Anisotropic $H_{c2}$, thermodynamic and transport measurements, and pressure dependence of $T_{c}$ in K$_{2}$Cr$_{3}$As$_{3}$ single crystals

1.7 MB·English

by  Tai Kong

Anisotropic H , thermodynamic and transport measurements, and pressure
c2
dependence of T in K Cr As single crystals
c 2 3 3
Tai Kong, Sergey L. Bud’ko, and Paul C. Canfield
AmesLaboratory,U.S.DOE,IowaandDepartmentofPhysicsandAstronomy,IowaStateUniversity,Ames,Iowa50011,USA
We present a detailed study of single crystalline K Cr As and analyze its thermodynamic and
2 3 3
transport properties, anisotropic H (T), and initial pressure-dependence of T . In zero-field, the
c2 c
temperature-dependent resistivity is metallic. Deviation from a linear temperature-dependence
is evident below 100 K and a T3-dependence is roughly followed from just above T (∼10 K)
c
to ∼ 40 K. Anisotropic H (T) data were measured up to 140 kOe with field applied along and
c2
5 perpendicular to the rod-like crystals. For the applied field perpendicular to the rod, H (T) is
c2
1 linear with a slope ∼-70 kOe/K. For field applied along the rod, the slope is about -120 kOe/K
0 below 70kOe. Above70 kOe, the magnitude of the slope decreases to∼-70 kOe/K.The electronic
2 specific heat coefficient, γ, just above T , is 73 mJ/mol K2; the Debye temperature, Θ , is
c D

n 220 K. The specific heat jump at the superconducting transition ∆C ∼ 2.2 γTc. Finally, for
a hydrostaticpressuresupto∼7kbar,Tc decreasesunderpressurelinearlyatarateof-0.034K/kbar.
J

2 PACS numbers: 74.70.Xa; 74.25.Op; 74.25.Bt; 74.62.Fj
2

] K2Cr3As3 has been recently discovered as a new su- side crucible and an empty (catch) crucible. The crys-
n perconducting material with a T of 6.1 K1. Hav- tals obtained are rod-like (Fig. 1(b)) and malleable. A
o c
ing a structure that contains (Cr As )2− chains, it rough powder x-ray diffraction pattern was collected on
c 3 3
- quickly arouses interest as a potentially new, quasi-one- ground/deformed crystals using a Rigaku Miniflex unit
r dimensional(Q1D)superconductor. Relatedcompounds, located in a N glove box. The data, along with a fit
p 2
u Rb2Cr3As3 and Cs2Cr3As3, with Tc values of about 4.8 to the crystallographic data given in Ref. 1 are shown
s Kand2.2Krespectivelywerereportedsoonafterthedis- in Fig. 1(d) and are consistent with the single crystals
t. covery of K2Cr3As32,3. Band structure calculation was adopting the hexagonal, a = 9.983 ˚A, c = 4.230 ˚A unit
a alsoconductedandcomparedwithexperimentalresults4. cell. Given the unit cell dimensions and single crystal
m
In the initial report1, data were acquired primarily on morphology, we identify the rod direction as being along
- polycrystalline samples of K Cr As . For Q1D super- the crystallographic c-axis.
d 2 3 3
conductors,itisbelievedthatwithmagneticfieldapplied Resistance was measured using a standard 4-probe
n
o along the chain, the upper critical field, Hc2, should be technique. DuPont 4929N silver paint was used to at-
c muchhigherthanthatwhenthefieldisalongotherdirec- tach platinum wires onto the sample in a N glove box.
2
[ tionsduetominimizedorbitalpairbreaking. Experimen- Electriccurrentwasappliedalongtherodforanisotropic

2 tally,thiswasobservedforQ1DsystemslikeLi0.9Mo6O17 Hc2 measurements (Fig. 1(c)). Long, straight samples
v and(TMTSF)ClO45,6. Inthispaper,wepresentdetailed were used and supported by flat plastic pads for all re-
4 anisotropic H (T) data via resistance measurements on sistivity measurements to avoid potential torque that
c2
5 K Cr As single crystals. In addition, with the recent could deform the crystals and thus change their align-
2 3 3
5 discovery of iso-structural compound, Rb Cr As , with ment. Resistivity was estimated assuming the sample
2 3 3
1
a larger unit cell and a lower T value, it is interesting to has a cylindrical shape. The absolute value of the re-
0 c
study the pressure-dependence of T of K Cr As . Re- sistivity is therefore only accurate to within a factor of
. c 2 3 3
1 sultsfromlow-fielddcmagnetizationmeasurementswith three. The temperature and field-dependent resistance
0
pressures up to 7 kbar will be presented. wasmeasuredinaQuantumDesign(QD)PhysicalProp-
5
K Cr As single crystals were grown using a high- erty Measurement System, PPMS-14 (T = 1.8-305 K, H
1 2 3 3
: temperature solution growth method7. A schematic = 0-140 kOe). Specific heat data were measured using
v drawing of the Matryoshka-like ampoule assembly for a QD PPMS via relaxation method. A 3He option was
i
X crystal synthesis is shown in Fig. 1(a). Elemental K, Cr, utilized to obtain specific heat data down to 0.4 K. Spe-
and As (in bulk/lump form) were packed in an alumina cific heat data were measured on a ”raft” assembled out
r
a crucible following the ratio listed in Ref. 1 (K:Cr:As = of several single crystals. Despite the fact that samples’
6:1:7). Crucibles and starting material were then welded shape and arrangement was not ideal for such measure-
into a tantalum tube and sealed in a silica ampoule un- ments,thecouplingconstantwashigh,between96%and
der partial argon atmosphere. To avoid possible explo- 100%.
sion due to the high vapor pressure of the un-reacted el- Thepressure-dependenceofthesuperconductingtran-
ements,thewholeampoulewasslowlyheatedupto1000 sition temperature, T , was determined via low-field (20
c
◦C over 2 days. It was then cooled down over ∼ 100 hrs Oe), zero-field-cooled (ZFC), dc magnetization measure-
to 700 ◦C, at which temperature the single crystals and ments in a QD Magnetic Property Measurement System
theremainingliquidwereseparatedinacentrifugebythe (MPMS) using a commercial, HMD, Be-Cu piston cylin-
alumina strainer that was placed in between the growth derpressurecell8. Daphneoil7373wasusedasthepres-
2
suremediumandPbwasusedasthemanometer9. Since temperatureswillrequireextremelyhighmagneticfields.
the samples are very air sensitive, exposure to air was In the normal state, despite a relatively large RRR
limited as much as possible to avoid oxidation. value, virtually no magnetoresistance was observed. The
right inset of Fig. 2 shows the normalized resistance as a
function of applied field for both transverse (H ⊥I) and
(a ) (b ) longitudinal (H (cid:107) I) directions of applied field. Right
(b )
above the T , the resistance stays close to constant up
s ilic a tu b e c
to 140 kOe. Given this null response, an upper limit
ta n ta lu m
tu b e of 2% (at 140 kOe) can be set on the low-temperature
magnetoresistance.
q u a rtz a lu m in a c ru c ib le s
w o o l a n d s tra in e r
m e lt o f e le m e n ts (c ) VI++ 1200 1.0
I+ V + V - I- H VI-- 1000 0 K)00..68 RK R2CRr3 ~A s530
(d ) (4(cid:1)
1 2 0 0 800 ))/0.4
sity (cps) 48 00 00 K 2C r3A s 3 dc aa ltcau la tio n mW ( cm)(cid:1) 460000 (-(0(cid:1)(cid:1)00..02 0 20000T 3 (K430)000 60000 e)1.1
Inten 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 200 ()/(0 OH(cid:1)(cid:1)01..90 71.05 KK
2 (cid:2)(cid:1)(d e g ) 0 40 80 120
H (kO e )
0
0 50 100 150 200 250 300
FIG. 1. (Color online) (a) A schematic drawing of the am-
T (K )
poule assembly for the material synthesis. (b) Typical habit
ofthesinglecrystalsofK Cr As onamillimetergridpaper.
2 3 3
(c) The contacts arrangements and external field direction FIG. 2. (Color online) Temperature-dependent resistivity of
for the resistance measurements. (d) X-ray diffraction data K Cr As . The left inset shows the normalized resistances
2 3 3
onground/deformedcrystals. Theblackcrossesrepresentthe versusT3 below40Kfor4differentsamples. Therightinset
experimentaldataandtheredsolidlinerepresentsthecalcu- shows the magnetoresistance measured at 7.5 K and 10 K.
lation based on the crystallographic information. For details Solid and hollow symbols represent transverse and longitudi-
of the crystal structure, readers are directed to Ref. 1. nal magnetoresistance respectively.
The temperature-dependence of the resistivity of Fig.3(a)and3(b)showthetemperature-dependentre-
K Cr As is metallic as shown in Fig. 2. The residual sistance, R(T), measured under different magnetic field
2 3 3
resistance ratio (RRR) is about 50, a factor of 5 better for H (cid:107) rod and H ⊥ rod respectively. Fig. 3(c) shows
tan the RRR∼10 found for the polycrystalline data1. A the anisotropic H (T) data for K Cr As from several
c2 2 3 3
clear, sharp, transition at 6.1 K indicates the supercon- samples. The superconducting transition is very sharp
ducting transition. At room-temperature, the resistivity in our resistivity measurements. The inset to Fig. 3(c)
isofthesameorderofmagnitudeasthereportedvalue1. shows that, at over 125 kOe, the onset and offset of the
However, in contrast to the reported linear temperature- transition differ by less than 0.25 K as opposed to an
dependence from 7 to 300 K in Ref. 1, we see a clear over0.6Kwidthat80kOeforpolycrystallinedata1. An
deviationfromlinearitybelow∼100K.Forthefoursam- offset criterion10 was used to determine T (see the in-
c
ples we have measured, we get slopes of 3.0, 2.8, 3.1 and set of Fig. 3(c)). For field applied perpendicular to the
3.1 from a log(ρ-ρ ) vs. logT plot between 10 and 40 K. rod,theT decreasesalmostlinearlywithincreasingmag-
0 c
ThereforeintheleftinsetofFig.2,weplottheresistance netic field. The slope is ∼ -70 kOe/K. For field applied
datafromseveralsamplesnormalizedtotheirvalueat40 along the rod, the initial slope is roughly -120 kOe/K,
KasafunctionofT3. ItisclearthataT3 powerlawde- and above 70 kOe the slope is close to -70 kOe/K, which
scribes these data well over the temperature region that is similar to that when field is applied perpendicular to
is shown. Slight deviation below 10 K might due to the the rod. Different batches of samples as well as field-
proximity to the superconducting transition. Although sweep data at fixed temperature give consistent results.
we did not see a temperature region where Fermi liquid In Fig. 3(c), data from Ref. 1 are plotted as blue solid
behavior is dominant, this could due to the fact that the diamonds. It is close to what we obtained for field per-
measurement temperature is not low enough comparing pendiculartotherodandtheslopeisconsistentwithour
with its Debye temperature. As will be discussed below, current results.
due to the extremely large H values associated with From one-band BCS theory, for a s-wave, isotropic
c2
thiscompound,measuringnormalstateresistivitytolow material, in the clean limit, the orbital Horb = -
c2
3
0.73|dH /dT | T 11. In our case, for field perpen- K2 and the Debye temperature, Θ , derived from β, is
c2 Tc c D
dicular to the rod, Horb ∼ 312 kOe. The Pauli limit around 220 K. These data are consistent with recently
c2
for a simple BCS superconductor is Hp = 1.84T = 110 reported values1. At the superconducting transition, the
c
kOe. The H of real systems will be influenced by both specificheatjumpisroughly2.2γT . Thisislargerthan
c2 c
Horb and Hp. The Maki parameter12 that describes thesimples-waveBCSpredictionandcomparabletothe
c2
the relative importance of the two critical field limits, value obtained in Ref. 1. Possibly, strong coupling is
√
α = 2Horb/Hp, is equal to 4. This suggests that at involved14. Below 1.5 K, we observe a clear upturn in
c2
low-temperature, the H might be Pauli limited. With C/T. Assuming that the normal state values of γ and β
c2
the current data up to 140 kOe that exceeds the one- stay constant below T , this upturn exacerbates the dif-
c
band BCS estimated Pauli limit, we see no clear sign of ficulty of having entropy conserved, which was already
saturation of H . Note that, with multi-band as well hinted at in the previously reported data down to 2 K1.
c2
as varying coupling strength, the Pauli limit can be dif- Additional, non-superconducting contributions, such as
ferent from one-band BCS prediction. For example, in impuritiesornuclearSchottkyanomaly,mayberesponsi-
many Fe-based superconductors, Hp values are signifi- bleforthislow-temperaturerise. Butwhateveritsorigin
cantly enhanced13. is, it makes fitting of the data to specific models prob-
lematic.

0.008
0.012 H || ro d H ^ ro d
0.010 0.006
4 0 0

0.008
0.004 3
)0.006 )
WR (000...000000024 = 140 kOeH H = 0 Oe WR (00..000002 = 140 kOeH H = 0 Oe 2ol K)23 00 00 g/CTe12 D C ~ 2 .2 gT c
3.5 4.0 4.5 5.0 5.5 6.0 6.5 3.5 4.0 4.5 5.0 5.5 6.0 6.5 /m 00 2 4 6 8 10
J
(a ) 3 0 0 T (K ) T (K ) (b ) (m T (K )
2 5 0 H ^ ro d K 2C r3A s 3 C/T1 0 0
H || ro d
J . K . B a o e t a l.
2 0 0 0
0 2 4 6 8 1 0
e)1 5 0 0.012 H = 125264 O e T (K )
H (kO1 0 0 W ()R00..000048 H || rod FIG. 4. (Color online) C/T plotted as a function of T down
to 0.4 K. Inset shows the C /γT as a function of T. The
e
5 0 0.000 electronic part of the specific heat, C , was obtained by sub-
e
0 2 4T (K ) 6 8 tracting βT3 from the total specific heat.
0
(c ) 0 1 2 3 4 5 6
T (K )
Atambientpressure,thenormalstatedcmagneticsus-
ceptibility (χ = M/H) is ∼ 0.9×10−3 emu/mol and de-
FIG. 3. (Color online) (a)/(b) R(T) data measured for H (cid:107) creases by more than 30% from 7 K to 300 K (Fig. 5).
rod/H ⊥ rod from 0 Oe up to 140 kOe in 20 uniform field
If we fit these data to a Currie-Weiss law, we find a
steps (∆H = 7368.4 Oe). (c) Anisotropic Hc2 of K2Cr3As3. temperature-independent susceptibility χ ∼ 0.7×10−3
Black and red symbols represent data for H (cid:107) rod and H ⊥ 0
emu/mol, a small effective moment of 0.36 µ /f.u. (or
rod. Blue points are from Ref. 1. Solid and open symbols B
0.21µ /Cr)andaCurie-Weisstemperature, Θ∼-40K.
show data from two different batches of samples. Triangles B
Atthispointintime,itisnotclearifsuchalocal-moment
aredatafromfield-sweepatfixedtemperatures. Squaresand
circles are data from temperature sweeps at fixed field. The fitisappropriateorintrinsicforthismaterial. Giventhat
insetshowsatypicalsuperconductingtransitionmeasuredat γ = 9 mJ/mol-atom K2 is relatively high, it is appropri-
125264 Oe with red solid lines and arrow indicating the cri- ate to contrast it with the magnetic susceptibility. As-
teriafordeterminingthetransitiontemperature(seemorein suming spin = 1/2, the estimated Wilson ratio15, R ,
W
text). is in a range of 0.9-1.1 by taking the low-temperature
magnetic susceptibility value. If we consider the Curie
The specific heat data from K Cr As are shown in tail as a result of impurity contribution and thus take
2 3 3
Fig. 4. A clear jump in the specific heat at around 6 the value of temperature-independent χ0, RW is about
K corresponds to the superconducting transition. In the 0.7. These values are close to what one would expect for
normal state, C = γT + βT3 fits the data quite well. a Fermi-liquid system (RW =1).
In the range of 7-10 K, we obtained a γ ∼ 73 mJ/mol Zero-field-cooled dc magnetization data are shown in
4
the right inset of Fig. 6. The superconducting transi-
tionappearssharplyat6.1K,consistentwithbothresis-
tance and specific heat measurements. To avoid oxida-
0 .0
tion, whichcouldaffectbothsamplemassandsupercon-
6 .1
ducting volume fraction, the sample mass was measured -0 .4
(cid:2)(cid:1)
in a glove box and exposure to air was minimized. p
4
At 2 K, the low-field M(H) data deviate from linear K 2C r3A s 3 -0 .8 H = 50 O e
field-dependence at around 70 Oe (Fig. 5, inset). The )6 .0 0 2 4 6 8
minimum in magnetization appears at around 400 Oe. (Kc ZH F=C20 O e T (K )
TiFnragokmHincgt1h/HeHcs1cp2=e=ci7fil0nc(Ohκee)a/at2nκjdu2,mHtpch2ea∼Gt TLHccpo2urabsria=nmg3et1the2erk,ROκu,etigsaen∼rds1u0r0es--. T5 .9 M (a.u.) P P b
lation: ∆C/Tc =(1/8πκ2)(dHc2/dT)2 |Tc16, weobtaina 5 6T (K ) 7 8
similarκvalueof116. Thishighvalueofκsuggeststhat
0 2 4 6 8
K Cr As is deep in the type II regime.
2 3 3
P (k b a r)
FIG. 6. (Color online) Pressure-dependence of T . Dotted
c
line is a guide for the eye. The left inset shows the raw data
0 .0 0 1 0 H = 5 0 k O e with Pb serving as a manometer. The right inset shows the
zero-field-cooled magnetization data under ambient pressure
measured at 50 Oe.
0 .0 0 0 8
ol) 0
/m0 .0 0 0 6 -100 T = 2 K
u
(em0 .0 0 0 4 u/mol)-200 tdheepernadnegneceofb1e0lo-4w0 1K0.0WKhearnedasrothueghdlyiffefroellnocwess bTe3twoeveenr
M/H0 .0 0 0 2 (emM--430000 K C r A s tphoertsianrgeleeacsriylystaelxlipnleainaendd bpyolygrcaryins-tbaolluinnedasraympscleatttrearinnsg-
0 400 800 1200 1600 2 3 3
and potential resistive anisotropies, the rather clear T3
H (O e )
0 .0 0 0 0 power law that we observe will require more experimen-
0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0
tal and theoretical investigation. Despite the fact that
T (K )
the temperature-dependence is different, if the RRR val-
ues reflect the intrinsic quality of the samples, and are
FIG. 5. The magnetic susceptibility measured at 50 kOe on not due to grain boundary scattering, the independence
a randomly oriented collection of single crystals. Inset shows of T on the value of RRR, or impurity scattering, sug-
c
the magnetization isotherm measured at 2 K up to 1500 Oe.
gests a conventional mechanism of its superconductivity.
Anisotropic H (T) data up to 140 kOe were obtained
c2
Thepressure-dependenceofT isplottedinFig.6. The from resistivity measurements. Up to 140 kOe, for field
c
superconducting transition of Pb was used to determine appliedperpendiculartotherod, H (T)islinearwitha
c2
the pressure within the pressure cell9. As shown in the slope of -70 kOe/K. For field along the rod, dH /dT |
c2 Tc
leftinsetofFig.6,bothsuperconductingtransitionsfrom is about -120 kOe/K. Above 70 kOe, the the slope de-
the Pb and the sample are clear. Up to 7 kbar, the creases to around -70 kOe/K. The T as well as the
c
T value for K Cr As decreases linearly with increas- slope of H is close to previously reported data1. The
c 2 3 3 c2
ing pressure at a rate of -0.034 K/kbar. Given that the anisotropy in H is not as large as one would generally
c2
larger-unit-celled Rb Cr As undergoes a superconduct- expect for a Q1D superconductor. Virtually zero mag-
2 3 3
ing transition at a slightly lower temperature, 4.8 K, the netoresistance was observed at temperatures right above
effects of chemical and physical pressure are clearly not the T . The electronic specific heat, γ, is 73 mJ/mol
c
equivalent in this material. K2 or 9 mJ/mol-atom K2. Although this is a relatively
In conclusion, we grew single crystals of K Cr As us- large value, the equally enhanced magnetic susceptibil-
2 3 3
ing a high-temperature solution growth method. Being ity leads to a Wilson ratio that is close to 1 and sug-
able to decant the molten solution at high-temperature gests Fermi-liquid-like properties. At ambient pressure,
allows us to get relatively large, free standing, high- H is close to 70 Oe, which result in a GL parameter
c1
quality single crystals, which also enables us to perform that is ∼100, taking 312 kOe as the estimated H . For
c2
allofourmeasurementsonsinglecrystalsortheirarrays. pressures up to 7 kbar, the superconducting transition
Incontrasttopreviouslyreported,lineartemperaturede- temperature, T , decreases linearly with a rate of -0.034
c
pendent resistivity from 300 K down to 7 K, resistivity K/kbar. ComparingtothenewlydiscoveredRb Cr As ,
2 3 3
of single crystal, with a RRR of 50 (RRR∼10 for poly- it seems to suggest that physical pressure and chemical
crystalline samples1), deviates from linear temperature- pressurehavedifferenteffectonthesuperconductivityin
5
these compounds. ACKNOWLEDGEMENTS
We would like to thank U. S. Kaluarachchi, A. E.
B¨ohmer, D. K. Finnemore, V. G. Kogan and V. Taufour
for useful discussions. This work was supported by the
Despite the fact that K Cr As can be considered to U.S.DepartmentofEnergy(DOE),OfficeofScience,Ba-
2 3 3
be close to Q1D in a crystallographic sense, the ”small” sic Energy Sciences, Materials Science and Engineering
anisotropyinH appearstosuggestarather3Dnature. Division. TheresearchwasperformedattheAmesLabo-
c2
In addition, the exotic pairing symmetry requires more ratory,whichisoperatedfortheU.S.DOEbyIowaState
detailed study. University under contract NO. DE-AC02-07CH11358.
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