Anisotropic thermodynamic and transport properties of single crystalline CaKFe 4 As 4
W. R. Meier, T. Kong, U. S. Kaluarachchi, V. Taufour, N. H. Jo, G. Drachuck, A. E. Böhmer, S. M. Saunders, A. Sapkota, A. Kreyssig, M. A. Tanatar, R. Prozorov, A. I. Goldman, Fedor F. Balakirev, Alex Gurevich, S. L. Bud'ko, P. C. Canfield
AAnisotropic thermodynamic and transport properties of single crystalline CaKFe As W. R. Meier,
1, 2
T. Kong,
1, 2
U. S. Kaluarachchi,
1, 2
V. Taufour, N. H. Jo,
1, 2
G. Drachuck,
1, 2
A.E. B¨ohmer, S. M. Saunders,
1, 2
A. Sapkota,
1, 2
A. Kreyssig,
1, 2
M. A. Tanatar,
1, 2
R. Prozorov,
1, 2
A. I. Goldman,
1, 2
Fedor F. Balakirev, Alex Gurevich, S. L. Bud’ko,
1, 2 and P. C. Canfield
1, 2 Ames Laboratory US DOE, Iowa State University, Ames, Iowa 50011, USA Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA National High Magnetic Field Laboratory, Los Alamos National Laboratory,MS-E536, Los Alamos, New Mexico 87545, USA Department of Physics, Old Dominion University, Norfolk, Virginia 23529, USA (Dated: July 14, 2016)Single crystalline, single phase CaKFe As has been grown out of a high temperature, quaternarymelt. Temperature dependent measurements of x-ray diffraction, anisotropic electrical resistivity,elastoresistivity, thermoelectric power, Hall effect, magnetization and specific heat, combined withfield dependent measurements of electrical resistivity and field and pressure dependent measurementsof magnetization indicate that CaKFe As is an ordered, stoichiometric, Fe-based superconductorwith a superconducting critical temperature, T c = 35.0 ± ≤ T ≤
300 K. All of these thermodynamicand transport data reveal striking similarities to that found for optimally- or slightly over-doped(Ba − x K x )Fe As , suggesting that stoichiometric CaKFe As is intrinsically close to what is referredto as ”optimal-doped” on a generalized, Fe-based superconductor, phase diagram. The anisotropicsuperconducting upper critical field, H c ( T ), of CaKFe As was determined up to 630 kOe. Theanisotropy parameter γ ( T ) = H ⊥ c /H (cid:107) c , for H applied perpendicular and parallel to the c-axis,decreases from (cid:39) . T c to (cid:39) . dH (cid:107) c /dT (cid:39) −
44 kOe/K and dH ⊥ c /dT (cid:39) −
109 kOe/Kat T c yield an electron mass anisotropy of m ⊥ /m (cid:107) (cid:39) / ξ (cid:107) (0) (cid:39) . ξ ⊥ (0) (cid:39) . H ⊥ c (0) can be extrapolated to (cid:39)
920 kOe,well above the BCS paramagnetic limit.
PACS numbers: 74.70.Xa; 74.25.Bt; 74.25F-; 74.62Fj
I. INTRODUCTION
BaFe As has become one of the archetypical exam-ples of Fe-based superconductivity . It was the first ofthe Ae Fe As (122) structures ( Ae = Ba, Sr, Ca) foundto support superconductivity (with K-substitution forBa) and was almost immediately studied in single crys-talline form . With the discovery that cobalt substitu-tion on the iron site could stabilize superconductivity ,extensive studies of Ba(Fe − x TM x ) As ( TM = transi-tion metal) series revealed the basic relations betweenthe structural, magnetic and electronic degrees of free-dom in these compounds as substitutions progressed fromunder-doped (rising T c , often coexisting with antiferro-magnetic (AFM) order), to optimally-doped (maximal T c near the disappearance of the AFM transition), to over-doped (dropping T c in paramagnetic state). SrFe As was also studied, albeit to a lesser degree for selectedsubstitutions on the Ae as well as TM sites. CaFe As , on the other hand, has proven more dif-ficult to modify with substitution. CaFe As is thelightest member of the Ae Fe As series and was dis-covered in single crystalline form only after the discov-ery of Fe-based superconductivity. CaFe As manifestsa strongly coupled, first order, magnetic and structuralphase transition and pressure studies of CaFe As ledto the discovery of a collapsed tetragonal (cT) phase for p > and a much wider appreciation ofthe proximity and influence of the cT phase in all ofthe Ae Fe As compounds. Systematic studies of tran-sition metal substitution in the Ca(Fe − x TM x ) As se-ries were only possible once the extreme strain and pres-sure sensitivity of the CaFe As host were appreciatedand it was realized that internal strain had to be con-trolled by careful post-growth annealing of single crys-talline samples . The incredible richness and sensi-tivity of the CaFe As system is attributed to the Ca-ionsbeing at or near the edge of the steric tolerance of theun-collapsed 122 structure.Recently, another consequence of the size of the Ca-ions has been discovered. Iyo et al. have found that afamily of ordered Ca A Fe As (1144) compounds can beformed for A = K, Rb, Cs where the key to the formationis the difference in ionic size between the Ca and the A ion. This family is not a (Ca − x A x )Fe As solid-solution,where the Ca and A ions randomly occupy a single crys-tallographic site, but rather is a distinct, quaternary,line compound in which the Ca and A sites form alter-nating planes along the crystallographic c -axis, separatedby FeAs slabs . In essence, the Ca A Fe As structureis identical to the CaFe As structure, just with layerby layer segregation of the Ca and A ions. The 1144structure was also found for Sr A Fe As ( A = Rb, Cs).Solid-solutions of Ca (Sr) 122 structures were found for a r X i v : . [ c ond - m a t . s up r- c on ] J u l A = Na (Na, K) respectively as well as for all attemptedBa-based systems. Superconducting transition temper-atures ( T c ) were inferred from both resistance and mag-netization data with T c values ranging between 31 and37 K. These T c -values are among the highest reportedfor bulk, fully ordered, stoichiometric Fe-based supercon-ductors. As such, CaKFe As offers a unique opportunityto study relatively high transition temperature, Fe-basedsuperconductivity in a highly ordered compound, at am-bient pressure.In their discovery paper, Iyo et al. synthesized andstudied polycrystalline samples. A vital next step is togrow and study single crystalline samples so the details ofthe intrinsic properties, including anisotropies, can be ex-amined. In this paper we outline experimental details forthe growth of single phase, single crystalline CaKFe As and present structural, thermodynamic, and transportdata as a function of temperature, field, and pressure.We find that CaKFe As is a rare example of an orderedFe-based superconductor that appears to be intrinsicallynear optimally- or slightly over-doped and has a T c valueof 35.0 ± II. CRYSTAL GROWTH AND EXPERIMENTALMETHODS
CaKFe As single crystals were grown by high temper-ature solution growth out of FeAs flux in a manner simi-lar to CaFe As and K Cr As . Lump, elemental K(Alfa Aesar 99.95%) and distilled Ca pieces (Ames Lab-oratory, Material Preparation Center (MPC) > . As . precursor in a ratio of K : Ca : Fe . As . =1.2 : 0.8 : 20, with a total mass of roughly two grams,in a fritted, alumina crucible set (Canfield Crucible Set,or CCS). The precursor was synthesized from As (AlfaAesar 99.9999%) and Fe (Alfa Aesar 99.9+%) powdersin a 1 : 1.05 atomic ratio in an argon filled fused-silicaampoule. The filled CCS was welded into a Ta cruciblewhich itself was sealed into a fused-silica ampoule . Thegrowth ampoule was heated over 1 hour to 650 ° C, heldfor 3 hours then heated over 2 hours to 1180 ° C, held atthis temperature for 5 hours, cooled to 1050 ° C over 2hours, and then slowly cooled from 1050 ° C to 930 ° C over30 hours. When this final temperature was reached, theassembly was removed from the furnace, inverted into acentrifuge and spun to expedite the separation of crystalsfrom the liquid flux .Single crystalline CaKFe As grows as mirror-like,metallic, micaceous plates of 0.1-0.2 mm thickness whichcan, in some cases, be limited in area by the inner di-ameter of the crucible (see inset to Fig. 3, below). Thecrystallographic c -axis is perpendicular to the plate sur-face. Single crystals of CaKFe As are not particularlyair sensitive and can remain in air for weeks without anynoticeable degradation of their appearance or physicalproperties. CaFe As and KFe As can be second phases in suchgrowths and care had to be taken in optimizing our fi-nal growth protocol as well as in selecting our crystalsto be sure that we have little or no amount of either ofthese phases. The ∼
170 K phase transition of CaFe As is most apparent in temperature dependent resistancemeasurements and the low temperature superconduct-ing phase transition in KFe As ( T c = 3.8 K ), as seenin the low field magnetization measurement, is the mostsensitive way to detect its presence. All samples usedin these studies were screened for both impurity phases.A more detailed discussion of how crystal growth wasoptimized to the current protocol, in part by minimiz-ing these diagnostic signatures of second phases, will bepresented in a separate paper.Single crystals of CaKFe As are soft, malleable, andnot amenable to grinding for powder x-ray diffractionmeasurements. In this sense, CaKFe As is mechanicallymore similar to CaFe As than to BaFe As . Diffrac-tion measurements on a single crystal were carried out in-house using a Rigaku MiniFlex II powder diffractometerin a Bragg-Brentano geometry with a Cu K α source anda graphite monochromator in front of the detector. Singlecrystal high-energy x-ray diffraction measurements weremade at station 6-ID-D at the Advanced Photon Source(APS) using an x-ray wavelength of λ = 0.123589 ˚A anda beam size of 100 × µ m . The synchrotron measure-ments were performed on a 0.5 × × sampleusing a He, closed-cycle, refrigerator. Three Be domeswere placed over the sample and evacuated with the mid-dle one functioning as heat shield, and a small amountof He gas was added to the inner dome to facilitate ther-mal coupling. The cryostat was mounted to the samplestage of a 6-circle diffractometer, and a MAR345 imageplate was positioned 1.487 m behind the sample to mea-sure the diffracted x-rays transmitted through the sam-ple spanning a scattering angle of | θ | ≤ ° . Datawere taken by recording an image while tilting the sam-ple along two rocking angles perpendicular to the inci-dent x-ray beam . ( hk
0) and ( h (cid:96) ) reciprocal planeswere recorded for temperatures from 300 K down to 6 K.Temperature and field dependent magnetization, re-sistance and specific heat measurements were carried outusing Quantum Design (QD), Magnetic Property Mea-surement Systems (MPMS) and Physical Property Mea-surement Systems (PPMS). Temperature dependent spe-cific heat measurements taken for H (cid:107) c in applied mag-netic field resulted in significant torque on the thin, plate-like samples. Even with care, the calorimeter platformrotated by (cid:46) ° as a result of measurements in appliedfield up to 140 kOe, and in some cases there was a loss ofsome sample mass due to exfoliation. As a result, specificheat data measured in applied fields are shown normal-ized to the zero-field data in the normal state. Hall resis-tivity data were collected using the AC transport optionof a QD PPMS in a four-wire geometry with switchingthe polarity of the magnetic field H (cid:107) c to remove anymagnetoresistive components due to misalignment of thevoltage contacts. Thermoelectric power (TEP) measure-ments were performed using a DC, alternating tempera-ture gradient technique with the temperature-field en-vironment provided by a QD PPMS unit.Optical imaging of the magnetic flux distributionwas performed in a He flow - type cryostat by usingthe magneto-optical Faraday effect. In the experimenta transparent bismuth-doped iron-garnet ferrimagnetic“indicator” film with in-plane magnetization is placeddirectly on top of the sample. In the images, brightnessis proportional to the value of B z ( (cid:126)r ) with black level setat B z ( (cid:126)r ) = 0 and the colors are related to the absoluteorientation of B z ( (cid:126)r ): green for out of page and yellowfor into the page directions for our setup. More detailson the technique and magneto-optical imaging of otherFe-based superconductors can be found elsewhere .The pressure dependence of T c was determined by mea-surements of pressure dependent magnetization. Data upto 1.2 GPa were taken in a commercial, piston-cylinder,HMD cell using Daphne 7373 as pressure medium andPb as a manometer . Data for p < using Daphne 7474 as pres-sure medium and utilizing ruby fluorescence at 77 K asa manometer. For both pressure cells, the temperature-field environment was provided by a QD MPMS unit.The samples for anisotropic resistivity measurementswere cleaved from larger crystals with sides along (cid:104) (cid:105) directions using a razor blade. Samples used forinter-plane ( I (cid:107) c ) measurements typically had dimen-sions of 0.5 × × ( a × b × c ). The samplesfor in-plane ( I ⊥ c ) measurements were typically of1.5 × × size. Contacts for standard fourprobe, in-plane resistivity measurements were solderedusing Sn . For inter-plane resistivity measurementswe used two-probe measurements, relying on the negligi-ble contact resistance. The top and bottom surfaces ofthe samples were covered with Sn solder and 50 µ msilver wires were attached to enable measurements in afour-probe configuration. Soldering produced contactswith typical resistances in the 10 µ Ω range. Inter-planeresistivity was measured using a two-probe techniquewith currents in 1 to 10 mA range (depending on sampleresistance which is typically 1 mΩ). A four-probe schemewas used to measure the sample resistance, R s , and con-tact resistance, R c , in series. Taking into account that R s (cid:29) R c , contact resistance represents a minor correc-tion of the order of 1 to 5%. This can be directly seen forour samples for temperatures below the superconducting T c , where R s = 0 and the measured resistance repre-sents R c . The details of the measurement procedurecan be found in Ref. 33. H c ( T ) was determined via magnetoresistance mea-surements with I ⊥ c . Both DuPont 4929N silver paintand Epotek-H20E silver epoxy were used to attach con-tact leads onto the samples (Pt for measurements staticfield measurements and twisted copper wires for pulsedfield measurements). For static fields below 140 kOe,resistance was measured using a QD PPMS-14 ( T = 1.8- A s ( 0 0 (cid:1) )F e A sF e A s (cid:1) = Intensity (a.u.) q ( 1 / Å ) C a K F e A s T = 3 0 0 K FIG. 1. (Color online) x-ray diffraction data showing (00 (cid:96) )diffraction peaks from in-lab diffraction measurements on asingle crystalline plate (upper data set) and high-energy x-ray diffraction measurements taken at APS (lower data set).Note that (cid:96) = odd (00 (cid:96) ) lines are consistent with the or-dered CaKFe As structure and are formally forbidden in a(Ca − x K x )Fe As structure .
305 K, H = 0-140 kOe, f = 17 Hz.). Higher field datawere obtained in a 630 kOe pulsed magnet at the NationalHigh Magnetic Field Laboratory (NHMFL), Los Alamos,using a high-frequency, synchronous digital lock-in tech-nique ( f = 148 kHz).Elastoresistivity was measured using a piezostack-based setup, similar to that described in Refs. 34 and 35.Samples of approximate dimensions, 1 × × ,were glued on one side of a Piezomechanik GmbH PSt150/5x5/7 piezostack, as shown in the inset in Fig. 14below. The change of sample resistance was measuredwith Lakeshore Model 372 AC Resistance Bridge as afunction of anisotropic strain, monitored in situ usingcrossed strain gauges glued to the opposite side of thepiezostack. The temperature environment was providedby a Janis SHI-950-T closed cycle cryostat. III. EXPERIMENTAL RESULTS
Figures 1 and 2 present x-ray diffraction data andthe temperature dependence of the CaKFe As unit celldimensions and volume, respectively. The presence of h + k + (cid:96) = odd peaks, which are forbidden for the I /mmm , Ae Fe As structure, indicates that, instead,CaKFe As assumes the ordered P /mmm structure. Given the relatively large c -axis dimension we are able todetect (00 (cid:96) ) peaks for all (cid:96) (cid:54)
12 in our in-house unit withCu K α radiation. The broad peak on the low- q side ofthe (002) peak in the in-house data set is from a thin filmof vacuum grease used to affix the thin CaKFe As plateto the zero-background single crystalline silicon sampleholder. Virtually no signatures of (00 (cid:96) ) peaks associated l = 0 . 1 2 3 5 8 9 Å a (Å) C a K F e A s ( 0 0 9 ) c (Å) V (Å3) T ( K ) FIG. 2. (Color online) Temperature dependence ofCaKFe As a - and c -lattice parameters as well as unit cellvolume as determined from (200) and (009) diffraction linesmeasured via high-energy x-ray diffraction. with CaFe As or KFe As are found. The agreement be-tween the in-house, Cu K α data, which comes from thesurface of the crystalline plate, and the high-energy x-raydata, which penetrates through the bulk of the sample,indicates that the sample is essentially single phase anduniform throughout its whole volume. The other, small,marked peaks are associated with traces (note that datais presented on a log scale) of FeAs and Fe As flux re-maining on the sample after decanting. The tempera-ture dependencies of the a - and c -lattice parameters ofthe CaKFe As sample, measured using high energy x-rays at the APS, are both monotonic and decrease withdecreasing temperature. There is no evidence of a struc-tural phase transition over our measured 6 K < T <
300 Ktemperature range. The room temperature lattice pa-rameters are close to reported values for polycrystallinesamples (a = 3.866 ˚A, c = 12.817 ˚A) as well as forsingle crystal samples (a = 3.8659 ˚A, c = 12.884 ˚A)The anisotropic, temperature dependent, normalizedelectrical resistivity and magnetization of CaKFe As areshown in Figs. 3 and 4. In-plane electrical resistance mea-surements, ρ a ( T ), were performed on multiple samples,both with soldered Sn and silver-epoxy contacts, reveal-ing a highly reproducible temperature dependence. Wealso performed measurements of ρ c ( T ) on two samples C a K F e A s (cid:1) c R R R ~ 7 (cid:2) / (cid:2) (cid:1) (300K) T ( K ) (cid:1) a R R R ~ 1 5
FIG. 3. (Color online) Temperature-dependent in-plane, ρ a ( T ), and inter-plane, ρ c ( T ), resistivity of CaKFe As , plot-ted using normalized resistivity scales, ρ ( T ) /ρ (300 K ). At300 K, ρ a ∼ µ Ω cm and ρ c ∼ µ Ω cm. Inset:picture of a CaKFe As single crystal shown over a mm-grid. and obtained qualitatively similar temperature depen-dencies of the electrical resistivity. CaKFe As manifestsvery similar temperature dependencies of ρ a and ρ c withonly slight differences for T <
150 K. We find residual re-sistivity ratios (RRR = ρ (300 K)/ ρ (35 K)) of 15 and 7 for ρ a and ρ c respectively. Although we present the electricalresistivity data as normalized, for ease of comparison, wecould estimate the room temperature resistivities of ρ a ∼ µ Ω cm and ρ c ∼ µ Ω cm. These values im-ply that the resistivity value measured on polycrystallinesamples ( ρ (300 K) ∼ µ Ω cm ) may suffer fromgrain boundary, or other, scattering. The anisotropic M ( T ) /H data was collected at 50 kOe in order to allowfor adequate signal from a thin, single crystalline plate.The H ⊥ c data are roughly 15% larger than the H (cid:107) c data and both data sets manifest a weak, essentially lin-ear increase upon cooling from 300 K to just above T c .For 35 K < T <
300 K, neither the temperature depen-dent electrical resistivity nor the magnetization manifestany features that can be associated with a structural,magnetic, or other electronic phase transition.Hall resistivity data, as a function of temperatureand magnetic field and thermoelectric power data as afunction of temperature, S ( T ), from measurements onCaKFe As are shown in Figs. 5 and 6 respectively. Theslope of Hall resistivity (the Hall coefficient) is positive(consistent with the sign of S ( T )) and linear in field up tothe maximum measured field of 140 kOe. The tempera-ture dependence of the ρ H /H is weak and close to linear.Although the carrier concentration, roughly evaluated us-ing a single band model, ranges from ∼ × cm − at40 K to ∼ × cm − at 200 K, CaKFe As undoubt- C a K F e A s H = 5 0 k O e H (cid:1) c H | | c M/H (emu/mol) T ( K ) FIG. 4. (Color online) Anisotropic, temperature depen-dent magnetization divided by applied field ( M ( T ) /H ) ofCaKFe As taken for H = 50 kOe applied along the crystal-lographic c -axis and perpendicular to the crystallographic c -axis. Due to T c at 35 K, data shown are for 40 K < T <
300 K. edly has multiple bands . Indeed, the temperature-dependent R H ( T ) = ρ H /H shown in Fig. 5 is consistentwith a multiband electronic structure of CaKFe As . Inthe simplest two-band model, the Hall constant is givenby R H ( T ) = ( R σ + R σ ) / ( σ + σ ) , where R , and σ , ( T ) are partial Hall constants and conductivities forband 1 and 2 . Hence, any difference in temperature de-pendencies of the mean free paths for the electrons/holesin band 1 and 2 would manifest itself in a temperature-dependent R H ( T ) even if R = 1 /q n and R = 1 /q n are independent of T , where n and n are partial carrierdensities in bands 1 and 2, and q and q are respectivecharges.The thermoelectric power S ( T ) is near 25 µ V/K atroom temperature, rises to over 45 µ V/K at 100 K andsmoothly drops to near 35 µ V/K just above T c = 35 K,as shown in Fig. 6. As is the case for the resistivity data,measurements of normal state thermoelectric power for T (cid:46)
35 K are precluded by the very large H c ( T ) valuesin the superconducting state (see below). Neither Halleffect nor thermoelectric power data have any features,other than anomaly at T c , that can be associated withany phase transition for 35 K < T <
300 K. The overallbehaviors of the Hall resistivity and thermoelectric powerare similar to those reported for optimally- or slightlyover-doped (Ba − x K x )Fe As . .Turning now to the superconducting phase transi-tion, Fig. 7 presents the low temperature, normalized,in-plane, electrical resistivity, low field magnetization,and the temperature dependent specific heat. As canbe seen, the superconducting phase transition is quitesharp and well defined. In each of these measurements T c = 35.0 ± (cid:1) H /H ( (cid:2) (cid:1) cm/kOe ) T ( K )C a K F e A s (cid:1) H ( (cid:2) (cid:1) cm) H ( k O e ) FIG. 5. (Color online) Temperature dependent Hall resistivitydivided by field, ρ H ( T ) /H , (Hall coefficient) of CaKFe As with H = 140 kOe applied along the crystallographic c -axis.Inset shows field dependent Hall resistivity ρ H at 40, 100, and200 K. S ( (cid:1) V/K) T ( K ) C a K F e A s S ( (cid:1) V/K) T ( K ) FIG. 6. Temperature dependent thermoelectric power ( S ( T ))for CaKFe As for temperature gradient applied perpendicu-lar to the crystallographic c -axis. in magnetization, an equi-entropic mid-point in specificheat, and an offset in resistivity. This value is resolvablyhigher than the T c = 33.1 K reported by Iyo et al. Wesee 1/4 π shielding in the zero-field-cooled (ZFC) magne-tization data; pinning and, as will be discussed below, κ are large enough in these samples that we only see asmall fraction of a 1/4 π Meissner effect in the field-cooled(FC) data.Magneto-optical imaging of new superconductors is an- - 1- 0 . 5000 . 1 0 1 0 2 0 3 0 4 001 0 0 0 Z F C F C x 2 5 ( c )( b ) (cid:2)(cid:1) H (cid:1) cH = 5 0 O e ( a ) I (cid:1) c (cid:3) / (cid:3) (300K) C a K F e A s T c
1 m m
CP / T (mJ/mol K2) T ( K ) FIG. 7. (Color online) Thermodynamic and transport datataken on CaKFe As near T c : (a) normalized electrical resis-tivity. Inset shows the magneto-optic image on a CaKFe As single crystal (see text for details). (b) FC and ZFC magneti-zation for H = 50 Oe for H applied perpendicular to the crys-tallographic c -axis (Note: the FC susceptibility data is mul-tiplied by 25 for clarity), (c) zero field specific heat C p ( T ) /T . other powerful tool to help confirm the bulk nature ofsuperconductivity via screening of the external magneticfield and study of the vortex physics and irreversible mag-netic properties. The inset of Fig. 7 shows magneto-optical imaging of a single crystals of CaKFe As . Theleft image shows magnetic flux trapped by a supercon-ductor due to vortex pinning. In the experiment the sam-ple was cooled in a 1 kOe magnetic field from above T c to 5 K and then the magnetic field was turned off. Mo-tion of escaping Abrikosov vortices is hindered by pinningcenters forming a pyramid - like distribution of vortexdensity, where height is proportional to B z ( (cid:126)r ). This isso-called remanent “Bean” critical state . The right im-age shows state of the sample after it was cooled withoutapplied field from above T c to 5 K at which point a 220Oe magnetic field was applied. This is superconductingshielding that mostly probes Meissner screening, whichat this low field is about 100%. (A H c value of approx-imately 440 Oe was obtained from London penetrationdepth measurements.) .Our magneto-optical and magnetization data showthat CaKFe As exhibits a classical irreversible magneticbehavior close to the critical state of a strong type-IIsuperconductor . These experiments indicate a veryrobust and uniform bulk superconductivity with criticalcurrent densities (estimated from B z ( (cid:126)r ) profiles) exceed- T c (K) p ( G P a )C a K F e A s H | | c M (10-6 emu) T ( K )
0 G P a 1 . 9 5 3 . 9
FIG. 8. (Color online) The superconducting critical temper-ature, T c , of CaKFe As as a function of applied pressure.Open square symbols from piston cylinder cell and filled sym-bols from moissanite anvil cell. Inset: M ( T ) measured in amoissanite anvil cell for p = 0, 1.95, and 3.9 GPa. C a K F e A s T = 1 . 8 5 K H (cid:1) c M (emu/cm3) H ( k O e ) (cid:3) (cid:2) (cid:1) = - 1 M (emu/cm3) H ( k O e ) FIG. 9. Magnetization as a function of magnetic field appliedperpendicular to the crystallographic c -axis of CaKFe As for T = 1.85 K. Inset: low field extended view and solid lineshowing ideal χ = − / π . ing 10 A/cm .The pressure dependence of T c was inferred from pres-sure dependent magnetization measurements. Figure 8shows that, although there is an initially weak suppres-sion of T c for p < < p < p = 3.9 GPa, T c has been sup-pressed to 28.5 K. As shown in the inset of Figure 8,the superconducting transition remains sharp up to the p = 3.9 GPa data point. Higher pressure measurementswill be needed to determine the ultimate, critical pressurefor superconductivity in this system.The superconducting state can also be studied as afunction of applied field. Figure 9 presents the M ( H )isotherm for T = 1.85 K with H applied within the planeof the crystalline plate (i.e. H ⊥ c ). As is shown in theinset, the initial slope is indeed − / π and the measure-ments start to deviate from this value for H (cid:46) H ⊥ c value consistent with the magneto-optical data in Fig. 7.Figure 10 presents the in-plane, electrical resistance datameasured in a QD PPMS using a static magnetic fieldfor H (cid:54)
140 kOe for H (cid:107) c and H ⊥ c . An example ofthe criteria used to determine H c ( T ) values is shown inthe upper panel of Fig. 10(a). Fig. 11 shows the field-dependent resistance measured at different temperaturesin a pulsed magnet. A temperature-independent back-ground was subtracted from the signal for clarity. Thebackground is attributed to the displacement of the sam-ple and its wiring by Lorentz force synchronous with lock-in excitation current. The resulting magnetic inductancevoltage is a product of field intensity and Lorentz force,leading to a stray background signal proportional to H .Similar onset and offset criteria were applied to extractthe superconducting field values at a given temperature.For H (cid:107) c at 15 K, only an offset value could be resolvedas shown in Fig. 11.Fig. 12 presents the anisotropic H c ( T ) curves for thetwo directions of applied field. These data make it im-mediately clear that CaKFe As , like other Fe-based su-perconductors with comparable T c -values, will have sub-stantial, low temperature H c values, and will likely havemoderate, but not substantial, H c ( T ) anisotropy, withthe H ⊥ c manifold being somewhat larger, at least athigher temperatures. Clearly, further measurements forapplied fields larger than 630 kOe will be needed to morefully determine the high field behavior of the supercon-ducting state in CaKFe As .Specific heat data for H (cid:107) c , H (cid:54)
140 kOe were also col-lected and are shown in Fig. 13. H c ( T ) data inferredfrom the specific heat data are also shown in Fig. 12(a).The H c ( T ) data inferred from the specific heat dataare distinguishably higher than those associated with theelectrical resistivity data for the same, H (cid:107) c , field orien-tation. The specific heat inferred H c ( T ) manifold is ac-tually closer to that found for H ⊥ c . Given that therewas some minor rotation of the specific heat platform (asdescribed in the experimental methods section) it is pos-sible that the difference between the H (cid:107) c ( T ) manifoldscould be associated with a very sharp, or rapid, angu-lar dependence of H c ( T ) that has a relative minima for H (cid:107) c and even for deviations of 10 ° from H (cid:107) c approachesthe H c ( T ) manifold for H ⊥ c . A second, more likely,explanation for the difference in H c ( T ) data for H (cid:107) c is that there are significant vortex flow effects that leadto an apparent reduction of the inferred T c for a givenapplied field and measurable difference between thermo-dynamically measured H c and irreversibility field, H irr ,
05 3 0 3 1 3 2 3 3 3 4 3 5 3 605 R (m (cid:1) ) H | | c o n s e to f f s e t C a K F e A s R (m (cid:1) ) T ( K ) H = H (cid:1) c FIG. 10. (Color online) Temperature dependent electrical re-sistance of CaKFe As for H applied parallel and perpendicu-lar to the crystallographic c -axis for representative fields H (cid:54)
140 kOe. Onset and offset criteria for T c are shown by dashedlines in the panel. inferred from transport measurements. IV. DISCUSSION
CaKFe As is an ordered example of a Fe-based su-perconductor with a relatively high T c value and no dis-cernible signature of any other ordering. The data pre-sented in Figs.3-13 are remarkably similar to that mea-sured for optimally- or slightly over-doped (Ba,K)Fe As and Ba(Fe,Co) As compounds. As argued previously ,the unambiguous appearance of h + k + (cid:96) = odd lines,specifically in this case (cid:96) = odd (00 (cid:96) ) lines, demonstratesa new, ordered structure rather than a (Ca . K . )Fe As solid solution in the body centered I /mmm structure.The residual resistivity ratio, RRR = 15 is also consis-tent with an ordered compound, although, by itself, notconclusive. There is no evidence of a structural phasetransition down to 6 K and there is no evidence of amagnetic or electronic phase transition other than su-perconductivity at T c = 35 ± T c is initially very shallow, almost pres-sure independent up to 1 GPa, followed by a sharperdrop for 1 GPa < p <
02 04 06 0 0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 002 04 06 0
O f f s e t 3 4 K 2 7 . 5 2 0 1 5 3 2 2 5 1 8 3 0 2 2 . 5 1 6 H | | c R (m (cid:1) ) O n s e t
C a K F e A s H (cid:1) c R (m (cid:1) ) H ( k O e ) FIG. 11. (Color online) Field-dependent resistance measuredin a 630 kOe pulsed magnet at different temperatures with(a) H (cid:107) c and (b) H ⊥ c . A temperature-independent back-ground signal was subtracted for clarity (see text). Dottedline and arrows indicate different criteria for determining H c (see text). of Ba(Fe − x Co x ) As and (Ba − x K x )Fe As across theunder-doped, optimally doped, over-doped parts of thephase diagram, CaKFe As appears to be near opti-mal doping.The anisotropic H c ( T ) data inferred from thetemperature-dependent and field-dependent resistancedata, summarized in Fig. 12, reveal multiple featuresabout CaKFe As . (1) The values of H c (0) both par-allel and perpendicular to the c -axis extrapolate to thefields well above the single-band BCS paramagnetic limit H p [ T ] = 1 . T c [ K ] (cid:39)
640 kOe, which is close to themaximum field in our pulse magnet. Thus, Pauli pair-breaking is essential, similar to the majority of otherFe-based superconductors . (2) As a result of differ-ent temperature dependencies of H (cid:107) c ( T ) and H ⊥ c ( T ) theanisotropy parameter γ ( T ) = H ⊥ c ( T ) /H (cid:107) c ( T ) decreasesas T decreases (see lower inset in Fig. 12(b)), consistentwith the interplay of orbital and Pauli pairbreaking .(3) No crossing of H (cid:107) c ( T ) and H ⊥ c ( T ) was observed for0 < H <
630 kOe, although a possibility that it mayhappen at higher fields cannot be ruled out.The initial ( H (cid:54)
140 kOe) H c ( T ) anisotropyshown in Fig. 12 is almost identical to that found ( b ) H c2 (kOe) T ( K ) C a K F e A s ( a ) H | | c H (cid:1) c C p O f f s e t O n s e t H c2 (kOe) T ( K ) g T ( K ) FIG. 12. (Color online) (a) Anisotropic H c ( T ) data forCaKFe As inferred from the temperature-dependent electri-cal resistivity data presented in Fig. 10. The H c ( T ) datafor H (cid:107) c inferred from temperature and field dependent spe-cific heat measurements (Fig. 13), using an equi-entropic mid-point criterion, are also shown. (b) Anisotropic H c ( T ) up to630 kOe, including the data shown in (a) for field below 140kOe. Black diamonds represent H ⊥ c ( T ). Red circles represent H (cid:107) c ( T ). Open and filled symbols indicate offset and onset cri-teria as described in the text. Black and red solid lines in themain figure are theoretically fitted curves to the onset cri-teria (see text). The inset shows the anisotropic parameter γ ( T ) = H ⊥ c /H (cid:107) c together with the theoretically fitted curve(black solid line). for (Ba . K . )Fe As . Indeed, based on thisand the other similarities to near optimally doped(Ba − x K x )Fe As , we can anticipate that the low tem-perature H c values will be relatively isotropic and inthe 600-800 kOe range. Taking the onset criteria, a morequantitative analysis of our H c ( T ) data shows that the dH c2 / dT values at T c are -109 kOe/K and -44 kOe/K for H ⊥ c and H (cid:107) c respectively. We can use the jump inzero-field specific heat data at T c (shown in Fig. 13) and C a K F e A s H | | c H = 0 k O e5 09 01 4 0 Cp (J/mol K) T ( K ) FIG. 13. (Color online) Temperature dependent specific heatdata for CaKFe As taken for H (cid:107) c = 0, 50, 90, 140 kOe. Thedata for finite H have been normalized to those for H = 0 kOein the normal state above T c . the Rutgers relation :∆ CT c = 18 πκ (cid:18) dH c dT (cid:19) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12) T = T c (1)where ∆ C = 8.33 × erg cm − K − and infer values of κ to be: 141 and 57 for H ⊥ c and H (cid:107) c respectively.In the two-band model the slope dH (cid:107) c /dT at T c can beexpressed in terms of the band parameters as follows dH (cid:107) c dT = φ πT c ξ ⊥ (2) ξ ⊥ = 12 (cid:20)(cid:18) λ − λ (cid:19) ξ + (cid:18) − λ − λ (cid:19) ξ (cid:21) , (3)where the effective Ginzburg-Landau coherence length ξ ⊥ determines the magnitude of the temperature-dependent ξ ⊥ ( T ) = ξ ⊥ τ − / near T c , τ = 1 − T /T c , φ is themagnetic flux quantum, λ = ( λ − + 4 λ λ ) / , λ − = λ − λ , λ and λ are dimensionless pairing con-stants in bands 1 and 2, and λ and λ are interbandpairing constants. Eqs. (2) and (3) are applicable forboth clean and dirty limits. In the clean limit, the par-tial coherence lengths ξ = (7 ζ (3) / / (cid:126) v / πk B T c and ξ = (7 ζ (3) / / (cid:126) v / πk B T c are proportional to the in-plane Fermi velocities v and v in bands 1 and 2. If the s ± pairing in Fe-based superconductors is dominated byinterband coupling , Eq. (3) yields ξ ⊥ → ( ξ + ξ ) / λ − (cid:28) λ .If both bands have the same mass anisotropy pa-rameter (cid:15) = m ⊥ /m (cid:107) <
1, the values of ξ ⊥ in the ab plane and ξ (cid:107) along the c -axis, can be estimated using the anisotropic scaling relations | dH (cid:107) c /dT | = φ / πξ ⊥ T c and | dH ⊥ c /dT | = φ / πξ ⊥ ξ (cid:107) T c . Hence, we obtain ξ ⊥ (cid:39) . ξ (cid:107) (cid:39) . ξ (cid:107) being about half the unit cell height alongthe c-axis. To see the ratio of ξ ⊥ to the mean free path l ,we estimate l using a single-band anisotropic Drude for-mula l = (cid:126) (3 π n √ (cid:15) ) / /ne ρ n . Taking ρ n = 20 µ Ω cmat T = T c which is 15 times smaller that ρ n at 300 K, n = 7 . × cm − and (cid:15) = m ⊥ /m (cid:107) = ( ξ (cid:107) /ξ ⊥ ) = 1 / l ≈
125 ˚A. This rough estimate suggests thatour sample is in a clean limit with ξ ⊥ (cid:28) l .To gain further insight into the behavior of H c ( T ),we fitted the experimental data using a two-band theorywhich takes into account both orbital and Pauli pair-breaking in the clean limit for two ellipsoidal Fermi sur-faces. In this case the equation for H (cid:107) c is given by , a G + a G + G G = 0 , (4) G = ln t + 2 e q Re ∞ (cid:88) n =0 (cid:90) ∞ q due − u × (cid:34) un + 1 / − t √ b tan − (cid:32) u √ bt ( n + 1 /
2) + iαb (cid:33)(cid:35) . (5)Here a = ( λ + λ − ) / w , a = ( λ − λ − ) / w , and w = λ λ − λ λ , t = T /T c . The function G is obtainedby replacing √ b → √ ηb , q → q √ s , g → g in G , where b = (cid:126) v H c πφ k B T c , α = 4 µφ k B T c (cid:126) v , (6) q = Q φ (cid:15) / πH c , η = v /v , s = (cid:15) /(cid:15) . (7)Here Q is the wave vector of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulations of the order parame-ter, v j is the in-plane Fermi velocity in band j = 1 , (cid:15) j = m ⊥ j /m (cid:107) j is the mass anisotropy ratio, µ is the mag-netic moment of a quasiparticle, α ≈ . α M , α M = H orbc / √ H p is the Maki paramagnetic parameter. Eqs.(4)-(5) do not not take into account spin-orbit effects,and the renormalized values of T c , v , v and µ includecorrections coming from the Fermi liquid and strong cou-pling effects. If H is applied along the symmetry axis, Q is parallel to H and the magnitude of Q is determinedby the condition ∂H c /∂Q = 0 of maximum H c . If (cid:15) = (cid:15) = (cid:15) , the anisotropic H c can be written in thescaling form H (cid:107) c ( T ) = H b ( t, η, α ) , H ⊥ c ( T ) = H √ (cid:15) b (cid:18) t, η, α √ (cid:15) (cid:19) , where H = 8 πφ k B T c / (cid:126) v and b is a solution of Eq.(4). The fit of the measured H c ( T ) to Eq. (4) for s ± pairing with λ = λ = 0, λ λ = 0 . η = 0 . α = 0 .
5, and (cid:15) = 1 / H wasadjusted to fit the magnitude of H (cid:107) c ( T ). The value of α is consistent with those which have been used previouslyto describe H c ( T ) of Ba − x K x As Fe .0The fit shows that the upper critical fields at T = 0extrapolate to H (cid:107) c (0) ≈
710 kOe and H ⊥ c (0) ≈ H (cid:107) c ( T ) being mostly determined byorbital effects moderately affected by the Pauli pair-breaking. By contrast, the shape of H ⊥ c ( T ) is consistentwith the essential Pauli pairbreaking in both bands, be-cause of large respective Maki parameters α ⊥ = α/ √ (cid:15) and α ⊥ = α/η √ (cid:15) . As a result, the anisotropy parame-ter γ ( T ) = H ⊥ c ( T ) /H (cid:107) c ( T ) decreases with T , which re-flects different temperature dependencies of the orbitally-limited and Pauli-limited upper critical fields.It should be mentioned that in the available field range0 < H <
630 kOe where the H c data were obtained, thefit is not very sensitive to the particular values of the pair-ing constants and the band asymmetry parameter η , yetit suggests the possibility of a FFLO state for T <
13 Kand for higher fields H parallel to the ab planes. In fact,the data shown in Fig. 12 could be fitted equally wellwith a single-band model in which H c ( T ) is defined bythe equation, G ( b ) = 0. More definite conclusions aboutmultiband orbital effects and FFLO states could be madeby analyzing low-temperature parts of the H (cid:107) c ( T ) and H ⊥ c ( T ), which would require even higher fields H > As from other orderedstoichiometric Fe-based superconducting compounds likeLiFeAs for which the entire anisotropic H c ( T ) has beenmeasured .Further insights into the magneto-transport behaviorof CaKFe As can be inferred from the fact that the resis-tance transition curves R ( T ) shown in Figs. 10 broadenas H increases. This indicates a possible effect of thermalfluctuations of vortices similar to that has been exten-sively studied in high- T c . Broadening of the supercon-ducting transition in CaKFe As under magnetic field isalso clearly seen in the behavior of the specific heat shownin Fig. 13.At H = 0 thermal fluctuations can be quantified bythe Ginzburg number Gi = 0 . πµ k B T c λ /φ ξ (cid:107) ) ex-pressed in terms of ξ (cid:107) and the London penetration depth λ at H (cid:107) c and T = 0. Using the values of λ = 133nm , ξ (cid:107) = 0 . T c = 35 K, we obtain thatCaKFe As would have Gi (cid:39) · − of the same orderof magnitude as Gi for BaFe As -based compounds, butsmaller than Gi ∼ − for YBa Cu O − x . The ir-reversibility field H p ( T ) associated with the offset pointof R ( T, H ) = 0 in Fig. 10 can be qualitatively evalu-ated in terms of melting and thermal depinning of vortexstructure. For instance, the melting field H m of the idealvortex lattice in a uniaxial superconductor at H (cid:107) c is de-fined by the equation h m / (1 − h m ) = (1 − t ) t /t , where h m = H m /H c , t = πc L /Gi / and c L = 0 . − . . For weak thermal fluctua-tions, H c − H m (cid:28) H c , the above equation for h m yields H c ( T ) − H m ( T ) (cid:39) H c (0) (cid:18) Giπ c L (cid:19) / (cid:18) − TT c (cid:19) / (8) A s C a K F e A s m - m ( B a K ) F e A s Elastoresistivity Coefficient T ( K ) FIG. 14. (Color online) Elastoresistivity coefficients of 2 m and m − m of CaKFe As (open and filled circles) mea-sured using crossed samples glued to a piezostack, shownschematically in the right inset. The 2 m coefficient data ofoptimally doped K-doped BaFe As (grey +’s) from Ref. 55are plotted for comparison. Taking c L = 0 .
15 and Gi = 4 · − in Eq. (8) gives( Gi/π c L ) / ≈ .
43, which shows that thermal fluctua-tions in CaKFe As are not weak, as also characteristicof the majority of Fe-based superconductors which areintermediate between the conventional low- T c supercon-ductors in which vortex fluctuations are negligible andhigh- T c cuprates in which the behavior of vortex matterat 77K is controlled by thermal fluctuations . Yet thewidth of the critical fluctuation region T c − T (cid:46) GiT c ∼ .
014 K is much smaller that the observed width of thesharp resistive transition ∆ T (cid:39) . H = 0 shown inFig. 7, as well as the width of the step in specific heat inzero field. This suggests that, in addition to thermal fluc-tuations of the order parameter, the resistive transitionat zero field can be broadened by extrinsic factors such asweak materials’ inhomogeneities in T c . As H increases,the field-induced broadening of the resistive transitionbecomes more pronounced, structural defects and inho-mogeneities in T c affecting both the thermally-activatedflux flow resistance and the vortex melting field .To further explore the similarity between CaKFe As and near-optimally doped (Ba − x K x )Fe As we deter-mined the elastoresistivity coefficients 2 m and m − m of CaKFe As using a piezo-stack-based setup;these data are presented in Fig. 14. For compari-son the 2 m coefficient data of near-optimally doped(Ba − x K x )Fe As from Ref. 55 are also shown. The elas-toresistivity coefficients are defined in the tetragonal unitcell. 2 m measures the size of the resistivity anisotropyalong the Fe-Fe bonds (the diagonals of the tetragonalunit cell) ρ [110] − ρ [1¯10] induced by the corresponding shear1strain ε [110] − ε [1¯10] ,2 m = 1 ρ d (cid:0) ρ [110] − ρ [1¯10] (cid:1) d (cid:0) ε [110] − ε [1¯10] (cid:1) . (9)In typical Fe-based superconductors, m is closely re-lated to the nematic susceptibility χ nem . It is expectedto diverge on approaching the nematic (tetragonal-to-orthorhombic) transition in under-doped samples , inwhich the Fe-Fe bonds become inequivalent. Similarly tothe optimally K-doped BaFe As , the 2 m coefficient ofCaKFe As indeed rises strongly with decreasing temper-ature, indicating proximity to a nematic transition. Notethat, despite its strong increase at low temperatures,2 m does not show Curie-Weiss type divergence foreither compound. In contrast, the elastoresistivity mode, m − m , shows only a weak temperature dependencein CaKFe As . It is related to the sensitivity of the re-sistivity anisotropy between the two tetragonal in-planeaxes to the corresponding shear strain m − m = 1 ρ d (cid:0) ρ [100] − ρ [010] (cid:1) d (cid:0) ε [100] − ε [010] (cid:1) . (10)This mode does not directly couple to the nematicorder parameter of typical under-doped Fe-based sys-tems. All in all, the elastoresistivity data of CaKFe As indicates that it is close to a nematic structural in-stability, similarly to other optimally-doped Fe-basedsuperconductors. CaKFe As can also be put in context of otherAeFe As -based (Ae = Ba, Sr, Ca) superconductors byplacing it on a ∆C p versus T c , or BNC, scaling plot(Fig. 15). The jump in specific heat of CaKFe As issharp and well defined (perhaps due, in part, to its fullyordered nature) and, combined with its T c value placesCaKFe As at the extreme, near optimally doped end ofthe BNC data set for AeFe As systems. V. CONCLUSIONS
We have synthesized single phase, single crystallinesamples of CaKFe As and measured temperature de-pendent unit cell dimensions, temperature and field de-pendent specific heat as well as thermoelectric power,Hall effect, elastoresistivity, and anisotropic temperatureand field dependent magnetization and electrical resistiv-ity. There is no indication of any phase transition, otherthan superconductivity with T c = 35.0 ± ≤ T ≤
300 K. The tem-perature dependence of our thermodynamic and trans-port measurements, the resistive anisotropy, the pressuredependence of T c , and the anisotropy and size of H c (T)are consistent with near optimally doped members of the(Ba − x K x )Fe As series. In addition CaKFe As fallsdirectly onto the BNC scaling plot at the near optimalend of the AeFe As structure manifold. All of these ( B a K x ) F e A s ( E u K ) F e A s ( K N a x ) F e A s ( B a N a x ) F e A s ( C a N a x ) F e A s B a ( F e
T M x ) A s B a ( F e
C o x C u y ) A s S r ( F e
N i ) A s C a ( F e
C o x ) A s (cid:1) Cp (mJ/mol-Fe K) T c ( K ) C a K F e A s FIG. 15. (Color online) Log-log plot of ∆ C p jump at T c versus T c (BNC plot [Refs. 6, 12, and 56]). Note thatdata for (Ba − x K x )Fe As are plotted for x < .
8. ForBa(Fe − x TM x ) As , TM = Ni, Co, Rh, Pd, Pt [Ref. 12].Dashed line has a slope corresponding to ∆C p ∼ T c and is aguide for the eyes. data indicate that stoichiometric CaKFe As is intrinsi-cally close to what is referred to as ”optimal-doped” ona generalized, Fe-based superconductor, phase diagram. ACKNOWLEDGMENTS
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