Heat capacity jump at Tc and pressure derivatives of superconducting transition temperature in the Ba1-xKxFe2As2 (0.2 < x < 1.0) series
Sergey L. Bud'ko, Mihai Sturza, Duck Young Chung, Mercouri G. Kanatzidis, Paul C. Canfield
aa r X i v : . [ c ond - m a t . s up r- c on ] M a r Heat capacity jump at T c and pressure derivatives ofsuperconducting transition temperature in the Ba − x K x Fe As ( . ≤ x ≤ . ) series Sergey L. Bud’ko , Mihai Sturza , Duck Young Chung ,Mercouri G. Kanatzidis , , and Paul C. Canfield Ames Laboratory, US DOE and Department of Physics and Astronomy,Iowa State University, Ames, IA 50011, USA Materials Science Division, Argonne National Laboratory,Argonne, Illinois 60439-4845, USA and Department of Chemistry, Northwestern University,Evanston, Illinois 60208-3113, USA (Dated: October 10, 2018)
Abstract
We present the evolution of the initial (up to ∼
10 kbar) hydrostatic, pressure dependencies of T c and of the ambient pressure jump in the heat capacity associated with the superconductingtransition as a function of K - doping in the Ba − x K x Fe As family of iron-based superconductors.The pressure derivatives show weak but distinct anomaly near x ∼ .
7. In the same concentrationregion ∆ C p | T c deviates from the ∆ C p ∝ T scaling found for most BaFe As - based superconduc-tors. These results are consistent with a Lifshitz transition, and possible significant modificationof the superconducting state, occuring near x ∼ . PACS numbers: 74.62.Fj, 74.70.Xa, 74.25.Bt, 74.62.Dh . INTRODUCTION For the last half decade a significant experimental and theoretical effort has concentratedon studies of the physical properties of Fe - based superconductors and related materials.
Of the several families of Fe-based superconductors discovered to date, the 122, AE Fe As ( AE = alkaline earth and Eu) family, is the most studied one. This family offers pos-sibilities for substitutions on all three crystallographic sites that can result in a complexcombination of steric and carrier-doping effects while maitaining simplicity of the crystalstructure. However, the main body of the published work on the 122 family has focusedon the AE (Fe − x TM x ) As series, in which the 3 d − , 4 d − , and sometimes 5 d − transitionmetals substitute for Fe. This is due to the reasonable ease of growing large, high quality,homogeneous single crystals.Despite the fact that in the 122 system, superconductivity, with a T c ≈
38 K, was firstreported on K-doping of BaFe As and this value of T c is still holding a record for bulksuperconductivity in the AE Fe As - related materials, detailed studies of the completeBa − x K x Fe As solid solution series are not so common, and concentrate mainly on theevolution of the crystallographic properties and the x − T phase diagram. One of the reasonsfor this is a persistent difficulty in determination of the reliable procedure for synthesis ofhomogeneous Ba − x K x Fe As single crystals in a wide range of K - concentration.In the hole-doped, Ba − x K x Fe As , series superconductivity is observed over a wide rangeof K - concentrations, 0 . . x ≤ . (as compared to 0 . . x . .
15 for the electron-doped Ba(Fe − x Co x ) As ). For underdoped Ba − x K x Fe As superconductivity and mag-netism microscopically co-exist (similarly to what was observed in the electron-dopedBa(Fe − x TM x ) As ). Near optimal doping, x ∼ .
4, several experiments and theoret-ical calculations give evidence for a nodeless, near constant, s ± superconducting gap thatchanges sign between hole and electron pockets. Recent ARPES measurements suggestthat the s ± superconducting gap exists in a wide doping range, 0 . ≤ x ≤ . As stands out among the members of the Ba − x K x Fe As series. The reported Fermisurface of KFe As differs from that of the optimally doped Ba − x K x Fe As having threehole pockets, two centered at the Γ point in the Brillouin zone, and one around the M point with no electron pockets. Quantum criticality, and nodal or d -wave superconductivity inKFe As was suggested in a number of publications. Possible evolution from s ± to d -wave2n the Ba − x K x Fe As series has also been discussed. Given the debates present in the literature regarding the evolution of physical proper-ties in the Ba − x K x Fe As series and its apparent difference from the extensively studied AE (Fe − x TM x ) As series, it is of importance to have a broad set of data on Ba − x K x Fe As ,in particular, data related to the superconducting state. In this work we present two datasetsobtained for the Ba − x K x Fe As series with K-concentrations covering underdoped, opti-mally doped, and overdoped regions, up to the end compound, pure KFe As . The firstset is comprised of the initial ( P .
10 kbar) pressure dependencies of the superconduct-ing transition temperatures, T c ( P ) and is alike the data reported for Ba(Fe − x Co x ) As . Such data have the potential to assess the possibility of equivalence of pressure and dop-ing that was suggested for several 122 series.
Moreover, under favorable circumstancessuch dataset can shed light on the details of superconductivity mechanism in the particularseries.
The second set consists of the data on the evolution of the jump in heat capacityat the superconducting transition. Many Fe - based, 122 superconductors follow the trendsuggested in Ref. 38 and expanded in Ref. 39, the so-called BNC scaling, ∆ C p | T c ∝ T c . Theunderdoped and optimally doped Ba − x K x Fe As appear to follow this trend as well, whereas the stoichiometric end-compound, KFe As , clearly deviates from the trend. De-tailed study of the ∆ C p | T c in the whole range of K concentrations might clarify the evolutionof superconducting properties in the series. II. EXPERIMENTAL DETAILS
Homogeneous, single phase, Ba − x K x Fe As polycrystalline powders with x = 0.2, 0.3,0.4, 0.6, 0.7, 0.8, 0.9 and 1.0 were synthesized by a procedure similar to that reportedearlier. The starting reagents, KAs, BaAs, and Fe As were prepared by heating elementalmixtures at 450 ◦ C, 650 ◦ C, and 850 ◦ C, respectively. For each composition a stoichiometricmixture of these binary compounds was thoroughly ground to a uniform and homogeneouspowder, loaded in an alumina crucible subsequently enclosed in a niobium tube and thensealed in a quartz tube, and pre-heated at 600 ◦ C for 12 h. This sintered mixture wasthen re-ground and pressed into a pellet which was again loaded in a niobium tube andsealed in a quartz tube. The pellet was heated to 800 ◦ C ≤ T ≤ ◦ C, dependingon the composition, for 24 to 48 h followed by quenching to room temperature in air. The3omogeneity of Ba − x K x Fe As polycrystalline powder was ensured by repeating this processmultiple times. The structure and quality of the final crystalline powders of Ba − x K x Fe As were confirmed by x-ray powder diffraction and magnetization measurements and the x values of all products were estimated by comparing the superconducting T c ’s observed withthose precisely determined in the phase diagram reported previously. For the end-membersample with x = 1 .
0, the single phase product was prepared by a flux reaction of Fe/KAs at1:6 ratio at 1000 ◦ C for 6 h. The pure crystals of KFe As were then isolated by dissolvingthe excess KAs flux in alcohol under a nitrogen atmosphere.The synthesis of Ba − x K x Fe As has been known to be delicate mainly because of highvapor pressures of K/As and an unfavorable kinetics toward the composition of optimallydoped state x = 0 . T c in the Ba − x K x Fe As series. Particularlyfor the underdoped region between x = 0 . x = 0 .
15 where the superconductivityof Ba − x K x Fe As emerges, it is very difficult to obtain highly homogeneous samples witha sharp single transition because of a very sensitive change in T c by a small variation incomposition in this region (see the phase diagram in Ref.10 or in Fig. 3 below). Therefore, inthis synthetic procedure a closed metal tube, with minimal volume, is necessary to suppressvaporization of K/As at high temperatures. Also for better control of K/Ba ratio duringthe reaction, the annealing temperature was gradually increased from 800 ◦ C for x = 0 . ◦ C for x = 0 .
2. About 10-20% of additional KAs in the reaction mixture after thepre-reaction is needed to compensate the loss of K/As that occurs by the extended periodof annealing at high temperature for all compositions. Handling of all materials was carriedout under a dry argon atmosphere.Low-field dc magnetization under pressure, was measured in a Quantum Design MagneticProperty Measurement System, MPMS-5, SQUID magnetometer using a a commercial,HMD, Be-Cu piston-cylinder pressure cell. Daphne oil 7373 was used as a pressure mediumand superconducting Pb or Sn (to have its superconducting transition well separated fromthat of the sample) as a low-temperature pressure gauge. . The heat capacity was measuredusing a hybrid adiabatic relaxation technique of the heat capacity option in a QuantumDesign Physical Property Measurement System, PPMS-9 or PPMS-14, instrument.4 II. RESULTSA. Pressure dependence of T c An example of M ( T ) data taken at different pressures is shown in Fig. 1. An onsetcriterion was used to determine T c . Since none of the samples was suffering from a distinctchange of the transition width under pressure, alternative criteria (like maximum in dM/dT )yield similar pressure dependencies. The pressure dependencies of the superconductingtransition temperatures for the samples with all K-concentrations studied in this work areshown in Fig. 2. For the underdoped sample, with x = 0 . T c increases under pressure, forsamples close to the optimally doped, x = 0 . , .
4, the T c ( P ) dependencies are basically flat,and for the overdoped samples, x ≥ . T c decreases under pressure. For all samples, exceptthe underdoped x = 0 . T c ( P ) behavior is linear, as such the pressure dependencies of T c can be well represented by dT c /dP values. The set of T c ( P ) data yields the ambientpressure T c ( x ) values defined as extrapolation to P = 0 data under pressure. These valuesare consistent with the superconducting transition temperatures obtained from the analysisof the ambient pressure specific heat data below, shown as stars in Fig. 2.A more compact way to look at the pressure dependence of T c in the Ba − x K x Fe As series is presented in Fig. 3, where the results of this work are plotted together with theliterature data that show consistency between different groups/samples in the overlap-ping concentration regions. The T c ( x ) data are consistent with the ambient pressure datain the literature and are shown for reference. The K-concentration dependent pressurederivatives, dT c /dP , and normalized, d (ln T c ) /dP show a clear trend and three differentK-concentrations regions. The pressure derivatives are positive and rather high for the sig-nificantly underdoped samples ( x ∼ . T c <
20 K). They become small and negative for0 . ≤ x ≤ .
7, this concentration range covers slightly underdoped, optimally doped, andpart of the overdoped samples; the concentration dependence of dT c /dP (or d (ln T c ) /dP )is close to linear in this middle region. On further increase of x the x -dependence of thepressure derivatives deviated from the shallow linear behavior (this trend is better seen inthe concentration dependence of the normalized pressure derivatives).Fig. 4 presents a comparison of the relative changes in superconducting transition tem-perature under pressure and with K - doping. For 0 . ≤ x ≤ . T c , suggested for other members of the 122 family. This scaling however fails for0 . < x ≤ . B. Jump in specific heat
All samples studied in this work except for x = 0 . T c (see Fig. 5 as an example). The T c and ∆ C p | T c values were determined by aprocedure consistent with that used in Ref. 38. For x = 0 . C p at T c value are expected to be rather large. The specific heat jump data forthe Ba − x K x Fe As series obtained in this work were added in Fig. 6 to the updated BNCplot taken from Ref. 41. Again, there appears to be a clear trend: for 0 . ≤ x ≤ . . ≤ x ≤ . As , consistent with the previously publishedvalue. This is clearly different from the studied Ba(Fe − x TM x ) As series, for which theBNC scaling was observed for the samples covering the full extent of the superconductingdome. IV. DISCUSSION AND SUMMARY
Both sets of measurements point out that some change in superconducting properties ofBa − x K x Fe As occurs near the x = 0 . suggested thatthe nodal line structure of the superconducting gap emerges at x ∼ . The anomaly in the evolution of the pressure derivatives withconcentration is consistent with what one would expect in the case of the Lifshitz transition, along the same lines as evolution of dT c /dP was understood in several cuprates. Theobserved violation of the BNC scaling hints that some significant changes might happen6n the nature of the superconducting state as well. These results delineate the differencebetween transition metal doping and K-doping in the BaFe As series concentration anddefine the K - concentration region where the superconducting state (possibly the orderparameter) is significantly modified. Further measurements for concentrations around 70%of K (in particular ARPES and thermal conductivity) would be desirable to understand theobserved anomalies. Acknowledgments
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10 15 20 25 30-0.010-0.0050.000 M ( e m u ) T (K)
Pb pressure gauge T c P Ba K Fe As
25 Oe, ZFC
FIG. 1: (Color online) Example of temperature dependent magnetization (zero-field-cooled, takenin 25 Oe applied magnetic field) of Ba . K . Fe As measured at 1.5, 3.9, 6.5, and 11.1 kbar. Thecriterion for T c (for P = 11 . x=0.2 x=0.3 x=0.4 x=0.6 x=0.7 x=0.8 x=0.9 x=1.0 T c ( K ) P (kbar) Ba K x Fe As FIG. 2: (Color online) Summary plot of the pressure dependence of T c for the samples studied inthis work. Dashed lines are linear fits to the data except for the x = 0 . P = 0. Stars are the T c values obtained in theanalysis of the ambient pressure heat capacity data below. .000.050.10 d ( l n T c ) / d P ( k ba r - ) Ba K x Fe As T c ( K ) x d T c / d P ( K / k ba r) FIG. 3: (Color online) T c , dT c /dP and d (ln T c ) /dP as a function of K-concentration inBa − x K x Fe As . Symbols: stars - this work, triangle - data for KFe As from Ref. 41, circles- data for four underdoped samples obtained by linear fits of the first 3-4 data points under pres-sure in Ref. 44. T c values are taken from the linear fits of T c ( P ). Two symbols for x = 0 . .0 0.2 0.4 0.6 0.8 1.0-0.050.000.050.10 x d ( l n T c ) / d P ( k ba r - ) Ba K x Fe As -2002040 d ( l n T c ) / d x FIG. 4: (Color online) K - concentration dependence of the normalized pressure derivatives, d (ln T c ) /dP = T c dT c /dP (left axis, circles), and the normalized concentration derivatives, d (ln T c ) /dx = T c dT c /dx (right axis, triangles) of the superconducting transition temperatures.Dashed line corresponds to the shared zero on Y -axes. C p / T ( m J / m o l K ) T (K) Ba K Fe As C p /T| T c T c FIG. 5: Temperature-dependent heat capacity of Ba . K . Fe As plotted as C p /T vs T . Criteriafor T c and ∆ C p | T c (isoentropic construct) are shown. Ba K x Fe As (this work) (Ba K x )Fe As Eu K Fe As LiFeAs FeTe Se Ba(Fe TM x ) As Ba(Fe Co x Cu y ) As Sr(Fe Ni ) As Ca(Fe Co x ) As C p ( m J / m o l K ) T c (K) FIG. 6: (Color online) ∆ C p at the superconducting transition vs T c for the Ba − x K x Fe As series,plotted together with literature data for various FeAs-based superconducting materials. Updatedplot is used to show the literature data. The line corresponds to ∆ C p ∝ T c . Numbers near thesymbols are K - concentration x . Two symbols for x = 0 .6 correspond to measurements on twosamples of slightly differing quality.