Superconducting properties of Rh$_{9}$In$_4$S$_4$ single crystals

0.8 MB·

by  Udhara S. Kaluarachchi

Superconducting properties of Rh In S single crystals
9 4 4
Udhara S. Kaluarachchi,1,2 Qisheng Lin,1 Weiwei Xie†,1,3 Valentin
Taufour,1 Sergey L. Bud’ko,1,2 Gordon J. Miller,1,3 and Paul C. Canfield1,2
1Ames Laboratory, U.S. DOE, Iowa State University, Ames, Iowa 50011, USA
2Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA
3Department of Chemistry, Iowa State University, Ames, Iowa 50011, USA
6 Thesynthesisandcrystallographic, thermodynamicandtransportpropertiesofsinglecrystalline
1
Rh9In4S4 were studied. The resistivity, magnetization and specific heat measurements all clearly
0
indicatebulksuperconductivitywithacriticaltemperature,Tc ∼2.25K.TheSommerfeldcoefficient
2 γ and theDebyetemperature(ΘD) were found to be34mJmol−1 K−2 and 217K respectively. The

r observed specific heat jump, ∆C/γTc=1.66, is larger than the expected BCS weak coupling value
a of 1.43. Ginzburg-Landau (GL) ratio of the low temperature GL-penetration depth, λGL≈5750˚A,
M
to the GL-coherence length, ξGL≈94˚A, is large: κ∼60. Furthermore, we observed a peak effect in
theresistivity measurement as a function of both temperatureand magnetic field.
1
1
I. INTRODUCTION and sealed in a silica ampule under a partial pressure of
]
n high purity argon gas. The sealed ampule was heated to
o Transition-metal chalcogenides show diverse 1150℃ over 12 hours and held there for 3 hours. After
c physical states such as charge density wave1–4, that, it was cooled to 950℃ over 50 hours and excess
-
r superconductivity5–9, ferromagnetism10,11 and semi- liquid was decanted using a centrifuge. Single crystals
p conducting behavior12,13. The ability to change their of Rh9In4S4 grew as tetragonal rods with typical size of
u properties by doping5,14,15 or pressure16,17 has recently ∼0.5×0.5×2mm3 as shown in the inset of Fig.2(b).
s
Single crystal X-ray diffraction data were collected
. attracted great attention. Of specific interest, some
t
a members of metal-rich chalcogenides10,18–20, A M X using a Bruker SMART APEX II CCD area-detector
m 2 3 2 diffractometer29 equipped with Mo K (λ = 0.71073˚A)
(A=Sn,Pb,In,Tl and Bi; M=Co,Ni,Rh and Pd; X=S α
- and Se) are superconducting at low temperatures9,21,22. radiation. Integration of intensity data was performed
d Interestingly Bi Rh Se 23 is a superconductor that bytheSAINT-Plusprogram,absorptioncorrections30by
n 2 3 2 SADABS , and least-squaresrefinements by SHELXL31,
shows a possible high-temperature (∼240K) charge
o
all in the SMART software package. Lattice parameters
c density wave transition. In contrast, the isostructural
[ Bi Rh S 10,24 has a high temperature structural phase were refined using single crystal diffraction data and are
2 3 2
summarizedinTableI.Atomic coordinatesanddisplace-
transition, but remains non-superconducting down to
3 0.5K, and the neighboring Bi Rh S 24 has no struc- ment parameters with full site occupancy for Rh9In4S4
v 2 3.5 2
are derived from the single crystal diffraction and given
8 tural phase transition, but becomes superconducting
in TableII. PowderX-ray diffraction data were collected
4 at Tc ≈1.7K. The discovery of superconductivity in
using a Rigaku Miniflex II diffractometer at room tem-
9 Bi Rh S motivated us to extend our exploration for
2 3.5 2
7 superconducting compounds to the Rh-In-S system, perature (Cu Kα radiation). Samples for powder X-ray
0 diffraction was prepared by grinding single crystals and
which has not yet been fully investigated with only one
1. compound, Rh In S 10, reported. spreading them onto a thin grease layer coated single
3 2 2
0 In this article,we presentdetails ofthe crystalgrowth crystal Si, zero background puck. Powder X-ray diffrac-
6 tion data were analyzed using the GSAS32,33 program.
andcharacterizationofthetransition-metalchalcogenide
1
superconductor Rh In S . Measurements of transport
: 9 4 4
v properties, magnetization and specific heat confirm bulk
TABLEI.LatticeparametersofRh9In4S4at293K.Allvalues
Xi superconductivity ofRh9In4S4 atTc ∼2.25K andwe re- are from single crystal diffraction data.
port other superconducting properties from the above
r Formula Rh9In4S4 (293K)
a measurements. The upper critical field, µ0Hc2, shows
Formula weight 1485.89
goodagreementwiththe Helfand-Werthamer(HW) the-
ory. We also present the observation of a peak effect in Z-formula units 2
this material by means of transport measurements. Space group I4/m m m (139)
a (˚A) 7.7953(3)
c (˚A) 8.8583(3)
II. EXPERIMENTAL METHODS Volume(˚A3) 538.25(5)
Density (g/cm3) 9.339
Single crystals of Rh In S were produced using a so-
9 4 4
lution growth technique22,25,26. A mixture of elemen- The ac resistivity (f=17Hz) was measuredas a func-
tal Rh, In and S was placed in a 2 mL fritted alumina tionoftemperature andfield by the standardfour probe
crucible27,28 with a molar ratio of Rh:In:S=55:22.5:22.5 method in a Quantum Design (QD), Physical Property
2
TABLE II. Atomic coordinates and equivalent isotropic dis-
placement parameters of Rh9In4S4 at 293K.
AtomWyck Symm. x y z Ueq
(˚A2)
In1 4e 4mm 0 0 0.1872(3) 0.027(1)
In2 4d -4m2 0.5 0 0.25 0.019(1)
Rh1 8f ..2/m 0.25 0.25 0.25 0.067(1)
Rh2 8i m2m 0.3011(3) 0 0 0.019(1)
Rh3 2b 4/mmm 0 0 0.5 0.012(1)
S 8h m.2m 0.2079(7) 0.2079(7) 0.5 0.038(2)
MeasurementSystem(PPMS)instrument. FourPtwires
with diameters of 25µm were attached to the samples
using Epotek-H20E silver epoxy or DuPont 4929N silver
paint. The contact resistance was ∼ 0.5Ω. The spe-
cific heat was measured by using the relaxation method
in the PPMS. The 3He option was used to obtain mea-
surements down to 0.4 K. The total uncertainty of the
specific heat data is ∼5%. The DC magnetization mea-
surements were performed in a QD, Magnetic Property
Measurement System (MPMS).
III. RESULTS
A. Structure
FIG. 2. (a) Reciprocal lattice viewed along (001) zone for
Rh9In4S4. Green dots denote a 2×2 main lattice reflections
of theaverage structuregiven in Table.I;four-fold, more dif-
fuse,clustersaroundthegreendotsdenoteweakreflectionsof
modulated lattice, with a modulation vector of [0.17 0.17 0]
(redarrow). (b)PowderdiffractionpatternofRh9In4S4. The
redlinerepresentsthecalculateddiffractionpatternbasedon
latticeparametersobtainedfromthesinglecrystaldiffraction
analysis. The blue line represents the difference between the
experimental and calculated intensities. The inset shows a
photoof single-crystalline Rh9In4S4 on amillimeter grid and
thearrow indicates the [1 0 0] direction.
in the tetragonal symmetry I4/mmm (a=7.7953(3)˚A,
c=8.8583(3)˚A,). Powderpatternwas fitted with LeBail
refinementandobtainedR =7.3%asshowninFig.2(b).
p
FIG.1. (a)UnitcellofRh9In4S4,withRh1-centeredoctahe- Lattice parameters obtained from this measurement are
drashaded in blue. Rh1and S atoms are shown as ellipsoids in good agreement (less than 0.2%) with single crystals
with 90% probability. (b)-(d) show the detailed configura- data.
tions of Rh1-, Rh2-, and Rh3-centered octahedra, together The composition was refined as Rh In S , consis-
9 4 4
with representative bond distances. Numbers overlaid with tent with Rh InS measuredby electronprobe micro-
2.2(1)
colored spheres denoted atoms listed in Table.II.
analyzer(EPMA).Thelatticeparametersandatomicco-
ordinatesarelistedinTable.IandTable.II,respectively.
Figure1(a) shows the unit cell of the average struc- As in the case of Bi Rh S 24, all Rh atoms in Rh In S
2 3 2 9 4 4
ture of Rh In S , which is described by the tetragonal are six-coordinatedforming slightly distortedoctahedra.
9 4 4
spacegroupI4/mmm. ThepowderX-raydiffractionpat- Of these, Rh1 and Rh2 are surrounded by 4 In and 2 S
tern of a ground, phase pure, single crystal of Rh In S atoms,whereasRh3by2Inand4Satoms,seeFig.1(b)-
9 4 4
is shown in Fig.2(b). According to single crystal X- (d). WhereasRh2andRh3octahedrasitonedgesorface
ray diffraction analyses (TableI), Rh In S crystallizes centersoftheunitcell,Rh1octahedraarelocatedat(1/4
9 4 4
3
1/4 1/4) and equivalent sites. The arrangementof these

Rh1-centeredoctahedraissimilartothoseinPerovskites, Rh9In4S4 I // [100]
200
except that they share edges (In1-In2) in the ab plane
c)
and vertices along c, whereas in Perovskites only cor- m)
ners are shared. Apparently, the pivot-and-rock motion c100 a)
150
orefstuhletisnegRinh1e-lcliepnstoeirdedeloocntgaahteiodnrafoisrrtehsetrRicht1edanindaSbaptloamnes,, m) ( cm)200
c 0
Fig.1(a). Viewing along the c axis, Rh1 and S atoms )
100 4 0 b) (
dfoerrmcaanzeiga-szialyglcehaadintsoesxtrtuenctduinregmaloodnuglac,tiaonnd, atsheoibrsdeirsvoerd- ( H (1/-0.5 ZFFCC
in many other structures, e.g., Sc Mg Cu Ga 34 M/
4 x 15−x 7.5 50 0.5 mT
Indeed, careful examination of reciprocal space from -1.0 175
2.0 2.5 0 150 300
single crystal intensity data confirms that the structure
T (K) T (K)
is a modulated structure. With a cut-off intensity of
0
3σ, we were able to identify a modulationvector of [0.17 0 50 100 150 200 250 300
0.17 0], see Fig.2(a). However, due to the weakness of
T (K)
the modulation reflections, no model of any modulated
structure has been acceptable (so far). Since the results FIG. 3. Temperature dependent resistivity of Rh9In4S4
along [1 0 0]. The insets show (a) the typical superconduct-
of an average structure refinement are sufficient for our
ing transition feature in resistivity data and the arrow in-
currentdiscussions,hereinwewillnolongerfocus onthe
dicates the offset criteria, which was used to obtained the
detailed modulated structure, but rather the averaged
Tc≈2.25K; (b) shows the ZFC and FC M/H of Rh9In4S4
structure. andthearrowrepresentstheonsetcriteriawhichwasusedto
obtain Tc≈2.24K; (c) shows the normal state resistivity in
expanded scale and weak negative curvature visible at high
B. Physical properties of Rh9In4S4 temperatures.

Figure3 shows the temperature dependent resistiv-
ity of Rh9In4S4 for current flowing along the [1 0 0] 100 2 K)
direction. The resistivity decreases monotonically ol-100
m
wioirthanddecarecalseianrgstheamrppetrraatnusriet,iosnhotwoinzegromreetsailslticivibtyehbave-- 2 K) 80 mJ/
low T =2.25K, indicating a superconducting transition ol- T ( 0
ofthiscmaterial(Fig.3(a)). The residualresistivityratio J/m 60 C/p 0 T120 (K2)20
(RRR) (ρ /ρ ) is 1.2. Figure3(b) show the zero- m
300K 5.5K (
field-cooled (ZFC) and field-cooled (FC) magnetization T 40
data of Rh9In4S4 and clearly indicates over 95% shield- C/p Rh9In4S4
ing fraction at 1.8K. Also in the experimental data we 20 BCS
cansee aweaknegativecurvatureinresistivityathigher
temperatures as shown in Fig.3(c).
0
Figure4 shows the low temperature specific heat data 0 1 2 3
of Rh In S . A fit for C /T =γ+βT2 from 2.3 to 3.5K T (K)
9 4 4 p
for the normal state, as shown in the inset of Fig.4, FIG. 4. Low temperature Cp/T vs T of Rh9In4S4. Red
yielded the Sommerfeld coefficient, γ=34mJmol−1K−2 solid line represents the BCS calculation. The inset shows
(or ∼2mJmol-atomic−1K−2), β=3.22mJmol−1K−4. the Cp/T vs T2 graph which was used to obtain γ, β and δ
From the β value we estimate the Debye temperature, values. The blue solid line in the inset represents a fit with
Θ =217K, using the relation Θ =(12π2nR/(5β))1/3, Cp/T=γ+βT2.
D D
where n is the number of atoms per formula unit and R
is the universal gas constant.
the BCS weak-coupling limit of 1.43. The red colored
Withalargesuperconductingvolumefraction,thespe-
line if Fig.4 represents the BCS35,36 calculation for the
cific heat data are expected to reveal a clear anomaly
weak limit.
at T . We obtained the T ≈2.22K and the specific
c c The electron-phonon coupling constant λ can be
heat jump of ∆C=125mJmol−1K−1 by using an equal e−ph
estimated from the McMillan equation37 for the super-
entropy construction to the low temperature specific
conducting transitiontemperature, forphononmediated
heat data. Given that T ≈2.25K from the resistivity,
c superconductors,
T ≈2.24KfromthemagnetizationandT ≈2.22Kfrom
c c
the specific heat, we can state T ∼2.25K for Rh In S .
c 9 4 4
∆C/γTc=1.66 is an important measure of electron- T = ΘD exp − 1.04(1+λe-ph) (1)
phonon coupling strength, which is stronger here, than c 1.45 (cid:20) λ −µ∗(1+0.62λ )(cid:21)
e-ph e-ph
4
whereµ∗,theCoulombpseudopotential,hasavalueoften
between0.1 and0.2andusually is takenas0.1337. Sim-
ilar values of µ∗ have been used in other Rh-containing
chalcogenides7,21,23. Using ΘD=217K and Tc=2.22K a) oofnfsseett 2 10 2 H =1.8 T
we estimated λ =0.56. A difference of µ from the as- 2.5 onset
e-ph )
sumed value of 0.13 will give a different value of λ . m
e-ph c
For example, λe-ph=0.5 if µ=0.1 and λe-ph=0.71 if 2.0 HWdirty 1
µ=0.2. The value of λe-ph indicates the sample is anin- (
termediatecoupledsuperconductor37. Theratiobetween offset
T) 0
BasC38S-ξcoher/eln=c(e0l.e1n8g~tnhρane2d)/m(keanTfrmee∗)p.atUhscinagnbtheewvraitluteens H (1.5 2 102 onset 0.8 1.0 1.2
BCS 0 B c T (K)
of ρ =180µΩcm, T =2.24K, m∗=m (1 + λ ) and m)
0 c e e-ph
assuming electron density for typical metal, n≈1027 − 1.0 c1 T=0.9 K
1028m−3, we can calculate ξ /l≈20-200. This value
BCS ( offset

is much greater than one, indicating that Rh9In4S4 is 0.5 0 H // [1 0 0]
unambiguously in the dirty limit. 1.0 1.5 2.0 2.5 I [1 0 0]
H (T) I=0.3 mA
0.0
a) H [0 1 1] 1.8 T 1.2 T 0.8 T 0.2 T b) 2.5 H* and T* 2 102 onset
150 I [1 0 0] A A A )
) m m m A m H =1.8 T
(cm15000 01.2 mA.6 mA0.3 mA I=0.1 0.3 mA Am 1.0=I 0.3 I=0.1 1.0 mA 0.3 mA I=0.1 m H (T)12..50 2 102 onset (c01 T0*.8 1.0offset
0 ) T (K)
m T= 1 K
0.5 1.0 1.5 2.0 2.5 1.0 c
T (K) 1
( H*
offset
b) H //[0 1 1]
H [0 1 1] 0.5 0
150 I [1 0 0] 1 K 0.5 K 0.4 K 1.5 2.0 I [1 0 0]
m) H (T) I=0.3 mA
A A
( c15000 H* 1.2 m mA 0.3 mA I=0.1 m H* =0.3 mA =0.3 mA 00 0.5 1.0T (K) 1.5 2.0
9 I I
0. FIG. 6. Upper critical field Hc2 vs T of Rh9In4S4 for (a)
0 H k I and (b) H ⊥ I configurations with current along a-
1.0 1.5 2.0 2.5 axis. Lower and upper insets show the criteria which was
H (T) used to obtained the data points. Solid and open symbols
represent the data obtained by field scans and temperature
FIG. 5. Low temperature resistivity as a function of (a) scansrespectively. Thebluesolidlinein(a)indicatestheHW
temperature and (b) field for several applied currents for calculationsforthedirtylimit. In(b),lowerandupperinsets
H k[0 1 1] configuration where current flow along the [100] show theresistivity anomalies dueto thepeak effect and H∗
direction. and T∗ data represent bysolid and open black squares.
Insometype-II superconductors,asharpmaximumin
the temperature or field dependence of critical current datashowakinkinbetweenonsetandoffsetofthetran-
observed below H (T) is called the ”peak effect”39–43. sition and, for further increase of the field (e.g. 1.8T),
c2
Severalmechanismshavebeenproposedforthe explana- the resistivity drops to zero before increasing to a finite
tionofthepeakeffectsuchasmatchingmechanism44,ele- value. For higher currents these anomalies in resistiv-
mentarypinningbyweaklysuperconductingregions45,46, ity become more prominent and at higher fields, resis-
reductioninelasticmoduliofthefluxline47 andthesyn- tivity just show a dip before increasing and then gradu-
chronization of the flux line lattice43,48. However, the ally going to zero. The anomalies in the resistance are
underlying physics is not yet fully understood so far. seen more clearly in the resistivity vs. magnetic field
Figure5(a) shows the temperature dependence of resis- at fixed temperatures for the different values of mea-
tivity data for several applied fields and measuring cur- suring current (H k [0 1 1] configuration) as shown in
rents for an H k [0 1 1] configuration. For I=0.1mA, Fig.5(b). With the increase of field, the resistivity is
at field of ∼0.2T the transition is quite sharp. However essentially zero up to a critical field (H∗) and it starts
for moderate fields, such as 0.8 or 1.2T, the resistivity to increase. For further increase of field, the resistiv-
5
ity reaches maximum and goes to zero again before in- where ∆(T) is temperature dependence of the supercon-
creasing to the normal state. For larger current, H∗ de- ducting gap energy and all parameters are in cgs units.
creases and height of the peak increases. It should be Near T ,
c
emphasized that there were no anomalies in the transi-
tionobservedwhenthecurrentisparalleltothemagnetic ∆2(T →Tc) = 8π72ζT(c32)kB2 (1− TTc)
fierealdl.coSmimpiolaurnpdesaikncelffuedcitngdaNtab4h9a,sCbeeRenu2o5b0s–e52rv,eNdbinSes2e5v3-, λ−2(T →Tc) = c2~4ρπ02,cgs ∆22(TTc→kBTc)
V3Si54,ReCr55,Yb3Rh4Sn1356,57 andMgB258–60 . How- λ2(T →T ) = λ2GL (4)
ever we observed this effect at low current densities, j, c (1−T )
Tc
between 0.3-3Acm−2 in contrast with other supercon-
where ζ is the Riemann zeta function and
ducting materials (j ≫10Acm−2)50–52,55,56,59,60.
ζ(3)≈1.202. The expression in Eq.4 can be
TheH−T phasediagramsobtainedfromthelowtem-
reduced and converted to SI units as λ(T →
perature R vs. T and R vs. H measurements are pre-
T )=0.00064 ρ /(T (1−T/T ))=λ / (1−T/T ),
sented in Fig.6 for I=0.3mA. Figure6(a) and (b) show c 0 c c GL c
H k[1 0 0] and H k[0 1 1] configurations and the upper where ρ0 is inpSI units. Using ρ0=180×p10−8Ωm and
T =2.25K, we can obtained λ =0.00064 ρ /T ≈
and lower insets of each figure show the criteria used to c GL 0 c
determine Hc2 and Tc. Open and closed symbols rep- 5750˚A. Based on ξGL and λGL values, estipmated GL
resent data obtained from temperature scans and field parameter κ=λGL/ξGL is ∼61. Jump of the specific
scansrespectively. Asnotedabove,thepeakeffectisonly heat and slope of Hc2 at Tc can be calculated from the
detectable in the H k [0 1 1] configuration. Comparison Rutger’s relation65,66
of H in H k [1 0 0] and H k [0 1 1] configurations
c2 ∆C/T =(1/8πκ2)(dH /dT)2| (5)
indicates virtually isotropic Hc2 behavior. c c2 Tc
Foraoneband,typeIIsuperconductortheorbitalup-
where ∆C in units of ergcm−3K−1 and slope
per critical field is given by Helfand-Werthamer (HW)61
H in units of OeK−1. Using the molar vol-
theory and can be estimated from H =-AT dH /dT, c2
c2 c c2 ume, V =162.1cm3mol−1 we obtain the converted
whereA=0.73forcleanlimitand0.69forthedirtylimit. m
∆C=7710ergcm−3K−1. From the value of H slope
The slopeofthe curveinthe vicinity ofT (forthe offset c2
c near T , dH /dT=16900OeK−1, we obtained a simi-
criteria) is -1.69TK−1. Using this value, the calculated c c2
larly large κ value of 57. This considerablylarge κ value
µ H is2.78Tforthecleanlimitand2.62Tforthedirty
0 c2 indicates that Rh In S is an extreme type II supercon-
limit. The blue solid line in Fig.6(a) represents the cal- 9 4 4
ductor. A summary of the measured and derived su-
culated HW curve for the dirty limit (Ref.61 equation
perconducting state parameters for Rh In S is given in
24), and it shows a goodagreementwith the experimen- 9 4 4
Table.III
tal data.
Byusingbothnormalstateandsuperconductingstate
specific heat data, one can obtain the thermodynamic TABLEIII.Measuredandderivedsuperconductingandrele-
criticalfield, µ0Hc(T) as a function of temperature from vantnormal-state parameters for Rh9In4S4
equation2 Rh9In4S4 property Value
Tc (K) 2.25(2)
µ V H (T)2 Tc γ (mJmol−1K−2) 34.0(4)
0 m c = ∆S(T′)dT′ (2) β (mJmol−1K−4) 3.22(5)
2 Z
T ΘD (K) 217
in which ∆S(T) is the entropy difference between the ∆C (mJmol−1K−1) 125(4)
normal and superconducting states and Vm (16.2×10−5 ∆C/γTc 1.66(6)
m3 mol−1) is the molar volume. The calculated value of λe−ph 0.56
µ0Hc(T =0)is25mTforRh9In4S4anditismuchsmaller ρ0 (µΩcm) 180
than µ H (0)=2.62T as expected for type II supercon-
0 c2 Hc2(T =0) (T) (clean limit) 2.78
ductor. The value of µ H (0) is well below the Pauli
paramagnetic limit62,630 ocf2 µ Hp (0)=1.84T =4.1T, Hc2(T =0) (T) (dirtylimit) 2.62
0 c2 c Hp(T =0) (T) 4.1
suggesting an orbital pair-breaking mechanism. c2
We also can estimate the Ginzburg-Landau(GL) co- Hc(T =0) (mT) 25
herence length36, ξ ≈94˚A by using the relation ξBCS/l 20-200
GL
d(µ H (T ))/dT =-Φ /(2πξ2 T ), in which Φ is the ξGL (˚A) 94
0 c2 c 0 GL c 0
quantum flux and estimated d(µ0Hc2(Tc))/dT to be - λGL (˚A) 5750
1.69TK−1 near Tc. London penetration depth for the κ=λGL/ξGL 61
dirty limit can be written as64, κ (from Rutger’srelation) 57
4π2∆(T)
λ−2(T) = tanh(∆(T)/(2T)) (3)
(c2~ρ )
0,cgs
6
IV. CONCLUSIONS ACKNOWLEDGMENTS
We report the synthesis, crystal structure and charac- We would like to thank W. Straszheim, Z. Lin and
terization(suchas resistivity,magnetizationandspecific K. Sun for experimental assistance and A. Kreyssig,
heat) of superconducting Rh In S with a bulk super- R. Prozorov, V.G. Kogan, T. Kong, M. Kramer and
9 4 4
conducting transition of T ∼2.25K and large value of R.J. Cava (Princeton University) for useful discussions.
c
GL parameter κ ∼60. Rh In S is found to be a type Thisworkwassupportedbythe U.S.DepartmentofEn-
9 4 4
IIandintermediate-couplingsuperconductor. Thecalcu- ergy (DOE), Office of Science, Basic Energy Sciences,
latedvaluesfortheSommerfeldcoefficientandtheDebye Materials Science and Engineering Division. The re-
temperatureare34mJmol−1K−2and217Krespectively. search was performed at the Ames Laboratory, which
The temperature dependence of the specific heat shows is operated for the U.S. DOE by Iowa State University
a larger jump ∆C/γT =1.66 at T , than the BCS weak under contract No. DE-AC02-07CH11358. V.T. is par-
c c
coupling limit. The upper field critical shows a good tiallysupportedbyCriticalMaterialInstitute,anEnergy
agreementwith the HW theory. We have showna direct Innovation Hub funded by U.S. DOE, Office of Energy
evidenceofapeakeffectfromresistivityinRh In S sin- Efficiency and Renewal Energy, Advanced Manufactur-
9 4 4
gle crystals as a function of both temperature and mag- ing Office.
neticfield. Furtherstudiesofsuperconductingproperties † Current address: Department of Chemistry, Prince-
and peak effect of this material will be useful to under- ton University, Princeton, NJ 08544, USA.
stand the nature of their mixed state and pinning prop-
erties.
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