Grazing Incidence Infrared Reflectivity of La$_{1.85}$Sr$_{0.15}$CuO$_4$ and NbN

7 Pages·0.17 MB·English

by  H. S. Somal

Grazing Incidence Infrared Reflectivity of La Sr CuO and NbN.
1.85 0.15 4
H. S. Somal,1 B. J. Feenstra, 1 J. Schu¨tzmann,1 Jae Hoon Kim,1,2 Z. H. Barber,3 V. H. M. Duijn,4 N. T. Hien,4, A.
A. Menovsky,4 Mario Palumbo, 5 and D. van der Marel1
1 Materials Science Centre,Laboratory of Solid State Physics, University of Groningen,
Nijenborgh 4, 9747 AG Groningen, The Netherlands.
2 Dept. of Physics, Yonsei University, Seoul 120-749, Korea.
3Dept. of Materials Science and Metallurgy, University of Cambridge, United Kingdom.
4Van der Waals-Zeeman Laboratory, University of Amsterdam, The Netherlands.
5 Physikalisches Institut, University of Bayreuth, D-95440 Bayreuth,Germany.
(15 september1995)
6 infrared spectroscopy offers the advantage of sensitivity
9 Infraredreflectivitymeasurements,usingp-polarizedlight to the bulk of the material, high energy resolution and
9 at a grazing angle of incidence, show an increased sensitivity
the factthat the opticalconductivity determinedby this
1 to theoptical conductivityof highly reflectingsuperconduct-
methodcanbe interpretedinatheoreticallywell-defined
ing materials. We demonstrate that when this measurement
n way as the current-current correlationfunction.
techniqueisapplied totheconventionals-wavesuperconduc-
a
Although mm-wave studies of the low-frequency pen-
J tor NbN,the results are in perfect agreement with BCS the-
6 ory. For the in-plane response of a La1.85Sr0.15CuO4 single etration depth have been successfully used to probe,
crystal, in the superconducting state, we find a reduction of via the temperature dependence, the possible existence

1 theopticalconductivityinthefrequencyrangebelow20meV. of nodes in the order parameter of YBa2Cu3O7, a di-
v The observed frequency dependence excludes an isotropic s- rect spectroscopic determination of the order parame-
8 wave gap, but agrees well with model calculations assuming ter with infrared/mm-wave techniques has been limited
1 a d-waveorder parameter. so far by several experimental factors: (1) The low fre-
0
quency limiting behavior of the reflectivity of a (non-
1
0 superconducting)metalisgivenbytheHagen-Rubensex-
6 pressionR=1 0.366(νρ )1/2withν inunitsofcm−1,
DC
9 The symmetry and magnitude of the superconducting ρ in units of Ωc−m, the reflectivity of a good conductor is
/
at order parameter belong to the key elements of theoret- high. For the high Tc cuprates ρ ≈ 100(µΩcm), so that
m ical models of the superconducting state of the high Tc for frequencies of the order of 3.5kBTc, and Tc = 30K,
cuprates. The issue of the order parameter-symmetry R=0.97. As a result the changes in reflectivity upon en-
-
d is intimately related to the question as to whether su- tering the superconducting state are difficult to detect,
n perconductivity is causedby localexchangecorrelations, especially because the changes take place gradually [8].
o anti-ferromagneticspin-fluctuatons,inter-layerpairingor (2)Therangeoforderparameterinducedchangesincon-
c
: electron-phononinteractions.[1]Muchofthe datawhich ductivity coincides with the frequency range of optical
v havebeeninterpretedasevidence ford-wavepairing,us- phonons. The electronic conductivity in the c-direction
i
X ing a wide variety of experimental techniques, were ob- is very small in these materials, therefore changes are
r tained on the double-layer compounds Bi2Sr2Ca1Cu2O8 maskedby the ratherstrongcontributionsdue to optical
a and YBa2Cu3O7. [2] However, for compounds with two phonons [9,10].
or more CuO layers per unit cell the presence of sev- In this paper we describe and demonstrate that the sit-
eral coupled charge reservoirs complicates the picture, uation with respect to problem (1) can be improved by
and increases the number of possible interpretations of using polarized light incident at a grazing angle. For p-
the experimental results [3], as was recently discussed polarisedlight the reflectivity is givenby the expression:
[4] for e.g. the experimentally observed sign reversals 2
(cid:12)ǫcosθ pǫ sin2θ(cid:12)
of the order parameter in YBa2Cu3O7 . On the other R (θ,ω)=(cid:12) − − (cid:12) (1)
hand the single layer cuprate superconductors, such as p (cid:12)(cid:12)ǫcosθ+pǫ sin2θ(cid:12)(cid:12)
(cid:12) − (cid:12)
La1−xSrxCuO4, have only a single band of electrons per For a metal in the limit where ωτ 1 the absorptiv-
oufnTietxhcpeeelerl,ximwpeehrniictmhaleinndtapatrlairn.ecsiuplltesfaocnilLitait1a−txeSsrtxhCeuinOt4erupsrientgatRioan- rtitoeyarcA1h/epscoa=smθ1,ax−uipmRutpoma=.nOacnon4stgθhlpeeoθ4tcπωhσ=erisharae≪cnncdoh,saipnncte4hdπωeσsbuwypheaerrcfeoancit--
man spectroscopy [5], specific heat measurements [6]
ducting state the dielectric properties at low frequencies
and inelastic neutron scattering [7] indicate a strong
aredominatedby the realpartof the dielectric function,
anisotropyoftheorderparameter,possiblyduetod-wave Re(ǫ) = c2(ωλ(T))−2, where λ(T) is the penetration
pairing. In this Letter we discuss a set ofinfraredexper- depth. Th−e absorbtivity A = 4 c−3ω2λ(T)34πσ van-
iments on La1.85Sr0.15CuO4. The classical technique of ishes as σ 0 below the gpap. cToshθerefore, by measuring
→
1
the reflectivity at a grazing angle of incidence with p- the c-axisplasmonshowsupveryprominently belowT ,
c
polarized light we enhance our sensitivity to changes in with E~ polarized parallel to the planes we observed no
σ with roughly a factor of 1/cosθ. In the present study distinct gapfeature in the caseof La1.85Sr0.15CuO4. Be-
we have chosen an angle θ = 80 3o, resulting in an cause the observed thermally induced changes are quite
±
enhancement factor of approximately 6. For the sam- subtle,wereproducedthemeasurementsseveraltimeson
ples studied in this paper the superconductivity induced two different crystals.
changes in reflectivity are of the order of 1 % at normal The absolute reflectivities are displayed in the upper
incidence. Thisisattheborderofwhatcanbemeasured panel of Fig. 1 for temperatures between 4 and 50 K.
experimentally (with a typical accuracy of about 0.5%). In the inset we show the reflectivity taken at normal
At θ =80o the level of superconducting induced changes incidence. Below 3 meV the extrapolation was based
is raised to a comfortable 10%. The grazing incidence upon a two fluid model as described in [12]. A Kramers-
methodisdifferentfromandcomplementarytoimprove- Kronig transformation gives the pseudo-dielectric func-
mentsincountingstatistics,e.g. byusinglargersamples, tion at 80o, and from this the dielectric function and
brighter sources, etc. the optical conductivity which is displayed in the lower
La1.85Sr0.15CuO4singlecrystalswithaTcof32Kwere panel of Fig. 1. In order to check the internal consis-
grownbythetravelingsolventfloatingzonemethod,and tency of the analysis, as well as agreement with pub-
cutalongthea-cplane. Thedimensionsofthe cleanand lishedvaluesofthepenetrationdepth,wecalculatedλ(ω)
polished crystal surface were approximately 7 mm along by two different methods. The skin depth, defined as
the a-axis and 4 mm along the c-axis. The samples were δ = c/(ωIm√ǫ), must be taken in the limit ω 0 to
→
mountedsuch,thattheplaneofscatteringcoincideswith obtain the superconducting penetration depth (inset of
the CuO-planes. The samples were mounted in a con- Fig. 1, lower panel). Alternatively, if the temperature
ventional flow cryostat using the two opposite windows dependence results from a transfer of spectral weight to
for scattering in a cone of 80 3o relative to the sur- the condensate peak at ω = 0, the penetration depth
±
face normal. A wire gridpolarizerwas used to select the followsfromthe Glover-Tinkham-Ferellsumrule formula
proper polarization. Special care was taken to prevent λ(ω)−2 =8R0∞+(σn(ω′)−σs(ω′))dω′. Inouranalysisthese
stray lightfrom reachingthe detectors. Although all the twovaluescoincidewithanaccuracybetterthan1%. We
measurementsreportedhereweretakenwithp-polarized thereforeconclude,thatthe’missing’areaintheconduc-
light, by rotating the wire-gridpolarizerby 90o, we were tivity is indeed transferred to the condensate peak, and
able to direct E~ ~c and detect the appearance of the is therefore inherently linked to the formation of the su-
k
c-axis plasmon as T drops below T [10]. This was used perconducting state. The values of λ = 4300 30˚A and
c
±
both as an in situ check for correct crystal orientation 4900 30˚Aat4and20Krespectivelyareingoodagree-
±
andasan’internal’indicatorofthe sample temperature. ment with measurements at 10 GHz [13].
NbN films of 400nm and 55nm thickness were prepared Ithasbeensuggested[14],thatthelowfrequencyelec-
onsubstratesofMgObyDCreactivemagnetronsputter- trodynamics can be understood as a sum of a temper-
ing,in agascompositionof3.0%CH4 /30.0%N2 /Ar, ature independent mid-infrared band and a Drude con-
◦
at a temperature of approximately 840 C to produce tribution which narrowsupon lowering the temperature.
high quality epitaxial growth [11]. The carbon addition This empirical decomposition of the data has been used
improvesfilmqualitywhichwascheckedbyX-raydiffrac- todescribenormalincidencereflectanceandconductivity
tion and high resolution electron microscopy. The films spectra for frequencies typically above 12 meV. For our
hadasuperconducting transitiontemperatureof16.5K, samplethemid-infraredbandcanbeparameterizedwith
and a resistivity ratio (300 K / 16.5K) close to unity. the function σ Reω/(ω+i[ω2 ω2]τ) where σ =800
Reflectivities at 80 degrees angle of incidence were (S/cm),h¯ω M0.16(eV)andMh¯−τ−1 =0.66(eV)M.Clearly
M
≈
measured at temperatures between 4 and 60 K. With a for h¯ω <40 (meV) the conductivity is dominatedby the
goldreference mirrorwe checkedthat the effects of ther- free carrier contribution. The suppression of conductiv-
malexpansionofthecryostatonourresultsisverysmall ity below 18 meV is markedly different from a narrow-
within this range of temperatures. Initially the normal ing (or depletion) of the Drude peak on a constant MIR
incidenceabsolutereflectivityat40Kwasmeasuredwith background. On the other hand there is also no gap in
highprecision(insetofFig. 1,upperpanel),wethencal- theobservedfrequencyrange. IfLa1.85Sr0.15CuO4 would
culatedthe dielectricfunction usingtheKramers-Kronig be an isotropic s-wavesuperconductor,then BCS theory
transformation, and from this the reference reflectivity predictsthatthegapshouldbeatapproximately10meV.
curveat40Kand80degreesangleofincidence. Absolute As there is no spurious background in the present spec-
reflectivities atall temperatures were obtained by multi- tra, it is clear from these data that such a BCS gap is
plying the reflectivity ratios to this reference curve, and absent.
by correcting for thermal expansion effects of the cryo- To verify, that our experimental method will indeed
stat as detected with a gold reference mirror in a sepa- showthepresenceofagapifthereisone,weshowinFig.
ratesession. Althoughunderconditionsofs-polarization 2 the conductivity obtained with the same grazing inci-
2
dence technique on a thick (400 nm) film of NbN. NbN ture of s and d-wave symmetry (’s+id’). In such cases a
thin films deposited on MgO are suitable for IR trans- lowerboundexistsonthedistributionofgapvaluesalong
mission spectroscopy, our measurements show that this the Fermi-surface. In the optical spectra a full gap only
materialbehaves like a classicalBCS superconductor,as opens below the lower bound of this distribution. From
can be seen from the quality of the fits in Fig. 2 (lower our data we conclude, that such a lower bound, if it ex-
panel). With T = 16.5K the gap is at approximately ists, must be located below 3 meV (1.3 k T ).
c B c
6 meV (2∆/k T 4, which is now quite close to the Usinggrazingincidencereflectivity,wedeterminedthe
B c
≃
lower limit of our window of observation (of 3 meV). In opticalconductivityofLa1.85Sr0.15CuO4 andNbNbelow
terms of ’cleanliness’ in the normal state, this material andnearthesuperconductingphasetransitiondowntoa
has an even higher reflectivity than high T supercon- photonenergyof3 meV.Inthe caseofNbNa clearBCS
c
ductors as the DC conductivity is about 14000 (S/cm). gapwasobserved. ForLa1.85Sr0.15CuO4 goodagreement
In this case, however, the changes in the measured re- was obtained with model calculations assuming d-wave
flectivityatgrazingincidencearequite large,andaclear pairing and scattering closer to the Born-limit.
gap opens up in the conductivity. As can be seen from Acknowledgements We gratefully acknowledge D.
the solid curves the agreement with simulations [15] as- Rainer and M. Graf for their theoretical support. This
suming an isotropic s-wave gap of 2∆= 4k T for NbN investigation was supported by the Netherlands Foun-
B c
[16] with intermediate scattering rate (h¯/τ = 14 meV)) dation for Fundamental Research on Matter (FOM)
is excellent. withfinancialaidfromtheNederlandseOrganisatievoor
In Fig. 3 we display our experimental data at Wetenschappelijk Onderzoek (NWO).
4 K and 40 K together with model calculations for
La1.85Sr0.15CuO4, based on BCS s-wave theory with fi-
nite scattering (2∆=3.5k T ) [15] and a weak coupling
B c
calculation with finite scattering rate assuming d-wave
pairing [17]. As parameters we took h¯/τ = 6 meV, and
ω = 0.73 eV. By fixing T at 32 K we also fixed the
p c [1] P.W. Anderson, Science 235, 1196 (1987); C. Gros, R.
value of the gap. For the case of d-wave pairing T is
c Joynt,T.M.Rice,Z.Phys.B68,425(1987); G.Kotliar,
quite strongly suppressed due to the presence of scatter-
Phys.Rev.B37,3664(1988); D.J.Scalapino,E.Loh,J.
ing [18]. In our calculations we had to take Tc0 = 64K, Hirsch, Phys. Rev.B 35, 6694 (1987); P.Monthoux and
whichisthenreducedto32Kduetoourassumedscatter- D. Pines, Phys. Rev.B 49, 4261 (1994); S. Chakravarty
ing rate of 6 meV. There is an intrinsic ambiguity in the and P.W. Anderson, Science 261, 337 (1993); O.V. Dol-
choice of the latter: Although the scatteringrate needed gov, and E.G. Maksimov, Physica C 178, 266 (1991).
to fit the data for T <50 K and ω > 6 meV is tempera- [2] D. A. Wollman et al., Phys. Rev. Lett. 71, 2134 (1993);
ture independent, the linear temperature dependence of W. N. Hardy et al., Phys. Rev. Lett 70, 3999 (1993);
the decay rate does still exist at lower (notably DC) fre- T.P. Devereaux et al., Phys. Rev. Lett. 72, 396 (1994);
quencies. Hencethephysicaloriginofthescatteringrate Z.X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993); Ch.
Renner, and O. Fisher, Physica C 235-240, 53 (1994).
seems not to be solely due to impurity scattering. The
[3] V.Z. Kresin, and S.A. Wolf, Phys. Rev. B 51, 1229
present weak-coupling calculations do not faithfully rep-
(1995).
resentthisaspectoftheproblem,buthavetheadvantage
[4] A.A.Golubov,andI.I.Mazin,PhysicaC243,153(1995).
ofusingonlyalimited numberofadjustableparameters. [5] X.K. Chen et al.,Phys. Rev.Lett. 73, 3290 (1994).
As Tc, 1/τ and ωp are fixed by experimentalconstraints, [6] M. Momono et al.,Physica C 235-240, 1739 (1994)
theonlyfreeparameterleftisthescatteringcrosssection [7] T.E.Mason,G.Aeppli,andH.A.MookPhys.Rev.Lett.
2
σsc = sin η, where η is the phase shift. The compari- 68, 1414 (1992); ibid. Phys. Rev. Lett. 71, 919 (1993);
son with experimental data in Fig. 3 strongly favours K. Yamada et al.,Phys. Rev.Lett. 75, 1626 (1995).
d-wave symmetry with σ =0.4, so that η 0.2π. The [8] K. Kamar´as et al.,Phys. Rev.Lett. 64, 84 (1990).
sc
≈
analysis of microwave surface impedence measurements [9] K. Tamasaku, Y. Nakamura, and S. Uchida Phys. Rev.
of YBa2Cu3Oy between 4 GHz - 40 GHz indicates that Lett. 69, 1455 (1992).
[10] J. H.Kim et al.,Physica C 247, 297 (1995).
for these materials the elastic scattering is very small,
[11] Z. H. Barber et al., IEEE Trans. Supercond., 3, 2054-
and close to the unitarity limit (0.98 < η < 1) [19,20].
2057, (1993).
The temperature dependence of the ab-plane penetra-
[12] D. van derMarel et al.,Phys.Rev.B 43, 8606 (1991).
tion depth of La2−xSrxCuO measured at 10 GHz drops [13] T.Shibauchi,T.Kimura,andK.Kishio,Phys.Rev.Lett.
slightlybelowtheBCS-predictionfors-wavepairing[13]. 72, 2263 (1994).
Thesedatadonotexcludethe possibilityofd-wavepair- [14] F.Gao et al.,Phys. Rev.B 47, 1036 (1993).
ing in the presence of impurity scattering, in which case [15] W.Zimmerman et al.,Physica C 108,99 (1991).
∆λ T2[21]. Althoughanisotropics-wavegapisclearly [16] D.R.Karecki et al., Phys.Rev.B 27 5460 (1983).
ruled∝out by our analysis, we can not rule out the possi- [17] M.J. Graf et al.,Phys.Rev.B 52 10588 (1995).
bilityofastronglyanisotropicgap,oranincoherentmix- [18] R. J. Radtke et al.,Phys. Rev.B 48, 653 (1993).
3
[19] P. J. Hirschfeld, W. O. Putikka, and D.J. Scalapino,
Phys. Rev. B 50, 10250 (1994); J. P. Carbotte et al.,
Phys.Rev.B 51, 11798 (1995).
[20] T.Jacobsetal.,J.ofPhys.Chem.Solids,inpress(1996).
[21] P.J.Hirschfeld,andN.Goldenfeld,Phys.Rev.B48,4219
(1993).
FIG. 1. Upper panel: Reflectivity of La1.85Sr0.15CuO4 at
80 degrees angle of incidence at 4 K (solid), 20 K (dashed),
27K(dotted),40K(dash-double-dotted)and50K(chained).
Inset: Reflectivityatnormalangleofincidencefor40K(solid)
and 300 K (dashed). Lower panel: Optical conductivity at
50 K (closed triangles), 40 K (circles), 2 K (lozenges), 20 K
(closed triangles) and4K(squares)obtainedfromthereflec-
tivitiesusingKramers-Kronigrelations. Inset: Skindepthfor
4 (solid) and 20 K (dashed). The solid dots are the penetra-
tion depthobtained from thef-sum rule.
FIG. 2. Upper panel: Optical conductivity of NbN cal-
culated from 80 degree angle of incidence reflection spectra
for 9 (closed circles), 13 (open squares) and 18 K (closed
diamonds). Solid curves: Theoretical calculations assuming
isotropics-wavepairing. Lowerpanel: Measuredtransmittiv-
ity ratios of a 55 nm thick NbN film on MgO (closed circles:
T(9K)/T(18K),opensymbols: T(13K)/T(18K))Thesolid
curves are calculated using the same parameters as for the
conductivity of thetop panel.
FIG. 3. Comparison of the experimental optical conduc-
tivity at 4 K (solid circles) and 40 K (open circles) to model
calculations for the optical conductivity of La1.85Sr0.15CuO4
assuminganintermediateimpurityscatteringrateatT=40K
(dash-double-dotted). The other curves are calculated for 4
Kassumingisotropics-wavepairing(chained),d-wavepairing
with σ = 0.1 (dotted), d-wave with σ = 0.4 (solid), d-wave
with σ=0.8 (dashed).
4
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