Table Of Content

The Electronic Specific Heat of Ba K Fe As from 2K to 380K. 1−x x 2 2 J.G. Storey1, J.W. Loram1, J.R. Cooper1, Z. Bukowski2 and J. Karpinski2 1Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, U.K. and 2Laboratory for Solid State Physics, ETH Zurich, Zurich, Switzerland (Dated: January 4, 2010) Using a differential technique, we have measured the specific heats of polycrystalline Ba K Fe As samples with x = 0, 0.1 and 0.3, between 2K and 380K and in magnetic fields 1−x x 2 2 0to13Tesla. Fromthisdatawehavedeterminedtheelectronicspecificheatcoefficientγ(≡C /T) el over the entire range for the three samples. The most heavily doped sample (x = 0.3) exhibits a largesuperconductinganomaly∆γ(T )∼48mJ/molK2 atT =35K,andwedeterminetheenergy c c gap, condensationenergy, superfluiddensityandcoherence length. Inthenormal stateforthe x= 0 1 0.3sample,γ ∼47mJ/molK2 isconstantfromTc to380K.Intheparentcompound(x=0)there 0 isalargealmostfirstorderanomalyatthespindensitywave(SDW)transitionatTo =136K.This 2 anomaly is smaller and broader for x = 0.1. At low T, γ is strongly reduced by the SDW gap for n both x = 0 and 0.1, but above To, γ for all three samples are similar. a PACSnumbers: 74.25.Bt,74.70.-b J 4 The electronic specific heat contains a wealth of quan- mina crucibles sealed in evacuated quartz ampoules. Fi- ] n titative information on the electronic spectrum over an nally, samples of Ba1−xKxFe2As2 with x = 0.1 and 0.3 o energy region ±100meV about the Fermi level, cru- were prepared from appropriate amounts of single-phase c cial to the understanding of high temperature supercon- BaFe As and KFe As . The components were mixed, 2 2 2 2 - r ductivity. Measurements of the electronic specific heat pressed into pellets, placed into alumina crucibles and p played an important role in revealing key properties of sealed in evacuated quartz tubes. The samples were an- u the copper-oxide based ‘cuprate’ high-temperature su- nealed for 50 h at 700◦C with one intermittent grind- s . perconductors (HTSCs). Some examples include the ing, and were characterized by room temperature pow- t a normal-state “pseudogap”[1–4], the bulk sample inho- derX-raydiffractionusingCuK radiation. Thediffrac- α m mogeneity length scale[5], and more recently the degree tionpatterns were indexedon thebasis ofthe tetragonal - to which the superconducting transition temperature is ThCr Si typestructure(spacegroupI4/mmm). Lattice d 2 2 suppressed due to superconducting fluctuations[6]. In parameters calculated by a least-squares method agree n o this work we extend such measurements to the recently wellwiththosereportedbyChenetal[8]. TracesofFeAs c discovered iron-arsenide based ‘pnictide’ HTSCs. Here as an impurity were detected for compositions with x = [ we present results obtained from polycrystalline samples 0.1 and 0.3. The samples for heat capacity measurement 1 of Ba1−xKxFe2As2 (x = 0, 0.1 and 0.3) using a high- weighed ∼ 0.8g. v resolution differential technique[7]. The total specific heats of the three samples are plot- 4 Withthistechniquewedirectlymeasurethedifference ted as γtot ≡ Ctot/T in Fig. 1. In the x = 0 sample 7 in the specific heats of a doped sample and the undoped there is a sharp and almost first order anomaly at the 4 reference sample (BaFe As ). This eliminates most of magneto-structural transition at T = 136K, in agree- 0 2 2 0 . the large phonon term from the raw data and yields a ment with published single crystal data[9]. For the x = 1 curve which is dominated by the difference in electronic 0.1 sample the corresponding anomaly at T = 135K is 0 0 0 termsbetweenthesampleandreference. Aftermakinga broaderandconsiderablyreducedinmagnitude,inagree- 1 smallcorrectionforanyresidualphononterm,thisdiffer- ment with the data of Rotter et al.[10] who have tracked : ence in electronic specific heats can be determined with T in the specific heat down to 105K in a sample with x v 0 i a resolution of ∼ 0.1 mJ/mol K2 at temperatures from = 0.2. The magnetic field dependence of this anomaly is X 1.8K to 380K and magnetic fields from 0 to 13T. During extremelyweakforbothsamples. Weseenoevidencefor r a measurement run the total specific heats of the sample a structural transition in the x = 0.3 sample (the very a and reference are also measured. weak anomaly at 67K in the differential data (Fig. 2(a)) The polycrystalline samples of Ba K Fe As were is probably due to an FeAs impurity phase[11]). The su- 1−x x 2 2 preparedbyasolidstatereactionmethodsimilartothat perconducting transition in this sample is clearly visible reported by Chen et al[8]. First, Fe As, BaAs, and in γtot at 35K, and the field dependence is shown in the 2 KAs were prepared from high purity As (99.999%), Fe inset to Fig. 1. (99.9%),Ba(99.9%)andK(99.95%)inevacuatedquartz Inthetemperaturerange2−8K,γtot =γ(0)+β(0)T2 ampoules at 800, 650 and 500◦C respectively. Next, atzerofieldwithγ(0)=5.1,9.3and1.8mJ/molK2 and the terminal compounds BaFe As and KFe As were β(0) = 0.45, 0.37 and 0.57 mJ/mol K4 for the x = 0, 0.1 2 2 2 2 synthesized at 950 and 700◦C respectively, from stoi- and 0.3 samples respectively. On the assumption that chiometric amounts of BaAs or KAs and Fe As in alu- β(0)isentirelyduetophononsweobtainDebyetemper- 2 2 to its saturation value 3nR (where n is the number of SC anomaly atoms/formula unit) shown by the dotted line in Fig. 1. 1250 650 0T ) Toextendtheusefulrangeofthehightemperatureregion -2 K 1000 600 13T we exploit the fact that the Debye temperature θD(T) -1 ol 550 deduced from Cv is generally only weakly T-dependent m forT >0.5θD(∞)(or∼180Kforthepresentmaterials). 750 J 28 30 32 34 36 Withthisconstraintweobtainlimitinghightemperature m Debye temperatures θ (∞) = 368, 360 and 356K and γ tot ( 500 xx == 00.1 high-T values γ(300K)D= 55, 47 and 47 mJ/mol K2 for x = 0.3 the 0, 0.1 and 0.3 samples. 250 3nR/T Differentialmeasurements(seeFig.2(a))betweeneach sample and the x = 0 reference give ∆γtot =∆γ+∆γph 0 (assuming ∆γan = 0). It is clear from Figs. 1 and 0 50 100 150 200 250 300 350 400 2(a) that the phonon terms for the three samples are Temperature (K) very similar. The broad negative peak at 35K seen in FIG. 1: (Color online) γtot ≡ Ctot/T of Ba K Fe As for ∆γtot(0.1,0)=γtot(x=0.1)−γtot(x=0),andwhichcan 1−x x 2 2 x = 0, 0.1 and 0.3. The dotted line shows the high temper- also be inferred in the data for ∆γtot(0.3,0) in the same ature limiting value of the lattice contribution, 3nR/T. The temperature region, is compatible with fractional in- inset shows the suppression of the superconducting anomaly creasesof0.018and0.030intheacousticphononfrequen- in magnetic fields from 1 to 13T in 1T increments. cies for the 0.1 and 0.3 samples relative to the x = 0 reference. Sinceweexpectthedifferenceofelectronicterms ∆γ(0.1,0) for the two non-superconducting samples to atures θD(0)=289, 298and 257Kforthethree samples. be only weakly T-dependent (at least below 100K), we We cannot, however, ignore the possibility that for the obtain ∆γph(0.1,0) = ∆γtot(0.1,0) − ∆γ(0.1,0) using superconducting 0.3 sample β(0) is enhanced by an elec- the low temperature value ∆γ(0.1,0) = −4.2 mJ/mol tronic component ∝ T2, leading to too low a value of K2. To ensure that the resulting ∆γph(0.1,0) has a θD(0). This would explain the reduced value of θD(0) T-dependence compatible with that of a phonon spec- forthissamplewhichcontradictsthetrendseenin∆γtot trum it was modelled with a histogram for the difference (Fig.2(a))thatacousticphononfrequencies,whichdom- phonon spectrum, as discussed previously[15]. Making inatethephononspecificheatinthistemperatureregion, this phonon correction removes the broad negative peak increase with doping. If the 0 and 0.1 samples have an in ∆γtot at 35K for this sample (Fig. 2(b)). As shown in initial electronic T2 term in γ(T) we would expect this the same figure, subtracting a phonon term ∆γph(0.3,0) to have a magnitude ∼ γnT2/To2 ∼ 0.003 mJ/mol K2 = 1.68∆γph(0.1,0) also removes the negative peak in if it is controlled by the same energy scale as T0. This ∆γtot(0.3,0). Following this correction, the electronic contribution to β would be negligible compared with the ∆γ(0.3,0)hasanadditionalnegativeT-dependencegiven measured β(0). by ∼ −20×10−6T3 mJ/mol K2 in the range 40 - 110K. We next discuss the separation of electronic and We conclude below that γ (T) for the 0.3 sample is T- n phonon contributions from the total specific heat over independent, and attribute this negative T-dependence a wider temperature range. The total specific heat co- to a corresponding positive term in the electronic spe- efficient is given by γtot = γ + γph + γan where the cific heat coefficient γ(x = 0) of the undoped sample in electronic term γ = C /T, the harmonic phonon term the SDW phase. el γph =C /T and the anharmonic phonon (dilation) term Aftercorrectingfor∆γph(0.3,0)wefindthatjustabove v γan = (C − C )/T[12]. C and C are the lattice T ,γ(x=0.3)∼47mJ/molK2. Thisisveryclosetothe p v p v c heat capacities at constant pressure and volume respec- value S/T(T ), where S = (cid:82)T γ(T)dT is the electronic c 0 tively. Theanharmonictermisgivenbyγan =VBβ2[12] entropy. By definition, S/T(T(cid:48)) is the average value of γ where V is the molar volume, B is the bulk modu- below T(cid:48). From conservation of entropy S/T(T ) is also c lus and β is the volume expansion coefficient. We as- the average value of the underlying normal state γ (T) n sume that γan is doping independent and use V = 61 below T . Therefore the result above is consistent with c cm3/mol[10], B ∼ 0.80×108 mJ/cm3[13], and β(300K) a T-independent γ (T) for T < T . In addition, this n c ∼ 50×10−6 /K[14] to obtain a room temperature value value for γ (T) below T is close to its high temperature n c γan(300K) ∼ 12 mJ/mol K2 for each sample. To a value estimated above, and it is reasonable to assume very good approximation β(T) ∝ Cv(T)[12] and thus that for this sample γn(T) is T-independent over the en- γan(T) = [Cv(T)/Cv(300K)]2 · γan(300K). A plot of tire temperature range. Subtracting this constant term γan(T) is shown in the inset to Fig. 2(a). from γtot(x = 0.3) gives γph(x = 0.3), which we then fit After correcting for γan(T), the electronic term γ can withanine-termhistogramforthephononspectrum[15]. be determined at high temperatures where C is close Finally, subtracting ∆γph(0.3,0) and ∆γph(0.3,0.1) from v 3 (a-12)mol K) 5705 12060 100 200γ an300 V) 1250 d wave Density of States mJ 25 me ∆γ tot ( 0 ∆ ( 10 0 1 E/∆ 2 s + id wave 0.3 - 0 0T 5 0.3 - 0 13T -25 0.1 - 0 0T s wave (b) 150 100 0 0 10 20 30 40 -2 K) 125 50 Temperature (K) -1 ol 100 00 50 100 150 200 250 300 350 FIG.3: (Coloronline)Temperaturedependenceofthesuper- mJ m 75 xx == 00..31 cdoentedrumctininegdSga/pT ewxittrhacthteadtcbaylccuolamtepdarfirnogmtmheodeexlpseorfimtheentdaelnly- γ ( x = 0 sity of states (shown in the inset) given by Eqns. 1-3. 50 25 theelectronictermcomesfromtheobservationofsimilar 0 0 20 40 60 80 100 anomalouscurvaturebetween15and20Kinthefieldde- pendence ∆γ(H)=γ(H,T)−γ(0,T) shown in the inset Temperature (K) to Fig. 4(a). Since the phonon term is H-independent, FIG. 2: (Color online) (a) The directly measured raw differ- this anomalous curvature in ∆γ(H) can only be of elec- enceinspecificheatsbetweenthedopedsamplesandundoped reference in 0 and 13T fields. The inset shows the anhar- tronic origin, and may signal the presence of a second monic phonon term γan. (b) The electronic specific heat of energy gap as inferred by Mu et al[17]. Ba1−xKxFe2As2 for x = 0, 0.1 and 0.3. To determine the magnitude and temperature dependence of the superconducting gap ∆ for x = 0.3 (shown inFig.3)wefirstsubtractfromγ thesmallresidualγ(0) γph(x=0.3) gives γph(x=0) and γph(x=0.1). = 1.8 mJ/mol K2 and then match the corrected S/T The electronic specific heats of the three samples are with that calculated assuming the following models for shown in Figure 2(b). Above 150K, γ is at most only the density of states (see Fig. 3 inset): weakly T-dependent and almost independent of doping. s-wave At low temperatures γ for the x = 0 and 0.1 samples (cid:112) is heavily reduced by factors of ∼ 11 and 5 respectively N(E)=E/ E2−∆2 (1) duetotheopeningofaspindensitywave(SDW)gapbe- low T ∼ 136K, and increases as ∼ 20×10−6T3 mJ/mol d-wave 0 K2 in the range 40 − 110K. Band splitting and signs of 1 (cid:88) (cid:112) partial gapping of the Fermi surface have been observed N(E)= E/ E2−∆2cos22θ (2) N θ intheSDWstateofBaFe As byangle-resolvedphotoe- θ 2 2 mission spectroscopy[16]. γ for the x = 0.3 sample is and s+id-wave dominated by the large superconducting anomaly with ∆γ(Tc) ≈ 48 mJ/mol K2, a normal-state γN(0) of about N(E)= 1 (cid:88)E/(cid:112)E2−0.98∆2cos22θ−0.02∆2 (3) 47 mJ/mol K2 and γ(0) = 1.8 mJ/mol K2 . Measure- N θ θ ments on a more overdoped crystal with x = 0.4 by Mu et al.[17] show an even larger ∆γ(Tc) ≈ 100 mJ/mol K2 where the summations over θ are from 0 to 45◦ and Nθ and γN(0) ≈ 63 mJ/mol K2, implying a further growth is the number of θ values. Although such modelling is in the density of states with doping. For our x =0.3 too crude to pin down the exact nature of the gap, the samplethesuperconductingcondensationenergyU(0)= rapid increase in ∆ below 15K in the case of the as- 10.6 J/mol, as determined from (cid:82)Tc(S −S )dT, where sumed d-wave gap function, shows that nodes on the 0 n s S and S are the normal and superconducting state en- Fermi surface are incompatible with the T-dependence n s tropies respectively. In Fig. 2(b), the curvature in γ for of γ observed at low temperature, even in the presence x =0.3 between 10 and 20K is reduced compared to the ofweakpairbreaking. Thes+id-wavegapfunctionpro- raw ∆γtot data (Fig. 2(a)) by the phonon correction de- ducesamorereasonable∆(T). Thisfunctioncompletely scribed above. Evidence that the remaining curvature gaps the Fermi surface but is strongly anisotropic. Such in γ may reflect a genuine anomalous T-dependence of anisotropycouldarisefromthepresenceofmultiplegaps 4 -1-2 ol K) 150 13T (a)T) 112400 Hc1 x 104 235000 γγ(H) - (0) (mJ m --11-0550 25..50 0T H, H, H (c1cc2 12468000000 κHHcc2 x 102 51120050000κ 0.0 (a) -20 0 10 20 30 0 0 (b) 16 -1 K) 100 13T 40 14 -1 mol A) 30 λ 12 -2 m) 0) (mJ 5705 ξλ, ( 20 ξ/100 1/λ2 6810 λµ2 1/ ( S( 10 4 H) - 25 2 S( (b) 0 0 0 5 10 15 20 25 30 35 40 0 1T Temperature (K) 2. 0 -1 mol) 2.0 13T 11..05 2.5K FBfrIeaGe0..3eKn5:e0r.3PgFyoel2l∆yAcFsr2(yHsdt,aeTlrlii)vn:eed(aav)freCormargiteitdchaeml fiifixeeelldddssdHtaept,eenHpdaern,acmHeetoe,frastnhodef 0) (J 1.5 00..05 Gλ,inssubpuerrgfl-uLiadnddeanusiptayra∝m1e/tλer2κa;n(db)suLpoenrdcoonndpcuecnteitncrg1atcioonhc2edreepntche H) - F( 1.0 0 2 4 H6 (T8)1012 length ξ. F( 0.5 (c) tronic entropy with field (see Fig. 4(b)). 1T 0.0 (cid:90) T 0 10 20 30 40 50 ∆S(H,T)= ∆γ(H,T)dT (5) Temperature (K) 0 FIG. 4: (Color online) (a) Magnetic field dependent change The change in free energy is obtained by integrating the in electronic specific heat γ(H)−γ(0) vs temperature, in 1T entropy over temperature (see Fig. 4(c)). increments, from the data in the inset of Fig. 1. (Inset) En- largement of the 0 to 30K region. (b) Field dependence of (cid:90) T theelectronicentropy,S(H)−S(0),calculatedfrom(a)using ∆F(H,T)=− ∆S(H,T)dT +∆F(H,0) (6) Eqn.5. (c)Fielddependenceofthefreeenergy,F(H)−F(0), 0 calculatedfrom(b)usingEqn.6. (Inset)AfittoF(H)−F(0) ∆F(H,0) is determined from the condition that the su- at 2.5K using Eqn. 8. perconducting contribution to ∆F(H,T) tends to zero for T (cid:29) T . At each temperature, the field dependence c of the free energy is fitted to a theoretical expression de- on different sheets of the Fermi surface, or from an in- rived from the model of Hao and Clem[18] for an s-wave trinsically anisotropic gap(s). superconductor. Weturnnowtotheinformationcontainedinthemag- (cid:18) (cid:19) aφ eβH netic field dependence of γ. The inset to Fig. 1 shows ∆Fs,rev(H,T) = 32π20λ2Hln Hc2 (7) the suppression of the superconducting anomaly in magnetic fields from 1 to 13T in 1T increments. Because the = a Hln(a H) (8) 1 2 phononspecificheatisindependentofmagneticfield,the changeinelectronicspecificheatwithfieldisobtainedby The coefficients a and β are weakly field dependent and subtracting the zero field data from the data measured are given by a ∼ 0.77 and β ∼ 1.44 in the range 0.02 < in a field (see Fig. 4(a)). H/H < 0.3. A fit to the free energy at 2.5K is shown c2 in the inset to Fig. 4(c). The penetration depth, λ, and the upper critical field, ∆γ(H,T)=γ(H,T)−γ(0,T) (4) H , are determined directly from the fit parameters a c2 1 and a . Then using the following Ginsburg-Landau rela- 2 Integrating over temperature gives the change in elec- tions we extract the: critical field H2 = (φ /4πλ2)H , c 0 c2 5 √ Ginsburg-Landau parameter κ = H /H 2, lower crit- [3] J.W.Loram,J.L.Luo,J.R.Cooper,W.Y.Liang,and c2 c ical field H = (φ lnκ)/(4πλ2), and superconducting J. L. Tallon, Physica C 341–348, 831 (2000). c1 0 coherence length ξ = (φ /2πH )1/2. The temperature [4] J. W. Loram, J. Luo, J. R. Cooper, W. Y. Liang, and 0 c2 J. L. Tallon, J. Phys. Chem. Solids. 62, 59 (2001). dependenciesofthesequantitiesisplottedinFig.5. The [5] J. W. Loram, J.L. Tallon, and W.Y. Liang, Phys. Rev. valuesshownarepolycrystallineaverages. Thelargeκ≈ B 69, 060502(R) (2004). 130 indicates the strong type II nature of this material. [6] J. L. Tallon, J. G. Storey, and J. L. Loram, Our Hc2 values are very similar to those obtained from arXiv:0908.4428 (2009). radio frequency penetration depth measurements on a [7] J. W. Loram, J. Phys. E 16, 367 (1983). single crystal with x = 0.45[19], and the value we ob- [8] H. Chen, Y. Ren, Y. Qiu, W. Bao, R. H. Liu, G. Wu, tain for λ(0) ≈ 260nm is similar to those measured by T. Wu, Y. L. Xie, X. F. Wang, Q. Huang, et al., EPL 85, 17006 (2009). infrared spectroscopy[20] and tunnel diode resonator[21] [9] J. K. Dong, L. Ding, H. Wang, X. F. Wang, T. Wu, techniques. G. Wu, X. H. Chen, and S. Y. Li, New J. Phys. 10, In summary, above 150K the electronic specific heats 123031 (2008). for the three samples are large and almost identical. For [10] M.Rotter,M.Tegel,I.Schellenberg,F.M.Schappacher, the x = 0 sample there is a large and almost first order R. Pöttgen, J. Deisenhofer, A. Gu¨nther, F. Schrettle, anomalyattheSDWtransitionatT =136K,whilstthe A. Loidl, and D. Johrendt, New J. Phys. 11, 025014 0 corresponding anomaly for the x = 0.1 sample at T = (2009). 0 135K is smaller and broader and more closely resembles [11] K. Selte, A. Kjekshus, and A. F. Andresen, Acta Chem. Scand. 26, 3101 (1972). a second order phase transition. At low temperatures, γ [12] N.W.AschcroftandN.D.Mermin,Solid State Physics. for these two samples is strongly reduced by the SDW (Holt Saunders, 1976). gapbyfactorsof11and5forx=0and0.1respectively. [13] S.A.J.Kimber,A.Kreyssig,Y.-Z.Zhang,H.O.Jeschke, Inthex=0.3samplethelargesuperconductinganomaly R. Valenti, F. Yokaichiya, E. Colombier, J. Yan, T. C. and associated value of S/T(T ) shows that the under- Hansen, T. Chatterji, et al., Nature Mat. 8, 471 (2009). c lying normal state γ at low temperature is close to its [14] S.L.Bud’ko,N.Ni,S.Nandi,G.M.Schmiedeshoff,and hightemperaturevalue. Thissuggeststhatasxreduces, P. C. Canfield, Phys. Rev. B 79, 054525 (2009). [15] J. W. Loram, K. A. Mirza, J. R. Cooper, and W. Y. the growth of the SDW gap and consequent reduction in Liang, Phys. Rev. Lett. 71, 1740 (1993). the density of states is responsible for the disappearance [16] L.X.Yang,Y.Zhang,H.W.Ou,J.F.Zhao,D.W.Shen, of superconductivity. The temperature dependence of γ B. Zhou, J. Wei, F. Chen, M. Xu, C. He, et al., Phys. (x = 0.3) supports a nodeless superconducting gap func- Rev. Lett. 102, 107002 (2009). tionthatisstronglyanisotropicabouttheFermisurface, [17] G. Mu, H. Luo, Z. Wang, L. Shan, C. Ren, and H. H. possibly due to the presence of multiple gaps. Wen, Phys. Rev. B 79, 174501 (2009). WegratefullyacknowledgefundingfromtheEngineer- [18] Z.HaoandJ.R.Clem,Phys.Rev.Lett.67,2371(1991). [19] M. M. Altarawneh, K. Collar, C. H. Mielke, N. Ni, S. L. ing and Physical Sciences Research Council (U.K.) and Bud’ko,andP.C.Canfield,Phys.Rev.B78,220505(R) the Swiss National Science Foundation pool MaNEP. (2008). [20] G. Li, W. Z. Hu, J. Dong, Z. Li, P. Zheng, G. F. Chen, J.L.Luo,andN.L.Wang,Phys.Rev.Lett.101,107004 (2008). [21] R. Prozorov, M. A. Tanatar, R. T. Gordon, C. Martin, [1] J. Loram, K. A. Mirza, J. R. Cooper, W. Y. Liang, and H.Kim,V.G.Kogan,N.Ni,M.E.Tillman,S.L.Bud’ko, J. M. Wade, J. Supercon. 7, 243 (1994). and P. C. Canfield, Physica C 469, 582 (2009). [2] J.W.Loram,K.A.Mirza,J.R.Cooper,andJ.L.Tallon, J. Phys. Chem. Solids 59, 2091 (1998).