Microwave Electrodynamics of the Electron-Doped Cuprate Superconductors Pr_(2-x)Ce_(x)CuO_(4-y) and Nd_(2-x)Ce_(x)CuO_(4-y)

4 Pages·0.1 MB·English

by  J. David Kokales

1
0
0
0 Microwave Electrodynamics of the Electron-Doped Cuprate
2
n Superconductors Pr2−xCexCuO4−y and Nd2−xCexCuO4−y
a
J J. David Kokales, Patrick Fournier, Lucia V. Mercaldo, Vladimir V. Talanov, Richard L. Greene, and
2 Steven M. Anlagea
1
aCenter for Superconductivity Research, Department of Physics,

] University of Maryland, College Park, MD 20742-4111
n
o
The pairing state symmetry of the electron-doped cuprate superconductors is thought to be s-wave in nature,
c
- incontrastwiththeirhole-dopedcounterpartswhichexhibitad-wavesymmetry. Were-examinethisissuebased
r
on recent improvementsin our electron-doped materials and our measurement techniques. Wereport microwave
p
u cavityperturbation measurementsof thetemperaturedependenceof thepenetration depthof Pr2−xCexCuO4−y
s and Nd2−xCexCuO4−y crystals. Our data strongly suggest that the pairing symmetry in these materials is not
. s-wave.
t
a
m
-
d
n 1. Introduction as the cuprate superconductorPr2−xCexCuO4−y
o (PCCO).
Existing experimental evidence suggests that
c The samples studied were crystals grown us-
[ the pairingstate symmetryinthe electron-doped ingadirectionalsolidificationtechniqueandhave

1 cuprate superconductors is s-wave in nature, in been characterized in previous studies [1][3][4].
contrastto the d-wavesymmetry observedin the
v Typically, these samples exhibited a transition
6 hole-dopedcuprates. Thereis no compellingthe- temperature of 19 K for PCCO and 24 K for
6 oretical reason for this difference. The strongest
NCCO with a transition width in the surface re-
1 evidence for s-wave symmetry comes from mea-
sistance of 1.5 K and residual normal state resis-
1
surementsofthe penetrationdepth[1]. However,
0 tivityvaluesofabout60µΩ-cm. Atypicalsample
it is possible that the paramagnetism of the Nd
0 size was 1 mm x 1 mm x 30 µm. The phase di-
0 rare-earthioninNd2−xCexCuO4−y(NCCO)may agram for the electron-doped cuprates [5] shows
/ have influenced the determination of the symme-
t thataceriumdopantconcentrationofx=0.15has
a try [2] from temperature-dependent penetration
the highest T . Based upon the resistivity, T ,
m c c
depth measurements [1].
andtransitionwidth,webelievethatoursamples
- In order to more definitively determine the
d are at the optimal doping level.
pairing state symmetry of the electron-doped
n
cuprates, we have again studied the low-
o
2. Experimental Method
c temperature behavior of the penetration depth,
: λ(T). The functional form of λ(T) is determined
v Thein-planepenetrationdepth,λ (T),aswell
ab
i by the low-energy excitations of the system, and as the surface resistance, R (T), were measured
X S
thus indirectly determines the pairing state sym-
using a superconducting niobium microwave res-
r metry of these materials. In addition, we are
a onant cylindrical cavity operating at 9.6 GHz in
now able to observe the behavior of the pene-
which the TE mode is stimulated. In this
011
tration depth to a lower temperature than was
mode, the magnetic field is maximum and the
donepreviously[1]. This,alongwiththe possible
electric field zero at the center of the cavity. The
roleofparamagnetisminpreviousmeasurements,
sample is placed on a hot finger in the center of
makesit prudentto study anelectron-dopedsys-
the cavity with its c-axis aligned parallel to H .
rf
tem which is not strongly paramagnetic, such
This induces screening currents in the copper-
2
oxide planes of the crystal. The sample temper- causing the cavity to expand slightly. This re-
ature was varied from 1.2 K up to above T . As sults in a constant drop in resonant frequency
c
the penetrationdepthchangeswithtemperature, with time. In order to minimize this effect, it
the resonant frequency, f(T), and quality factor, is necessary to isolate the cavity from the helium
Q(T), of the cavity change. By measuring these bath, while still maintaining a good thermal link
shifts in f(T) and Q(T), quantities such as the betweenthetwo. Toachievethis,wesurroundthe
temperaturedependenceof∆λ(T)andR (T)can resonant cavity with a vacuum jacket. Thermal
s
be deduced. Further details of this technique are linksweremaintainedbydirectsurface-to-surface
given elsewhere [4]. contact between the cavity and this outer cylin-
There are some important improvements to der at certain points. The result of this improve-
this technique that are reportedhere for the first ment was to reduce any drift in frequency due to
time. In the past [1], four issues were of major changesintheheliumhydrostaticpressuretoless
concern regarding the microwaveresonant cavity than the random noise present in the data.
technique. These involved the base temperature, Finally, the orientation of the sample in the
the reproducibility of the background,the effects cavity is different from previous experiments [1].
ofchangingliquidheliumhydrostaticpressureon H is now applied parallel to the c-axis of the
rf
the dimensions of the resonator,and the orienta- sample, whereas in the past, it was parallel to
tion of the sample with respect to H . the a-b plane of the crystal. This change has
rf
In our present design, we are able to reach a two effects. First, the rare-earth paramagnetism
base temperature of 1.2 K without the use of an is stronger when H is applied in the plane [6].
rf
exchange gas, which can corrupt the data. This Thus, by changing the orientation we were able
has been accomplished by pumping on the he- tosignificantlyreducetheparamagneticinfluence
lium bath and providing a stronger thermal link onourmeasurements. Secondly,theformerorien-
between the sample and the helium bath. By tationinducedc-axiscurrentsinthesample. This
reachingalowerbasetemperature,weareableto led to the simultaneous measurement of λ (T)
ab
exploresamplepropertiesina regionoftempera- and λ (T), making it difficult to analyze the in-
c
tureinwhichthedistinctionbetweenthedifferent plane penetration depth without c-axis contribu-
possible pairing state symmetries is most appar- tions. However,with H now applied parallelto
rf
ent. Furthermore,it is at the lowertemperatures the c-axis, only a-b plane currents are induced.
whereanyparamagneticinfluence wouldbemost This allows for a direct measurement of λ (T).
ab
evident.
Afurther improvementwasrealizedby perma-
3. Results
nently mounting the sample rod to the base of
the apparatus. To obtain useful data, it is nec- The surface resistance as a function of T/T
c
essary to introduce the sample to the proper po- is presented in figure 1 for one PCCO and one
sition within the resonant cavity. This position NCCO crystal studied. Note that both samples
has a minimal Erf, and the Hrf is notonly max- display a single transition at Tc. Furthermore,
imum, but aligned in a known direction, in our the datahavethe samebehavioruntilthe PCCO
case,alongthe axisofthe cylindricalcavity. Fur- crystalsurfaceresistancesaturatesattheresidual
thermore,by havingthe sample rodpermanently resistance value. The homogeneity of the crys-
secured, we can ensure that the sample will be tals is attested to by the nature of the transi-
introduced to the same location within the cav- tion. Furthermore, the width of the transition,
ity every time. This is critical in order for the about 0.15 T , is typical for our samples. This,
c
background measurements to be reproducible. alongwiththeirreasonablevaluesofT ,indicates
c
Also,wehaveaddressedtheissueofthehelium that the doping is near optimal levels. There-
hydrostatic pressure. As the level of the liquid fore, the low temperature behavior of the pene-
helium drops over the course of an experimental tration depth for these samples should be repre-
run,thepressureitexertsonthecavitydecreases, sentativeoftheelectron-dopedcupratesupercon-
3
ductors, with minimal extrinsic influences. This 0.16
PCCO
is in contrast to the behavior of other crystals
which displayedmuchbroader transitions as well
as step-like features in R (T), indicative of ad- 0.12 NCCO
S
ditionalsuperconductingtransitions. Thesecrys-
talsalsoshowedmultiple transitionsinthe c-axis
)
0.08
resistivity,werejudgedtobeinhomogeneous,and W (
s
subsequently rejected. R
The low temperature behavior of the change
0.04
in penetration depth, ∆λ(T), has been used as
an indication of the pairing symmetry [1][4]. In
the case of BCS s-wave symmetry, ∆λ(T) is ex-
0
pected to behave exponentially, the exact behav- 0 0.4 0.8 1.2 1.6
ior dependent upon the zero-temperature pene- T/T
c
tration depth, λ(0), and the energy gap, ∆(0).
The asymptotic BCS s-wave form is: ∆λ(T) =
λ(0)(π∆(0)/2k T)1/2e−∆(0)/kBT for T<<T /2.
B c
In figure 2 we show ∆λ(T) for an NCCO crys-
Figure 1. Surface resistance, R (T/T ), for
tal and a PCCO crystal up to 0.45T , as well as S c
c
PCCO (open circles) and NCCO (closed trian-
the asymptotic BCS s-wave model using λ(0) =
1500˚Aand2∆(0)/k T =3.50. Thedataforthe gles)crystals,measuredat9.6GHz,asafunction
B c
of T/T .
electron-dopedcrystalsclearlydiffersfromasim- c
ple BCS s-wave behavior, with the PCCO data
exhibiting clear deviations from an exponential
behavior at T/T <0.3. Nevertheless, we can
c data due to the much weaker paramagnetism in
force the data to fit the asymptotic s-wave BCS
this compound [6]. Thus, the PCCO data should
form,givenabove,allowingbothλ(0)and∆(0)to
more closely reflect the intrinsic behavior of the
vary. ForthePCCOcrystalwefoundλ(0)=1800
penetration depth. A more detailed analysis of
˚Aand2∆(0)/k T =2.75. Similarly,theNCCO
B c this data, and data on thin films, is forthcoming
crystal yields λ(0) = 2725 ˚A and 2∆(0)/k T =
B c in which we conclude that our data fits best to a
2.35. Inbothcaseswefindsmallgapvalues,much
dirty d-wave model [9].
lessthan the 3.5expected fromBCS theory. The
gapvalues are also much smaller than previously
4. Discussion
reported in NCCO [1][4][7][8].
Also of note in figure 2 is the upturn in the Alff et al. recently obtained ∆λ(T)/λ(0) data
NCCO ∆λ(T) data at low temperatures. We on NCCO and PCCO grain boundary junctions
believe that this upturn is due to the paramag- in thin films [10]. They concluded that their
netism of the Nd3+ ions, and its presence may data was consistent with an s-wave scenario. In
explain why previous studies, which did not take the case of NCCO, they applied the same para-
this into account, found NCCO to be an s-wave magnetic correction to their NCCO data which
superconductor. In the fit considered above, we Cooper used to arrive at a d-wave explanation
accounted for the paramagnetism by excluding [2]. This is evidence ofhow sensitivethe finalde-
data below 0.16 Tc from our analysis. At tem- termination of the pairing state symmetry is to
peratures above 0.16 Tc, we believe the param- the choice ofparametersforthe Curie-Weiss law.
agnetic influence is less than in previous studies Although not shown here, we can also force our
due to the difference in orientation of the sam- ∆λ(T) data for a number of PCCO crystals to
ple. Itisimportanttorealizethatasimilarpara- fit to an s-wave form. In general however, this
magnetic upturn is not observed in the PCCO requires using unphysically large λ(0) and small
4
250 5. Conclusion
In conclusion, we have successfully employed
200
a microwave resonant cavity system to mea-
surethepenetrationdepthandsurfaceresistance
150
Å) of NCCO and PCCO crystals down to 1.2 K.
( PCCO Thisdatasupportstheconjecturethatrare-earth
100
Dl paramagnetism might affect the observed pene-
trationdepthtemperaturedependenceinNCCO.
50
NCCO
By analyzing the functional form of this temper-
asymptotic ature dependence, we conclude that the pairing
0
BCS s-wave
symmetry of the electron-doped cuprate super-
0.1 0.2 0.3 0.4
conductors is not a standard s-wave and is more
T/T
c likely d-wave in nature.
This work was supported by NSF DMR-
9732736, NSF DMR-9624021, and the Maryland
Center for Superconductivity Research. We ac-
Figure 2. ∆λ(T/T ) as a function of T/T for knowledgediscussionswithD.H.WuandR.Pro-
c c
crystals of PCCO (open circles), NCCO (closed zorov.
triangles),andtheasymptoticBCSs-wavemodel
REFERENCES
(dashed line). The solid lines are fits to an
asymptotic BCS s-wave of the form ∆λ(T) =
1. D. H. Wu, J. Mao, S. N. Mao, J. L. Peng,
λ(0)(π∆(0)/2k T)1/2e−∆(0)/kBT Note: PCCO
B X. X. Xi, T. Venkatesan, and R. L. Greene,
dataisoffsetandNCCOdataisfitforT>0.16T .
c Phys. Rev. Lett. 70, 85 (1993).
2. J.R.Cooper,Phys.Rev.B54,R3753(1996).
3. J.L. Peng,Z. Y. Li, andR. L. Greene,Phys-
ica C 177, 79 (1991).
∆(0) values. Alff et al. reported a value for 4. S. M. Anlage, D. H. Wu, J. Mao, S. N. Mao,
2∆(0)/kBTc of about 2.9. This is less than the X. X. Xi, T. Venkatesan, J. L. Peng, and R.
BCS value of 3.5, but compares well with our s- L. Greene, Phys. Rev. B 50, 523 (1994).
wave fit gap values. However, we interpret this 5. E. Maiser, P. Fournier, J. L. Peng, F. M.
as a reason for rejecting an s-wave behavior. Al- Araujo-Moreira,T.Venkatesan,R.L.Greene,
though both we and Alff et al. obtained very and G. Czjzek, Physica C 297, 15 (1998).
similar data, we believe that the paramater val- 6. Y. Dalichaouch, M. C. de Andrade, and M.
ues exclude a standard BCS s-wave explanation. B. Maple, Physica C 218, 309 (1993).
However,therearesomes-wavescenarioswhich 7. C. W. Schneider, Z. H. Barber, J. E. Evetts,
might be viable. For instance, gapless super- S. N. Mao, X. X. Xi, and T. Venkatesan,
conductivity could lead to T2 behavior for the Physica C 233, 77 (1994).
temperature dependent penetration depth at low 8. A.Andreone,A.Cassinese,A.DiChiara,and
temperatures. Furthermore,thepresenceofmag- R. Vaglio, Phys. Rev. B 49, 6392 (1994).
netic impurities could potentially reduce the size 9. J.D.Kokales,L.V.Mercaldo,V.V.Talanov,
of the activation gap. This could then explain P. Fournier, R. L. Greene, and S. M. Anlage,
the small values for ∆(0) we obtain when fitting to be published.
to an s-wave functional form. Nevertheless, the 10. L. Alff, S. Meyer, S. Kleefisch, U. Schoop, A.
data is not consistent with a large-gap isotropic Marx,H.Sato,M.Naito,andR.Gross,Phys.
BCS s-wave behavior. Rev. Lett. 83, 2644 (1999).