Heavy-ion irradiation of UBe13 superconductors

6 Pages·0.15 MB·English

by  H. A. Radovan

,
Heavy-ionirradiationofUBe superconductors
13
H.A. Radovan1, E. Behne1, R.J. Zieve1, J.S. Kim2, G.R. Stewart2, W.-K. Kwok3, andR.D. Field4
1Physics Department, University of California at Davis
3 2Physics Department, University of Florida
0 3Argonne National Laboratory, Division of Materials Science
0 4Los Alamos National Laboratory,
2 Division of Materials Science and Technology

n
a Weirradiatetheheavyfermionsuperconductors(U,Th)Be13withhigh-energyheavyions. Damagefromthe
J ionsaffectsbothheatcapacityandmagnetizationmeasurements,althoughmuchlessdramaticallythaninother
superconductors. Fromthesedataandfromdirectimaging,weconcludethattheirradiationdoesnotcreatethe
0
amorphouscolumnardefectsobservedinhigh-temperaturesuperconductorsandothermaterials. Wealsofind
1
thatthedamagesuppressesthetwosuperconducting transitionsofU0.97Th0.03Be13 bycomparable amounts,
unliketheirresponsetoothertypesofdefects.
]
n
o PACSnumbers:74.70.Tx,61.80.Jh
c
-
r
p I. INTRODUCTION VortexmotionisalsoreducedinU1−xThxBe13forzero-field-
u cooling as compared to the field-cooling case [7]. Domain
s wallpinningmayexplainthiseffectaswell,sincecoolingin
. Microscopic lattice disorder can have interesting effects,
t afieldshouldleadtolargerdomainsandfewerdomainwalls.
a particularly on unconventional superconductors. Sensitiv-
Theatypicalvortexbehaviorandthe distinctionbetweenthe
m ity of the critical temperature T to non-magnetic scatterers
c
two superconducting phases suggests that vortices may also
- serves as evidence of non-s-wave electron-pairing. Defects
d can be introduced during sample fabrication, or induced af- haveinterestinginteractionswithothertypesofpinsites,such
n ascolumnardefects.
terwards by irradiation. The latter possibility encompasses
o Here we investigate heavy-ion irradiation of (U,Th)Be .
both point defects created by light ions and other particles, 13
c We show that calculations predict columnar tracks to form.
[ and amorphouscolumns created by high-energyheavy ions.
These columnardefects, which have been heavily studied in However,heatcapacitymeasurements,imaging,andmagneti-

2 zationmeasurementssuggestthatsuchtracksarenotactually
high-temperaturesuperconductors(HTS),serveashighlyeffi-
v present. We also discuss how heavy-ion damage affects the
cientpinningcentersforvorticesandalterasample’sresponse
2 differentsuperconductingphases.
toamagneticfield.
4
4 Little work has been done on anothergroup of unconven-
7 tionalsuperconductors,theheavyfermion(HF)systems. The
0 twoordersofmagnitudedifferenceinthecriticaltemperatures II. IRRADIATIONDAMAGE
2
ofHTSandHFsuperconductorschangesthescaleforthermal
0 effects.ThermalfluctuationswhichcomplicateHTSbehavior Thethermalspikemodelexplainsdamagecreationinboth
/
t shouldbeabsentinHF. elements and alloys [8, 9, 10]. In this model, the heavy ion
a
loses energy primarily to the electrons, which in turn ex-
m The spectacular response of one heavy fermion material,
UBe , to thorium doping makes it a good candidate for in- cite phonons. The electron-phonon coupling strength g de-
- 13
termineshowfasttheenergyistransferedtothelattice,while
d vestigatingotherformsoflatticedisorder.T (x)isnotmono-
c
n tonicforU1−xThxBe13, anda secondthermodynamicphase thethermalconductivitiesκeandκpofelectronsandphonons
o transition appears for 0.019 < x < 0.043 [1, 2]. No other governhowtheenergyspreadsthroughthesample. Thecou-
c pleddifferentialequations
dopant has such effects. The Be as well as the U is sensi-
:
v tivetosubstitutiondetails. Thesuperconductingtransitionis
Xi suppressedbelow0.015K forUBe12.94Cu0.06 [3], while the Ce∂Te = ∂ (κe∂Te)+ κe∂Te −g(Te−Tp)+A(r,t)
sameamountofBhasvirtuallynoeffect[4]. ∂t ∂r ∂r r ∂r
r
a Multiple superconducting phases indicate an unconven-
tionalorderparameter. AsecondHFmaterial,UPt3,alsoex- ∂Tp ∂ ∂Tp κp∂Tp
C = (κ )+ +g(T −T )
hibitsa doubletransition[5]. Furthermore,the lowerphases p p e p
∂t ∂r ∂r r ∂r
ofbothUPt3 andU1−xThxBe13 haveasignificantlyreduced
vortexrelaxationrate,whileinpureUBe13therelaxationrate describe the energy transfer. Here κe and the specific heat
islinearintemperature[6]. Thismaybeevidenceoftimere- Ce of the electron system are functionsof the electron tem-
versalsymmetrybreakinginthelowerphase. Iftimereversal peratureTe, whileκp andthelatticespecificheatCp depend
symmetryisbroken,spontaneousmagneticfieldscanappear. on the phonon temperature T . S = −dE| is the energy
p e dx e
Boundariesbetweendifferentmagneticdomainscanobstruct loss from the heavy ion to the electronsin the target. As S
e
vortexmotion,leadingtotheobserveddropinrelaxationrate. increases, a threshold value allows formation of amorphous
2
5
TABLEI:ParametersforthermalspikecalculationsinUBe13.
30
Debyetemperature,Θ 620K [12]
D
4 m)
Meltingtemperature,Tm 2273K [13] V/n
Resistivity,ρ 110µΩ-cmat300K [14] m) (keSe20 E (MeV/amu)
VAatolemncice,dzensity,na 12.×1 1023/cm3 [15] us (n3 0 10 20
di
CCep 44..31××110033eerrgg//ccmm33KK efect ra2
κe 2.2×103T erg/cmK D
κp 9.9×107/T erg/cmK [16] 1
tracks. With furtherincrease thetrack radiusgrows. Forthe
0
20 30 40
radialdistributionoftheoriginalionenergylossweuse
Se(keV/nm)
1 (1− r+θ )0.927
A(r,t)∝ [ rmax+θ ] FIG.1:PredicteddefectradiusinUBe13.Thetwocurvesuseheatof
r r+θ fusion2×1010erg/cm3(•)and4×1010erg/cm3(◦).Inset:SRIM
simulationofelectronicenergylossfor238U67+ (2)and208Pb56+
(•)ionsinUBe13.Thearrowsindicatetheenergyofthebeamsused
×[1+ K(r−L)e−(r−L)/M]e−(t−to)2/2t2o, forourirradiations.
M
asin[11].HereK =19β1/3,L=0.1nm,M =(1.5+0.5β)
nm,andβistheionvelocityrelativetothespeedoflight.The thoughthemixingenthalpyisunknown,2×1010 erg/cm3 is
maximumranger =6×10−6(2mc2β2)1.079cm,wherem amorereasonableestimatefortheheatoffusion.
max 1−β2 Finally,fortheelectron-phononcouplingweuse[8]
istheelectronmassingramsandcthespeedoflightincm/s.
The time t is of order 10−15 s and θ = 9.84× 10−9 cm.
o π4k4n2Θ2 ρ 1
ThenormalizationofA(r,t)ischosensothatthetotalenergy g = B e D .
transfertotheelectronsequalsSe. Thisformula,particularly 18L¯h2(6π2na)2/3Te
theterminvolvingK,L,andM,comesfromfitstoobserved
HereL=0.245erg-Ω/KistheLorentznumber.
radiation distributions in water [11]. Thermalspike calcula-
Figure 1 shows the defect radius obtained by solving the
tionsusingtheseequationssuccessfullypredicttheexistence
thermalspikeequationsnumerically.Thevaluesarecompara-
andevenradiusofcolumnardefectsinavarietyofpuremetals
bletothoseofCeandYalloys[9],whichhavesimilarresistiv-
andalloys[8].
ity,Debyetemperature,andheatofformationtoUBe . The
Numericalsolutionof these equationsrequiresknowledge 13
high atomic density of UBe increases its sensitivity to ir-
ofvariousparametersofthe material. TableIshowstheval- 13
radiation,whiletheunusualtemperatureindependenceofthe
ues we use. Since most of the simulation is at high temper-
resistivitydecreasesthesensitivity.
ature, we use high-temperature limits in several cases. The
electronic and lattice specific heats are C = 1.5k n and
e B e
C =3k n . Thedensityofatomsinthelatticeisn ,while
p B a a
the electron densityis n = zn with z the averagevalence III. SAMPLEPREPARATIONANDIMAGING
e a
oftheatomscomposingthematerial. Fortheelectronicther-
mal conductivity κ we use the Wiedemann-Franz law. Al- Our samples are polycrystalline UBe and
e 13
though in most metals the high-temperature electrical resis- U Th Be pieces with a grain size of about 100
0.97 0.03 13
tivity is proportionalto temperature,in UBe the resistivity µm, prepared by arc melting in an argon atmosphere and
13
is nearlyconstant, so κ is itself proportionalto temperature subsequent annealing at 1400◦ C in a beryllium atmosphere
e
[14]. Forthelatticethermalconductivityκ weexpecta1/T for 1000hours[17]. Before irradiation, samples are thinned
p
temperaturedependenceandobtaintheprefactorfromthe90 to 25 µm to prevent ion implantation, with a typical lateral
Kvalue[16]. dimensionof1mm. TheirradiationisperformedatATLAS,
Theheatoffusionofacompoundequalsthelatentheatof Argonne National Laboratory with 1.4 GeV 238U67+ and
its componentelements, plus the differencebetween the liq- 208Pb56+ ions. The ion velocitiesare 5.9 MeV/amu and 6.7
uidstatemixingenthalpyandthesolidenthalpyofformation. MeV/amu, respectively. The matching fields B , at which
Φ
Typical values are 1010 to 1011 erg/cm3. In this case the U thevortexdensityandtrackdensityareequal,rangefrom0.1
andBelatentheatscontribute2×1010 erg/cm3. Theheatof T and 7 T, correspondingto typical lateral track separations
formationatroomtemperatureis−2×1010erg/cm3[13],so from 155 to 18.5 nm. The 208Pb56+ ions were used for the
4×1010erg/cm3isanupperboundontheheatoffusion.Al- 3 T and 7 T samples, while the 238U67+ were used for the
3
TABLEII:Effectsofirradiationontransitionsin(U,Th)Be13.
Tc(0T) Tc(3T) Tc(5T) Tc(7T) %changeat7T
UBe13 770 750 715∗ -7.1
U0.97Th0.03Be13(Tc1) 625 620∗ 613 530 -15.2
U0.97Th0.03Be13(Tc2) 412 400 345 -16.3
Transitiontemperaturesmarkedby(*)comefrommagnetizationmeasurements,theremainderfromheatcapacity.
remaining samples. The irradiation takes up to two hours, 4
dependingon dosage. Because of the verysmall probability
that two ions will reach the sample at nearly the same time
and position, we assume that each ion acts independentlyin
3
damagingthesample.
The inset of Figure 1 shows the electronic energyloss S
e
as a function of the incident beam energy, obtained from a 2K)
Stopping and Range of Ions in Matter (SRIM-98 code [18]) ole2
m
simulation. The beamenergyusedfor theirradiationisnear (J/
the maximum and gives S = 31.2 keV/nm for uranium, T
e /
C
S = 27.6 keV/nm for lead. The correspondingnuclearen-
e
ergylossesarenegligible,0.05keV/nmand0.04keV/nm,re- 1
spectively.Thepredictedstoppingdistancesare56µmand60
µm,morethantwicethesamplethickness. Fromourthermal
spikecalculation,theirradiationshouldproducedefectswith
0
radius2.8nm(uranium)or2.2nm(lead). 200 300 400 500 600 700
After irradiation, both the 2.0 T UBe and 7.0 T
13 Temperature (mK)
U Th Be crystals were further thinned and viewed
0.97 0.03 13
in both a Philips CM-30 transmission electron microscope
FIG.2: Zero-fieldheat capacityof unirradiated(2), 5Tirradiated
(TEM)andaJEOL3000Fhighresolutiontransmissionelec-
tronmicroscope.TheplanesusedfortheimagesontheJEOL (•),and7Tirradiated(∆)U0.97Th0.03Be13.
machinelimitedtheresolutiontoabout0.5nm. AtB =2.0
Φ
Tthedefectsshouldbeabout32nmapart. Thetotalviewing
areaofabout73,000nm2shouldcontainabout70defectsbut
infactshowsnoevidenceofamorphouscolumns.Forthe7.0 ter,a[50:50]AuCrthinfilmheater,andafinecopperwireas
T sample, the imagingarea of over54,000nm2 should have aheatlink.
nearly200defects.Weagainfindnodamageofradiusgreater Figure 2 shows C/T for the unirradiated, 5 T, and 7 T
than2nm,andonlysixcandidateswithradiusfrom1nmto U Th Be samples. Sincewedonotknowtheprecise
0.97 0.03 13
2nm. Ofthese,closerexaminationshowsthatthreeareedge samplesizes, we use a multiplicativeconstantto setthenor-
dislocations. The remaining candidates could also be dislo- malstate valueofC/T to1.1J/moleK2 foreachcurve. We
cations,viewedfromanglesthatdonotclearlyshowalattice donotadjustthemeasuredheatcapacityforanycontribution
planeending. Wefindnocompellingreasontoidentifythem from the thermometer, heater, or mount; but comparing the
with columnar tracks, since they do not match the expected curvesshowntopreviousheatcapacitymeasurementsonbulk
defectseither in size or in density. We concludethatcolum- samplessuggeststhatbackgroundeffectsarelessthan30%of
nardefectsareeitherabsentinoursampleorfarsmallerthan oursignal. Inanycase,thebackgroundshouldnotaffectour
anticipatedfromourthermalspikemodelcalculations. determinationoftheT suppressionortransitionwidth.
c
We emphasize that the microscopes we used can detect Irradiationdoes not measurablychange T up to B = 2
c Φ
amorphousregionsoftheexpectedsize. Atransmissionelec- T. As shownin Figure 2 for U Th Be , C/T changes
0.97 0.03 13
tronmicroscopesuccessfullyimagedcolumnardefectsofra- shapeonlyslightlyevenatadefectdensityof5T,broadening
dius 5 nm in UO2 [19]. High resolution TEM has detected byseveralmK[22]. AtthehigherdefectdensityofBΦ =7T,
columnar defects with radius down to 1 nm, for example in thetransitionsdochangeshape. Theuppertransitionwidens
tinoxide[20]andBi2Sr2CaCu2O8+δ [21]. byroughlyafactoroftwo,andbothdecreasesignificantlyin
amplitude. Here width is defined by identifying the change
in C/T across the transition and using the temperature dif-
IV. HEATCAPACITYMEASUREMENTS ferencebetweenthe10%and90%valuesoftheheatcapacity.
IrradiationhasasimilareffectonpureUBe ,reducingT and
13 c
Wemeasureheatcapacityonadilutionrefrigeratorattem- slightlybroadeningthetransition,whileretainingtheshapeof
peraturesdownto100mKandmagneticfieldsupto8Tesla. theC/T curveupto5T.TableIIsummarizestheeffectsofir-
WeusearelaxationmethodwithaRuO thinfilmthermome- radiationontransitiontemperaturesforbothcompounds.The
2
4
marked transitions come from magnetization measurements 15
ratherthanheatcapacity,aswillbediscussedlater.
Since the 208Pb56+ ions used for irradiation have less en-
ergylossthanthe238U67+ ions,theyproducesmallerdefects s) 10
s
inathermalspikecalculation. Dependingonthevalueofthe u
a
g
heatofformation,theuraniumatomsmightevenproducede- (
M
fects while the lead atoms do not. We note here that the Tc ∆ 5
depression for the 3 T sample is consistent with the others.
The7Tsampleshave,ifanything,alargerchangeinT than
c
expectedfromthelowerirradiationdosages. Thusitappears
0
that the 208Pb56+ ions do as much damage as the 238U67+
ions,despitetheirsmallerenergyloss.
It is tempting to take the nearly identical percentage sup-
pression of the two thoriated transitions as evidence that
3
bothsuperconductingphaseshavethesamepairingsymmetry. 2)
K
However, the lower transition is between two superconduct-
ol
ingphases,ratherthanbetweenasuperconductingandanor- m2
J/
malphase. Theusualargumentsonhowimpuritiesaffectthe (
T
transitiondonotapply. Wedonotethattheheavy-ionirradi- / Tc2
C
ationproducesadifferentresponsefromeithernon-magnetic 1
ormagneticsubstitutionalimpurities[23].Non-magnetic(La) Tc1
impurities depress the upper transition but leave the lower
0
transition unchanged, while magnetic (Gd) impurities sup- 200 400 600 800
press the lower transition more than twice as stronglyas the
T (mK)
upperone[23]. Thesecontrastingbehaviorsofthetwo tran-
sitions for different types of defects emphasize the extreme
sensitivityofthe(U,Th)Be systemtochangesinelectronic FIG.3:Comparisonofmagnetizationandheatcapacityforunirradi-
13
structure. atedU0.97Th0.03Be13.Theverticallinesmarkthetwotransitions.
The T suppression proves that the irradiation did create
c
somedamagewithinthecrystals. However,thesmallamount
of suppression, like the lack of visible columnsin the imag-
tothecriticalcurrentj ;andwemeasurebothitstemperature
c
ing,suggeststhatthedamageisnotintheformofamorphous
anditsfielddependence.
columns. Forcomparison,Uionsata 2Tmatchingfieldre-
Figure 3 compares hysteresis loop width and heat capac-
duceTcofYBa2Cu3O7−xby5.3%[24],morethanwefindat ity for a sample. As T increases, the hysteresis loop width
5 T. Althoughin principleour low T reductioncould occur
c decreases, closingat the same superconductingT measured
c
frominsensitivitytodefects,ratherthananabsenceofdefects,
withheatcapacity.Forthe3Tthoriatedand7Tpuresamples,
HF superconductorsare more sensitive than other supercon-
the T valuesin Table II are determinedfrom magnetization
c
ductorstobothneutronandlight-ionirradiation[3,25]. Even
ratherthanheatcapacitydata.
ourB =7TeslairradiationaffectsT farlessthanthepoint
φ c We note that ∆M(T) in Figure 3 shows no feature at the
defectwork[3].
lower transition. By contrast, magnetic relaxation measure-
mentsshowasharpdropinthevortexcreeprateatthelower
transition[6]. UPt ,theotherHFcompoundwithtwotransi-
3
V. MAGNETIZATIONMEASUREMENTS tions, showsthe samebehavior: a dropinthe relaxationrate
atthelowertransition[6],butnofeatureinthemagnetization
Themotionofsuperconductingvorticesisparticularlysen- itself[27].Oneexplanationofthedifferencebetweenthetwo
sitivetodefects. Columnartracksstronglypinvortices,even measurementsisthatthemechanismofvortexmotionchanges
whenthetracksaremisalignedwiththemagneticfieldbyup atthelowertransition,whilethepinningstrengthitselfunder-
to40◦[26]. Ourimagingworkcouldmissincompleteormis- goesnosharpchange.However,anotherpossibilityliesinthe
alignedcolumnswhichwouldbedetectedinasample’smag- magnetic field history of the relaxation measurements. Vor-
neticbehavior. texcreepisonlysuppressedwhenthesampleisexposedtoa
For these measurementswe use bismuth Hall probeswith sufficientlylargemagneticfield,typically1kOe,beforehav-
active area 10×15 µm2. We place the sample flat atop the ingthefieldreducedtozerofortherelaxationmeasurements
substratefortheHallprobe.Theprobemeasurestotalfieldat [28]. Ourhysteresisloops, with maximumwidthof 200Oe,
aspotnearthesurfaceofthesample, fromwhichwe extract may simply be in a different regime where the vortex creep
the local magnetization of the superconductor. We typically showsnosignatureatthelowertransition.
ramp the applied magnetic field at 15 gauss per minute, and The magnetizationdata confirm that columnar defects are
take hysteresis loops large enough to allow for full penetra- eitherabsentorfarsmallerthanexpected. Increasedpinning
tion. The width of the hysteresis loop, ∆M, is proportional fromthecolumnswouldappearaswiderhysteresisloops,but
5
ourloopwidthsarecomparableforunirradiatedandirradiated VI. CONCLUSION
samples. Inothersuperconductorscolumnardefectsproduce
large effects from commensurability near integral multiples
of B , but our hysteresisloops have no features whatsoever
Φ We have irradiated (U,Th)Be crystals with high-energy
13
inB. Onepossibilityisthatanydefectsaretoomuchsmaller
U and Pb ions at fluences up to B = 7 T. The irradiation
than100A˚,thesuperconductingcoherencelength[14],topin Φ
damagereducesbothsuperconductingtransitiontemperatures
vortices.
ofU Th Be byover15%forthe7Tbombardment,as
0.97 0.03 13
Ourmagnetizationmeasurementsdoshowevidenceofde- wellasloweringj andreducingitstemperaturedependence.
c
fect creation. Figure 4 shows loop width versus normal- Unlike in previous work with substitutional impurities [23],
izedtemperaturefor(U,Th)Be13crystalsofseveralirradiation irradiationcausesasimilarTcreductionforthetwotransitions
doses,takenatzeronominalfield. Thewidthfollowsapower ofU Th Be .
0.97 0.03 13
law∆M(T)=∆M(0)(1− T )αovertheentiretemperature
Tc
rangemeasured,approximately0.3TctoTc. Fortheunirradi- Despite the measured Tc reduction, transmission electron
atedandthe5Tsamplesα=1.8,whileforthe7Tspecimen microscopeandhysteresismeasurementssuggestthatthede-
α is reduced to 1.4. Although the magnitude agreementbe- fectsarenottheamorphoustracksfoundinHTS.Ourcalcu-
tweenthe5Tandunirradiatedsamplesispartlycoincidental, lationsoftheirradiationprocesspredictcolumnardefectfor-
the 7 T sample has significantly the smallest ∆M observed. mationforS downto23keV/nm.Oursamplesareirradiated
e
Boththemagnitudeandslopechangeareprobablyduetothe abovethethresholdvalue,atS ≈ 30keV/nm. Theresulting
e
damage. AswiththestrongerTc suppressioninthe7Tsam- defects should have diameter 5 to 6 nm, a defect size com-
ple mentioned earlier, this hints that the 5 T irradiation is a parabletothe10nmsuperconductingcoherencelength. The
thresholdforstrongdamageinour(U,Th)Be crystals.
13 lackofpinningbythedefectsandtheirabsencefromtheTEM
imagesmeanseitherthattheactualradiusismuchsmalleror
100 thatonlyincompletecolumnsorpointdefectsform.Wefavor
the third option. We rule out the first possibility because of
the similarity between 208Pb56+ and 238U67+ irradiation: if
thecolumnradiusweremuchsmallerfor238U67+ ions,then
10 notracksshouldappearatallfor208Pb56+ ions. Thelackof
ss) signalinthemagnetizationindicatesthatthesampledoesnot
u
ga haveevenincompletecolumns,whichwouldstillpinvortices
(
M 1 effectively. SincethereductionsofTc andjc showthatsome
∆ damageis present, we assume we have insteadcreatedpoint
defects.
0.1 The conditions for creation of columnar defects are im-
portantto understand, particularlyas the use of such defects
spreads from HTS to other materials. It is unclear whether
thediscrepancybetweentheexperimentandthethermalspike
0.1 1 calculationcomesfromthevalueschosenforthe parameters
1− T orfromadeeperproblemwiththemodel. Thethermalspike
Tc model has successfully predicted radiation damage both in
otheralloys[9]andinelements,includinguraniumandberyl-
FIG.4:Hysteresisloopwidthvs.reducedtemperatureforthreetho-
lium [8]. The simplest explanation would be incorrect pa-
riatedsamples: unirradiated(•),andirradiatedwithmatchingfields
of5T(△)and7T(2). rameters. Althoughweuse conservativechoices,suchasas-
suming resistivity constant rather than linear in temperature,
ourhigh-temperatureextrapolationsforρorκ maybeincor-
p
rect. Many-electroneffectsproduceavarietyofunusuallow-
Models for networks of superconductinggrains give α = temperatureeffectsinUBe13andotherheavyfermionmateri-
1 for superconductor-insulator-superconductor (SIS) tunnel als,andperhapscouldinfluencehigher-temperaturebehavior
junctions [29] and α = 2 for superconductor-normal- aswell.
superconductor(SNS)junctions[30]. Anintermediatepower
law for j (T), with α near 1.5, has been measured in vari- WealsoshowthatthelowertransitionofU Th Be
c 0.97 0.03 13
ousmaterials,includingtheHFmaterialCeCu Si [31]. The is not detectable in j (T), despite the sharp change in mag-
2 2 c
intermediatevaluesmaycomefrommixturesofSISandSNS neticrelaxationratepreviouslyobserved.Thismayarisefrom
junctionsinthesamples.Similarly,thechangeinexponentfor differencesinmeasurementprocedurebetweenourworkand
our 7 T sample is consistent with irradiation damagechang- therelaxationratestudies. Anotherpossibilityisthatvortices
ing the characteristics of the grain network. We find the inthetwosuperconductingphasesofU Th Be differ
0.97 0.03 13
same power-law behavior in external magnetic fields up to onlyintheirbehaviorawayfromthecriticalcurrentj ,which
c
µ H =2kG,withtheexponentindependentoffield. magnetizationmeasurementswouldnotprobe.
0
6
VII. ACKNOWLEDGEMENTS DMR-9733898(UCD)andbyDOEunderW-31-109-ENG-38
(ANL), DE-FG05-86ER45268(Florida), and W-7405-ENG-
We would like to thank P.C. Canfield and J.L. Smith for 36(LANL).
fruitfuldiscussions. ThisworkwassupportedbyNSFunder
[1] H.R.Ott,H.Rudigier,Z.Fisk,andJ.L.Smith,“Phasetransition thesecondtransitioninU1−xThxBe13,”Phys.Rev.B44,6921
in the superconducting state of U1−xThxBe13 (x = 0-0.06),” (1991).
Phys.Rev.B31,1651(1985). [18] J.F.Ziegler,“Thestoppingandrangeofionsinmatter(SRIM),”
[2] R.H. Heffner et al., “New phase diagram for (U,Th)Be13: A IBM-Research,http://www.research.ibm.com/ionbeams/.
muon-spin resonance and Hc1 study,” Phys. Rev. Lett. 65, [19] T.Wissetal.,“RadiationdamageinUO2byswiftheavyions,”
2816(1990). Nucl.Instr.andMeth.B122,583(1997).
[3] B.Andrakaetal.,“Neutronirradiationofheavy-fermionsuper- [20] A.Berthelotetal.,“Irradiationofatinoxidenanometricpow-
conductors,”Phys.Rev.B38,6402(1988). der withswift heavyions,” Nucl. Instr.and Meth. B166-167,
[4] E.T.Ahrensetal.,“NMRstudyofU(Be,B)13inthenormaland 927(2000).
superconductingstates,”Phys.Rev.B59,1432(1999). [21] N.Kurodaetal.,“Effectsofdefectmorphologyontheproper-
[5] R.A.Fisheretal.,“SpecificheatofUPt3: Evidenceforuncon- tiesofthevortexsysteminBi2Sr2CaCu2O8+δ irradiatedwith
ventionalsuperconductivity,”Phys.Rev.Lett.62,1411(1989). heavyions,”Phys.Rev.B63,224502(2001).
[6] A.C. Mota, E. Dumont, and J.L. Smith, “Strong vortex [22] H.A.Radovanetal.,“Reductionofcriticaltemperaturesinpure
pinning in the low-temperature superconducting phase of andthoriatedUBe13bycolumnardefects,”PhysicaC341-348,
(U1−xThx)Be13,”J.LowTemp.Phys.117,1477(1999). 1953(2000).
[7] R.J.Zieveetal.,“Anomalousfluxpinninginatorusofthoriated [23] E.-W. Scheidt, T. Schreiner, and G.R. Stewart, “Influence
UBe13,”Phys.Rev.B51,12041(1995). of La and Gd impurities on the two phase transitions in
[8] Z.G.Wang,C.Dufour,E.Paumier,andM.Toulemonde,“The U0.97Th0.03Be13,”J.LowTemp.Phys.114,151(1999).
Se sensitivity of metals under swift-heavy-ion irradiation: A [24] L.M.Pauliusetal.,“Effectsof1-GeVuraniumionirradiation
transientthermalprocess,”J.Phys.Cond.Mat.6,6733(1994). onvortexpinninginsinglecrystalsofthehigh-temperaturesu-
[9] M. Ghidini et al., “Amorphization of rare earth-cobalt inter- perconductorYBa2Cu3O7−δ,”Phys.Rev.B56,913(1997).
metallicalloysbyswiftheavy-ionirradiation,”J.Phys.Cond. [25] G.AdrianandH.Adrian,“Latticedisordereffectsonsupercon-
Mat.8,8191(1996). ductivityandelectricalresistivityofheavy-fermionCeCu2Si2-
[10] J.P.Nozieresetal.,“Swiftheavyionsformagneticnanostruc- films,”Europhys.Lett.3,819(1987).
tures,”Nucl.Instr.Meth.B146,250(1998). [26] D.H. Kim et al., “Effect of tilted columnar defects on vortex
[11] M.P.R.Waligo´rski,R.N.Hamm,andR.Katz,“Theradialdis- pinninginYBa2Cu3Oxfilms,”Phys.Rev.B64,184518(2001).
tributionofdosearoundthepathofaheavyioninliquidwater,” [27] E. Shung, T.F. Rosenbaum, and M. Sigrist, “Vortex pinning
Nucl.TracksRadiat.Meas.11,309(1986). andstabilityinthelowfield,superconductingphasesofUPt3,”
[12] G.R. Stewart, “Heavy-fermion systems,” Rev. Mod. Phys. 56, Phys.Rev.Lett.80,1078(1998).
755(1984). [28] A.C.Mota,E.Dumont,J.L.Smith,andY.Maeno,“Unconven-
[13] R.Hultgrenetal.,SelectedValuesoftheThermodynamicProp- tionalstrongpinninginmultiphasesuperconductors,” Physica
ertiesofBinaryAlloys, (AmericanSocietyforMetals, Metals C332,272(2000).
Park,OH,1973). [29] V.AmbegaokarandA.Baratoff,“Tunnelingbetweensupercon-
[14] R.H.HeffnerandM.R.Norman,“Heavyfermionsuperconduc- ductors,” Phys. Rev. Lett.10, 486 (1963) and Phys. Rev. Lett.
tivity,”CommentsCond.Mat.Phys.17,361(1996). Erratum11,104(1963).
[15] M.W.McElfreshetal.,“Structureoftheheavy-fermionsuper- [30] P.G. de Gennes, “Boundary effects in superconductors,” Rev.
conductorUBe13,”ActaCryst.C46,1579(1990). Mod.Phys.36,225(1964).
[16] F.G.Alievetal.,“AnisotropyoftheuppercriticalfieldnearTc [31] A.Pollinietal.,“Fluxdynamicsandlow-fieldmagneticprop-
andthepropertiesofURu2Si2andUBe13inthenormalstate,” ertiesoftheheavy-fermionsuperconductorCeCu2Si2,”J.Low
J.LowTemp.Phys.85,359(1991). Temp.Phys.90,15(1993).
[17] J.S. Kim, B. Andraka, and G.R. Stewart, “Investigation of