpanelofFig.3. Thesuperconductivity-induced
sionofspectralweightatlowRamanshifts. Thisformula
dropof the x’x’intensity atlow excitationenergiesleads
allows a simultaneous description of R∗(ω).
to a superconductivity-induced enhancement of the res-
onance profile of the x’x’ O(4) mode intensity.
III. RESULTS Figure 4 yields the excitation energy h¯ωc = 2.1 ±
0.1 cm−1 where the O(4) mode exhibits equal intensity
in x’x’ and x’y’ geometries. This is also the energy of
InthetoppanelsofFig.2wepresentspectraofYb-123
the crossover between the superconductivity-induced in-
obtainedat15Knominaltemperatureinx’x’(A +B )
1g 2g crease and decreaseof the x’x’ intensity shown in Fig. 3,
and in x’y’ (B ) geometry with excitation energies of
1g i. e. 2.0-2.4 eV. While the measurements have been car-
2.71 eV and 1.96 eV. The original spectra have been
riedoutin this detail forYb-123only, spectra ofEr-123,
scaledtoequalbackgroundintensityforclarity. Exciting
Sm-123, and Nd-123 at low temperature exhibit a simi-
with 2.71 eV all phonons show up mainly in the spec-
lar behavior as shown in the inset of Fig. 4. There the
tra of the expected polarization geometry. For the x’x’
geometry we have the Ba mode at 120 cm−1, Cu(2) at ratio of the x’x’ and x’y’ O(4) mode intensity is plotted
against the excitation energy. It exhibits no significant
150 cm−1, O(2)+O(3) at 440 cm−1, and O(4) at 500
cm−1. For the x’y’ geometry the O(2)-O(3) mode ap- dopingdependence. TheO(2)-O(3)modedisplaysasim-
pears at 340 cm−1. In contrast, exciting with 1.96 eV ilar behavior in the x’y’ as the O(4) mode in the x’x’
symmetry. In Fig. 5 the temperature dependence of its
the O(4) mode has nearly vanished in x’x’ geometry but
intensityisplottedforexcitationenergiesh¯ω =1.68eV,
only slightly changedin x’y’symmetry. Nearly the same i
1.96 eV, 2.41 eV, and 2.71 eV. Above T the intensity is
behavior is observed for the resonance of the intensity c
only slightly affected by the temperature, below T the
c
2
intensity drops only for excitation energies below h¯ω . of the Yb-123 single crystal. Thus, the drop below T is
c c
The intensity of the Cu(2) mode shows a strong in- masked in this strong increase, especially as Friedl et al.
crease with decreasing temperature above T but also recorded xx+yy data which include x’y’ where no inten-
c
a slight drop below T . The intensity at low tempera- sity drop appears. In underdoped R-123 the O(2)-O(3)
c
tures is approximately 70%–80% of the highest value at mode is known to show a strong intensity gain.3 Thus,
T . While this ratio is independent of excitation energy the intensity drop of the O(2)-O(3) mode can only be
c
andpolarizationgeometrytheresonanceenergyitselfde- observedinoverdopedsamplesasthedropisnotmasked
pends on the polarization geometry as shown in Fig. 6. by an intensity gain.
Gaussianprofilesguidetheeyeandhelptodeterminethe Shermanet al.8 explainedthe increaseofthetotalB
1g
resonance energy of the Cu(2) mode intensity, which is mode intensity below T of Y-123 in terms of an exten-
c
about2.1eVfor x’x’andwellbelow2.0 eVforx’y’sym- sionof the number of intermediate electronic states near
metry. The Ba mode which is not shown here exhibits a theFermisurfacethatparticipateinthe Ramanprocess.
slight intensity gain below T , which seems to be unaf- Accordingly, the doping dependence of the gain of the
c
fectedbyh¯ω . Thex’x’intensityis resonantat2.6eVor O(2)-O(3) mode intensity can be explained in this pic-
c
even higher energy, the x’y’ intensity follows this profile ture by the vicinity to the Fermi-level. Analogously, an
with about 30% of the intensity in x’x’ geometry. intensity dropmeans a reduction of the number of inter-
mediate states which is not consistent with this model.
Possibly the intensity gain and the intensity drop have
IV. DISCUSSION AND CONCLUSIONS different origins, which are doping dependent and inde-
pendent, respectively.
Summarizing our data we find a characteristic energy Due to the different resonance profiles in x’x’ and x’y’
¯hω ≈2.1eVwhichseparatestheregionsofredandblue geometry the drop of the phonon intensities can only be
c
excitations. It is very similar to the crossing point at explained in the framework of a resonant theory which
2.2 eV observed in the imaginary part of the dielectric mustaccountforthebandsoftheinitialandfinalstates.
function13 of Bi-2212. For red excitation the R-123 sys- Calculations for the phonons of Y-123 in the supercon-
tem exhibits a superconductivity-induceddropofthe in- ducting state which have been performed by Heyen et
tensityoftheO(4)modeinx’x’andtheO(2)-O(3)mode al.19 and which are based on the local-density approxi-
in x’y’ symmetry, for blue excitation the drop is absent. mation and the linear muffin-tin-orbital method do not
Additionally, for red excitations the symmetry selection show any signature of an intensity drop around 2 eV for
rule of the O(4) mode is violated as the x’y’ intensity xx/yy and zz symmetry. The calculated xx/yy intensity
exceeds the x’x’ intensity. The maximum of the inten- of the O(4) mode has a local intensity minimum at 2.0
sity of the Cu(2) mode in x’x’ symmetry coincides with eV but at 1.6 eV the predicted intensity is more than
¯hω . Alltheseeffectsarecharacterizedby¯hω indicating twice the intensity at 2.0 eV excitation energy which is
c c
a common microscopic origin. Low temperature mea- strong contrast to our data.
surements of overdopedEr-123 as well as of underdoped As no appropriate theory is available we try an in-
Sm-123 and Nd-123 show a similar behavior as Yb-123, terpretation in a simple picture: The intensity drop is
especially the symmetry violation of the O(4) mode for observedfor the Cu(2) mode and, forexcitationenergies
excitation energiesbelow ¯hωc. Thus h¯ωc could be a gen- belowh¯ωc,fortheplane-relatedO(2)-O(3)mode andfor
eral property of the R-123 system without a significant the x’x’ O(4) mode. This indicates that plane bands are
doping dependence. responsible for the observed resonance effect. In case of
Friedl et al.18 observed a superconductivity-induced the O(4) mode two processes seem to contribute to the
gainofthexxphononintensitiesofY-123filmsonSrTiO phonon intensity, as the strongly resonant x’x’ intensity
3
substrates,whichareindependentofexcitationenergyin exhibits the dropbelowh¯ωc and the x’y’intensity shows
therangeof1.92eVto2.60eV,adropofintensityisob- no resonance and no superconductivity-induced effects.
servedonlyfortheCu(2)mode. Thedifferencesbetween As the characteristic energy ¯hωc which separates the re-
their data and the data presented here may in princi- gionswithandwithoutthesuperconductivity-inducedin-
ple result from the different doping levels of Y-123 and tensity drop is the same for the O(4) mode as for the
Yb-123. But as we have noted above, the effects are O(2)-O(3)mode, we conclude that the relevantinitial or
mainly independent of doping, our explanation for the final state bands are the same. Thus, we attribute the
discrepancies between Friedl’s and our data is the fol- x’x’intensitytoaprocessinvolvingthatplanebands. On
lowing: As the lattice constant of Y-123 (3.82/3.88 ˚A) theotherhandthex’y’intensityisattributedtothechain
is smaller than that of SrTiO (3.91 ˚A) and as the ther- bands. Another hint for this interpretation is that the
3
mal expansion coefficient of Y-123 (11.7 ˚A/K) exceeds pairingmechanismis believedto be locatedin the CuO2
thatofSrTiO (9.4˚A/K),thelatticemismatchincreases planes. Thus, superconductivity-induced effects would
3
with decreasing temperature. The additional stress may be expected for processes which involve plane bands.
explain the high intensity increase I(100K):I(250K)≈2.5 Within a simple band structurepicture the opening of
oftheY-123filmsincomparisontoI(100K):I(300K)≈1.3 the gap cannot explain the threshold of h¯ωc directly: If
theopeningofthegapwouldenhancetheenergydistance
3
betweenthepossibleinitialandfinalstatesforanallowed V. SUMMARY
transitiontoavaluewhichexceedstheexcitationenergy,
thisprocesswouldalsobesuppressedforlowerexcitation Aresonanceenhancementoftheintegratedphononin-
energiesin the normalstate. Figure 5 clearly showsthat tensity is observedfor the O(4) mode in x’x’ and for the
thebehaviorofthephononintensityfor1.96eVand1.68 O(2)-O(3)mode in x’y’polarizationgeometry. It results
eV excitations is essentially the same. Thus, only a fun- mainly from an intensity drop for temperatures below
damentalchangeofthe bandstructurecouldexplainthe T at excitation energies less then ¯hω ≈ 2.1 eV. This
c c
differentbehaviorforblueandredexcitation. Asthex’x’ drop is also observed for the Cu(2) mode, which has its
intensityoftheCu(2)modehasitsmaximumrightatthe maximum x’x’ intensity right at this excitation energy.
critical energy h¯ωc (see Fig. 6) the fundamental change We believe that the charge-transferis responsiblefor the
with the superconducting transitionshouldtake place in intensity drop of all three phonon modes, directly for
a plane band involving the Cu(2) atom. As mentioned Cu(2) and indirectly via the order parameter for O(4)
above the O(4) mode intensity in x’x’ and x’y’ symme- and O(2)-O(3). As the x’y’ intensity of the O(4) mode
tryresultsfromdifferentprocessesduetothecouplingto shows hardly any resonance we believe that its origin is
the Cu(2)-O(2)-O(3)plane bands and to the Cu(1)-O(1) completely different from the one of the x’x’ intensity.
chain bands, respectively.
In comparison to the superconducting gap 2∆
the critical energy h¯ω is quite a large energy. ACKNOWLEDGMENTS
c
Superconductivity-inducedhigh-energyeffectshavebeen
observed previously by thermal difference reflectance
The authors thank M. Ru¨bhausen and M. V.
(TDR) spectroscopy14 and by ellipsometry.13 In the el-
Klein for stimulating discussions and for performing
lipsometry data a crossing point in ε at 2 eV separates
2 the ellipsometry measurements of Yb-123. Finan-
two spectral regions of different behavior in their tem-
cial support of the Deutsche Forschungsgemeinschaft
perature dependencies. The TDR spectra of Y-123 and
via the Graduiertenkolleg “Physik nanostrukturierter
other high-temperature superconductors exhibit a devi-
Festko¨rper” is gratefully acknowledged.
ation from unity in the ratio R /R of the supercon-
S N
ducting to normal state spectra at high photon ener-
gies (≈2.0 eV). Within the Eliashberg theory the devia-
tioncanonly be explainedif the electron-bosoncoupling
function contains a high-energy component in addition
to the electron-phonon interaction leading to an order
parameter which is non-zero for similar energies. The ∗ Present Address: Basler AG, An der Strusbek 60-62, D-
microscopic origin of the high-energy interaction is most 22926 Ahrensburg,Germany.
likelya d9−d10LCu-O charge-transferwithin the CuO2 1E.Altendorf,X.K.Chen,J.C.Irwin,R.Liang,andW.N.
planes.14 Hardy,Phys. Rev.B 47, 8140, 1993.
The Cu(2) mode intensity seems to correlate with the 2V. G. Hadjiev, Xingjiang Zhou, T. Strohm, M. Cardona,
charge-transfer excitation at about 2.1 eV. The inten- Q.M. Lin, and C. W. Chu, Phys.Rev.B 58, 1043, 1998.
sity drop of this mode below T is independent of exci- 3A.Bock,S.Ostertun,R.DasSharma,M.Ru¨bhausen,and
c
tation energy and supports the interpretation of a mod- K.-O.Subke,Phys.Rev.B 60, 3532, 1999.
ified charge-transfer-mechanism in the superconducting 4R.Zeyherand G. Zwicknagel, Z. Phys.B 78, 175, 1990.
state. On the other hand the O(2)-O(3) mode in x’y’ 5E.J.Nicol,C.Jiang,andJ.P.Carbotte,Phys.Rev.B47,
and the O(4) mode in x’x’ geometry behave completely 8131, 1993.
different for excitation energies above and below h¯ω . 6T. P. Devereaux,Phys. Rev.B 50, 10287, 1994.
c 7B. Normand, H. Kohno, and H. Fukuyama, Phys. Rev. B
This indicates that the underlying mechanism is not the
53, 856, 1996.
modified charge-transfer itself but the opening of the
8E. Ya. Sherman, R. Li, and R. Feile, Phys. Rev. B 52,
gap, which is non-zero for high energies as argued by
Holcomb et al.14 Thus, superconductivity-induced high- R15757, 1995.
9O. V. Misochko, E. Ya. Sherman, N. Umesaki, K. Sakai,
energy effects which cannot be detected in transport ex-
and S. Nakashima, Phys.Rev. B 59, 11495, 1999.
periments, leave their signature in resonant Raman ex- 10T.Wolf,W.Goldacker,B.Obst,G.Roth,andR.Flukiger,
periments through different behavior of the phonon in- J. Crystal Growth 96, 1010, 1989.
tensity above and below h¯ωc as well as in other optical 11Y.Xu and W. Guan, Phys. Rev.B 45, 3176, 1992.
experiments.13,14 12M. Ru¨bhausen, C. T. Rieck, N. Dieckmann, K.-O. Subke,
A.Bock, and U.Merkt, Phys. Rev.B 56, 14797, 1997.
13M. Ru¨bhausen, A. Gozar, M. V. Klein, P. Guptasarma,
and D. G. Hinks,submitted to Phys. Rev.B
14M. J. Holcomb, C. L. Perry, J. P. Collman, and W. A.
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4
16J.L.Tallon,C.Bernhard,H.Shaked,R.L.Hitterman,and
J. D. Jorgensen, Phys. Rev.B 51, 12911, 1995.
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C.T.Rieck,P.Guptasarma,D.G.Hinks,andM.V.Klein,
Phys.Rev. Lett.82, 5349, 1999.
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Solid StateCommun. 78, 291, 1991.
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5
8 9
x'x' 2.71 eV x'y'
8 2.41 eV
6 Yb-123
1.96 eV
7
ε s)
4 2 nit 2.71 eV
b. u 6 0
dielectric function -220 ε1 ωp ection (arb. u.)111...020 x'x' O(4) mode intensity (ar 5432 21..4916 eeVV 00
-4 s
oss-0.8 x'y' 1
cr
1.68 eV
-6 0 0
1.7 2.0 2.3 2.6
0 100 200 0 100 200 300
0.8 1.1 1.4 1.7 2.0 2.3 2.6 2.9 3.2 3.5 3.8 temperature (K)
energy (eV) FIG. 3. Temperature dependence of the integrated O(4)
FIG.1. Complex dielectric function ε1+iε2 of Yb-123 at Raman intensity in Yb-123 in x’x’ (closed symbols) and x’y’
roomtemperature. TheinsetdepictstheRamancross-section (open symbols) polarizations for excitation energies 2.71 eV
forthex’x’(toppanel)andthex’y’(bottompanel)polariza- (triangles), 2.41 eV (diamonds), 1.96 eV (circles), and 1.68
tion symmetries. Lines mark theaverage values. eV (squares). Solid lines serve as guides to the eye, dashed
lines indicate Tc. Thex’y’ data are offset as indicated.
8
7 Yb-123 x'x' 2.71 eV x'y' 4
6 T nom=15K 1.96 eV s) 7 3 Yb
b. units) 543 sity (arb. unit 65 I : Ix'x'x'y'21 NESrmd
sity (ar 21 e inten 43 0 1.7 2.0 2.3 2.6
n d
e o
int 02 O(4) m 2
1
1
0 0
0 200 400 600 0 200 400 600 800 1.7 2.0 2.3 2.6
Raman shift (cm-1) energy (eV)
FIG.2. RamanspectraofYb-123inx’x’andx’y’polariza- FIG. 4. O(4) intensity of Yb-123 at 15 K in x’x’ (closed
tion geometries taken with excitation energies ¯hωi =2.71 eV symbols) and x’y’ (open symbols) polarization geometry.
(dashed lines) and 1.96 eV (solid) at 15 K cryostat tempera- Lines are guides to the eye. The inset shows the ratio of
ture. Thelowerpanelsshowthebackgroundspectraobtained the x’x’ and x’y’ intensity at 15 K for various R-123 single
by subtraction of thephonons. crystals that correspond to different doping levels.
6
10
O(2)-O(3) x'y'
s) 8
nit
u
b.
ar 6
y (
sit
n
e
nt 4
n i
o
n
o
h 2
p
2.71 eV 1.96 eV
2.41 eV 1.68 eV
0
0 100 200 300
temperature (K)
FIG. 5. Temperature dependence of the O(2)-O(3) inten-
sity of Yb-123 for excitation energies ¯hωi = 2.71 eV (tri-
angles), 2.41 eV (diamonds), 1.96 eV (circles), and 1.68 eV
(squares). Thedotted line indicates Tc.
1.0
y y
sit 0.2 Cu(2) sit
n n
e e
nt nt
n i 0.5 n i
o o
n 0.1 n
o o
h h
p p
y' x'
x' x'
0.0 0.0
1.7 2.0 2.3 2.6
excitation energy (eV)
FIG. 6. Resonance of the intensity of the Cu(2) mode in
Yb-123 at 15 K in x’x’ (closed symbols) and x’y’(open sym-
bols) geometry. Dotted Gaussian profiles guide theeye.
7