57Fe Mo¨ssbauer study of stoichiometric iron based superconductor CaKFe As : a comparison to KFe As 4 4 2 2 and CaFe As 2 2 7 1 0 Sergey L. Bud’ko∗, Tai Kong1, William R. Meier 2 Ames Laboratory US DOE and Department of Physics and Astronomy, Iowa State n a University, Ames, IA 50011, USA J Xiaoming Ma 5 1 Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China. ] n Department of Physics, South University of Science and Technology of China, Shenzhen, o Guangdong 518055, China c - Paul C. Canfield r p Ames Laboratory US DOE and Department of Physics and Astronomy, Iowa State u University, Ames, IA 50011, USA s . t a m - d n Abstract o c 57Fe M¨ossbauer spectra at different temperatures between ∼5 K and ∼300 [ K were measured on an oriented mosaic of single crystals of CaKFe As . The 4 4 1 data indicate that CaKFe4As4 is a well formed compound with narrow spectral v lines,notracesofother,Fe-containing,secondaryphasesinthespectraandno 4 static magnetic order. There is no discernible feature at the superconducting 0 transitiontemperatureinanyofthehyperfineparameters. Thetemperaturede- 1 pendenceofthequadrupolesplittingapproximatelyfollowstheempirical“T3/2 4 0 law”. . ThehyperfineparametersofCaKFe As arecomparedwiththoseforKFe As 1 4 4 2 2 measuredinthiswork, andtheliteraturedataforCaFe As , andwerefoundto 0 2 2 7 be in between those for these two, ordered, 122 compounds, in agreement with 1 the gross view of CaKFe As as a structural analog of KFe As and CaFe As 4 4 2 2 2 2 v: that has alternating Ca - and K - layers in the structure. i X Keywords: superconductors, M¨ossbauer spectroscopy, hyperfine parameters r a ∗Correspondingauthor Email address: [email protected](SergeyL.Bud’ko) 1currentlyatDepartmentofChemistry,PrincetonUniversity Preprint submitted to Journal of Physics and Chemistry of Solids January 17, 2017 1. Introduction The discovery of iron-based superconductors [1] was followed by an out- pouring of theoretical and experimental studies of those and related materials [2, 3, 4, 5]. Of these studies some were addressing specific details of the su- perconducting and the associated vortex state, whereas others were targeted comprehensive characterization of the general physical properties of iron-based superconductorsandrelatedmaterials. M¨ossbauereffectspectroscopyiswidely accepted as one of the most sensitive techniques in terms of energy resolution. Historically, this technique has been applied to studies of superconductors for decades,[6] however its sensitivity specifically to the superconducting state is ambiguous. [7]ItisquitenaturalthatM¨ossbauerspectroscopywaswidelyused for studies of iron-based superconductors that naturally contain the common M¨ossbauer nuclide, 57Fe, in the structure,[8, 9, 10, 11, 12]: no additional dop- ing with 57Fe (that can alter the properties of the material) is needed, and use of partially enriched Fe was required in only few, very specific cases. This techniquewasverysuccessfulinaddressingtheevolutionofmagneticorder,[13] structuralphasetransitions,[14]andphasepurity[15,16,17]inthesematerials. Recently,anewfamilyofiron-basedsuperconductorswithratherhighsuper- conducting transition temperature, T ∼ 31−36 K, has been discovered. [18] c It was found that structurally ordered CaAFe As (1144) compounds can be 4 4 formedforA=K,Rb,Cs,andthekeytotheformationisthedifferenceinionic sizesbetweentheCaandtheAion. Thisfamilyisnota(Ca A )Fe As solid 1−x x 2 2 solution, where the Ca and A ions randomly occupy a single crystallographic site. [19] Along the c-axis, the Ca and A ions in this family form alternating planesthatareseparatedbytheFe-Asslabs(Fig. 1). Inessence,theCaAFe As 4 4 structure is similar to the CaFe As structure, just with layer by layer segrega- 2 2 tion of the Ca and A ions. The ordering of the layers causes a change of the space group from I4/mmm to P4/mmm and the Fe site in the 1144 structure hasitspointsymmetryloweredtoorthorhombic(fromthetetragonalinthe122 structure). The1144structurewasalsofoundforSrAFe As (A=Rb, Cs)[18] 4 4 and EuAFe As (A = Rb,Cs). [21, 22] 4 4 We were able to grow single-crystalline, single-phase samples of CaKFe As 4 4 and measure their anisotropic thermodynamic and transport properties. [23] The data indicated that CaKFe As is an ordered stoichiometric superconduc- 4 4 tor with T = 35 K and no other phase transition for 1.8 K ≤ T ≤ 300 K. It c appeared to have properties very close to what is referred to as an optimally- doped, on a generalized phase diagram, iron-based superconductor. Being an ordered stoichiometric compound with a high value of T and a single crystal- c lographic Fe site, CaKFe As offers an exceptional opportunity to determine 4 4 whether any of the hyperfine parameters exhibit an anomaly at superconduct- ing transition. Additionally, this time with a local probe, we can evaluate the phase purity (in terms of possible Fe-containing phases) of the samples and the presenceofstaticmagneticmomentontheironsite. Furthermore, wecancom- pare the temperature dependencies of the hyperfine parameters with those of the closely related compounds, CaFe As and KFe As . 2 2 2 2 2 In this work we will present results of the 57Fe M¨ossbauer spectroscopy measurements between ∼ 5 K and ∼ 300 K on a mosaic of the oriented sin- gle crystals of CaKFe As and will compare the results with similar sets of 4 4 data for CaFe As and KFe As . Whereas there are available literature data 2 2 2 2 for CaFe As , [14, 24, 25] the published M¨ossbauer data for KFe As appar- 2 2 2 2 ently is limited to three temperature points [13] so we have chosen to collect a comprehensive set of data for KFe As as a part of this work. 2 2 2. Experimental CaKFe As single crystals were grown by high temperature solution growth 4 4 out of excess FeAs. The growth and basic physical properties are described in detail in Ref. [23]. The crystals were screened as described in Ref. [23] to avoidpossiblecontaminationsbyCaFe As andKFe As minorityphases. The 2 2 2 2 superconducting transition in the CaKFe As crystals used for the M¨ossbauer 4 4 study was sharp with T ∼35 K (Fig. 2). c KFe As single crystals were also grown using a high-temperature solution 2 2 growthtechnique. Startingelementswerepackedinanaluminafrit-disccrucible set [26] with a molar ratio of K:Fe:As = 8:2:10. The crucible set together with thematerialwerethenweldedinaTatubeandsealedinasilicaampouleunder a partial Ar atmosphere. A detailed drawing of such an assembly can be found in Ref [27]. The ampoule was slowly heated up to 920◦ C over ∼40 hours, held at 920◦ C for 10 hours, quickly cooled to 850◦ C over 3 hours and then slowly cooled to 700◦ C over 3 days. At 700◦ C, the silica ampoule was inverted and decanted in a centrifuge. Remaining solution (primarily K-As) on the single crystals was rinsed off using ethanol. The resulting crystals had high residual resistivityratio(ρ(300K)/ρ(5K)∼500)andT valuesconsistentwithotherhigh c quality KFe As crystals. [28, 29] 2 2 M¨ossbauer spectroscopy measurements were performed using a SEE Co. conventional, constant acceleration type spectrometer in transmission geome- try with a 57Co(Rh) source kept at room temperature. Both for CaKFe As 4 4 and KFe As the absorber was prepared as a mosaic of single crystals held on 2 2 a paper disk by a small amount of Apiezon N grease. The gaps between the individual crystals were kept as small as possible. The mosaic had the c axis perpendicular to the disks and arbitrary in-plane orientation for each of the crystals. The c axis of the crystals in the mosaic was parallel to the M¨ossbauer γ beam. TheabsorberwascooledtoadesiredtemperatureusingaJanismodel SHI-850-5 closed cycle refrigerator (with vibration damping). The driver ve- locity was calibrated using an α-Fe foil, and all isomer shifts (IS) are quoted relative to the α-Fe foil at room temperature. The M¨ossbauer spectra were fit- tedusingeitherthecommercialsoftwarepackageMossWinn, [30]ortheMossA package [31] with both analyses giving very similar results. 3 3. Results and Discussion 3.1. CaKFe As 4 4 A subset of M¨ossbauer spectra for CaKFe As , taken at different temper- 4 4 atures, is shown in Fig. 3. The absorption lines are asymmetric, suggesting that each spectrum is a quadrupole split doublet with rather small value of the quadrupolesplitting, QS.Therearenoextrafeaturesobserved, confirmingthat the samples are single phase. The results of fits to these data are shown in Fig. 4. Thelinewidthofthespectra(Fig. 4d-FWHM)variesbetween∼0.23−0.26 mm/s and is consistent with well ordered crystals. None of the hyperfine pa- rameters has a detectable feature at T = 35 K that rises above the scattering c of the data or the error bars. Fig. 4a presents measured isomer shift (IS) which increases upon cooling. The isomer shift includes contributions from both the chemical shift and the second-order Doppler shift. The latter is known to increase convexly upon de- creasingtemperature,duetogradualdepopulationoftheexcitedphononstates, butshouldbeconstantatlowtemperature,becauseofthequantummechanical zero-point motion. The chemical shift should not depend on temperature. The main contribution to the temperature dependence of the isomer shift then is considered to be from the second-order Doppler shift, and is usually described by the Debye model: [32] 9k T (cid:18) T (cid:19)3(cid:90) ΘD/T x3dx IS(T)=IS(0)− B , (1) 2 Mc Θ ex−1 D 0 where c is the velocity of light, M is the mass of the 57Fe nucleus, and IS(0) is the temperature-independent part. For the isomer shift data in Fig.4a Debye fit yields Θ =370±9 K. D The quadrupole splitting increases with decrease of temperature (Fig. 4b). The behavior can be described reasonably well with the empirical “T3/2 law” [33],QS(T)=QS (1−βT3/2),whereQS(T)istemperaturedependentquadrupole 0 splitting, QS is its value at T = 0 K, β is a parameter that was found [33] to 0 varybetween1×10−5and7×10−5K−3/2. Inourcasethevalueofβ ≈1.6×10−5 K−3/2 falls within the expected range. Whereas the physics behind the “T3/2 law” is not fully understood (it is consideredthatthatitoriginatesfromthermalvibrationsofthelattice[34]),this relationdescribesreasonablywellthetemperaturedependenciesofQS observed in non-cubic metals. [33, 35, 36, 37] The spectral area under the doublet increases on cooling (Fig. 4c). The temperature dependence of the spectral area can also be fitted with the Debye model [32]: (cid:40) −3E2 (cid:34)1 (cid:18) T (cid:19)2(cid:90) ΘD/T xdx (cid:35)(cid:41) f =exp γ + , (2) k Θ Mc2 4 Θ ex−1 B D D 0 4 where f is the recoilless fraction, which is proportional to the area for a thin sample and E is the γ-ray energy. The estimate of the Debye temperature γ from the fit gives Θ = 247 ± 1 K, a value that is about 125 K less than D the value estimated by temperature dependence of IS. Although part of this discrepancycouldbeduetodeviationsfromthethinabsorberconditionsofthe measurements,itshouldbementionedthatsimilardifferenceswerefoundearlier instudiesofLu Fe Si ,FeSe Te and57FedopedYBa Cu O compounds. 2 3 5 0.5 0.5 2 3 6.8 [7, 38, 39] This discrepancy may be explained by the fact the area reflects the average mean-square displacements, whereas IS is related to the mean-square velocityoftheM¨ossbaueratom. Bothquantitiesmayrespondinadifferentway to lattice anharmonicities. The temperature dependent linewidth of the spectra is shown in Fig. 4d. Overall the linewidth increases by a few percent on cooling from room temper- ature to the base temperature. The observed spectral lines for CaKFe As are 4 4 somewhat narrower than those in CaFe As [14, 24] and KFe As (see below) 2 2 2 2 singlecrystalmeasurements,andmeasurablysharperthantheM¨ossbauerspec- tra lines in the substituted Ca(Fe Co ) As [40] that vary in the range 0.965 0.035 2 2 of 0.28 - 0.35 mm/s between room temperature and 5 K. This suggests that CaKFe As crystals used in this work are well ordered. 4 4 IntheAFe As (A=Ba,Sr,Ca,Cs,Rb,K)compoundsthepointsymmetry 2 2 (−4m2) and the location of the Fe site in the crystal structure constrains the principal axis of the local electric field gradient tensor to the c-crystalline axis; as a result, a doublet lines intensity ratio of 3:1 is expected for the mosaic with the c - axis parallel to the γ - beam. Per contra, in the CaKFe As the point 4 4 symmetry(2mm)oftheFesiteformallydoesnotimposesuchconstrain[18]and some deviation from the 3 : 1 ratio is expected. This said, the Fe - As1 and Fe -As2bondlengthsaswellasAs1-Fe-As1andAs2-Fe-As2bondsanglesare very similar and we would not expect significant difference from the AFe As 2 2 case. The experimentally observed room temperature ratio is ∼ 2.3 : 1, and it decreasesto∼1.9:1atthebasetemperature(Fig. 4e). Verysimilardeviations from the 3:1 ratio were observed for measurements on CaFe As single crystals 2 2 [14, 25, 41] and several possible reasons for the doublet lines intensity ratio being different from 3:1 were discussed, e.g. a thick absorber conditions of the measurements and some misorientation of the crystals that form the absorber mosaic. Thesamearguments,inadditiontothedifferentpointgroupsymmetry for Fe, are probably appropriate when considering the CaKFe As results. 4 4 3.2. KFe As 2 2 Fig. 5 shows a subset of M¨ossbauer spectra of KFe As taken at different 2 2 temperatures. The asymmetry is even less pronounced than in the CaKFe As 4 4 spectra above. Still, good fit of the data can be obtained by using a doublet with small quadrupole splitting. For KFe As , similarly to the CaKFe As , 2 2 4 4 the principal axis of the local electric field gradient tensor should be parallel to the c-crystalline axis and the doublet lines intensity ratio of 3:1 is expected. If the fits are performed with this ratio left as a free parameter, within the 5 error bars the expected A1/A2=3 is obtained for all temperatures. To reduce the uncertainty in particular, in the small values of quadrupole splitting, we repeated the fits with fixed the A1/A2 = 3 parameter. The results are shown in Fig. 6. In comparison with the data obtained on powders at three different temperatures, [13], our linewidth is smaller and values of the isomer shift are bigger, although the overall changes, ∆IS, from room temperature to the base temperatures are very similar. Thelinewidthanditstemperaturedependence(Fig. 6d)aresimilartothose observedforCaKFe As . Thetemperaturedependentisomershiftandspectral 4 4 area are well fit using the Debye model, as described above (Fig. 6a,c). These fits yield the values of Θ of 474±20 K (from IS(T)) and 325±7 K (from D temperature dependent spectral area). In comparison with CaKFe As , the 4 4 DebyetemperaturesarehigherinKFe As ,suggestingthatthelatticeisstiffer. 2 2 The values of quadrupole splitting (Fig. 6b) for KFe As are significantly 2 2 smaller than those for CaKFe As , moreover QS decreases with decrease of 4 4 temperature, as opposed to increase following the “T3/2 law” in CaKFe As . 4 4 Although the theoretical foundations of the empirical “T3/2 law” are not well understoodanddifferent(constant,vsT3/2)QS(T)behaviorhasbeenobserved for related (Ce FeCo Sb vs Ce Fe Sb ) materials,[36] this observation 0.35 3 12 0.98 4 12 in iron-arsenides calls for further studies. 3.3. Comparison of CaKFe As , KFe As , and CaFe As 4 4 2 2 2 2 Since, naively speaking, the CaKFe As structure can be viewed as being 4 4 costructed from the alternating slabs of CaFe As and KFe As structures, it 2 2 2 2 would be of use to compare the 57Fe hyperfine parameters of these three com- pounds. Whereas CaKFe As and KFe As do not exhibit static magnetic or- 4 4 2 2 der or a structural transition below room temperature, CaFe As is known to 2 2 be more complex. CaFe As grown out of Sn flux [42] exhibits concomitant 2 2 structural (high temperature tetragonal to low temperature orthorhombic) and magnetic (paramagnetic to low temperature antiferromagnetic) transitions at ≈ 173 K. [42, 43]. In the following we will refer to this sample as CaFe As - 2 2 AFM and use the hyperfine parameters from the single crystal work, Ref. [24]. IntheCaFe As samplegrownoutofFeAsflux,byjudiciouschoiceofannealing 2 2 / quenching conditions [41] we can stabilize low temperature ambient pressure collapsed tetragonal (cT) phase with the structural transition at ≈ 90 K. This sample will be referred in the following as CaFe As - cT, and the hyperfine 2 2 parameters from the ref. [14] will be used. ThehyperfineparametersfortheCaKFe As ,KFe As ,andCaFe As com- 4 4 2 2 2 2 pounds at room temperature and the base temperature are summarized in the Table 1. The temperature dependencies are presented in the plots below. The spectral linewidths of these compounds are very similar (Fig. 7). The smallest one is observed for CaKFe As , possibly pointing out to very well formed crys- 4 4 tals. The isomer shift in CaKFe As (Fig. 8). has values in between those for 4 4 KFe As and CaFe As . Note that the IS(T) for CaFe As - cT has a small 2 2 2 2 2 2 butdistinctfeatureassociatedwiththecTtransition. Similarly,thequadrupole splitting of CaKFe As (Fig. 9) has values in between the values for two other 4 4 6 compounds. Both, CaFe As - cT and CaFe As - AFM have clear features 2 2 2 2 associated with the cT and the structural / AFM transitions, respectively. It is curious (although it might be a mere coincidence) that QS(T) of CaKFe As 4 4 and the absolute values of QS(T) of CaFe As - AFM below the structural / 2 2 AFM transition are laying basically on top of each other. As for the overall temperature behavior, it appears that only for KFe As QS(T) decreases with 2 2 decrease of temperature. It would be of interest to see if different temperature dependences are observed in quadrupole frequencies when measured in these materials by 75As nuclear magnetic resonance. As for normalized (at the re- spective base temperatures) spectral areas (Fig. ??), again, CaFe As - cT 2 2 and CaFe As - AFM have anomalies at the corresponding transitions. The 2 2 data points for CaKFe As , CaFe As - cT and CaFe As - AFM (below the 4 4 2 2 2 2 structural/AFMtransition)are,grosslyspeaking,followingthesametempera- ture dependence. The data for KFe As are somewhat distinct, pointing either 2 2 to stiffer phonon spectrum or some additional contribution to the temperature dependence of the spectral area in this compound. 4. Summary The measurements of 57Fe M¨ossbauer spectra on oriented mosaics of sin- gle crystals of CaKFe As and KFe As were performed and the results were 4 4 2 2 compared with the literature data for CaFe As . 2 2 CaKFe As can be characterized as a well formed compound with narrow 4 4 spectral lines and no traces of other, Fe - containing, secondary phases in the spectra. There is no feature in hyperfine parameters at T and no indica- c tion of static magnetic order. The values of the 57Fe hyperfine parameters of CaKFe As areinbetweenthoseforKFe As andCaFe As ,inagreementwith 4 4 2 2 2 2 the gross view of CaKFe As as a structural analog of KFe As and CaFe As 4 4 2 2 2 2 with alternating Ca - and K - layers in the structure. The QS(T) generally follows the empirical “T3/2 law”. Debye fits of the temperature dependencies of the isomer shift and the spectral area yield the Debye temperatures of ∼370 K and ∼247 K respectively. KFe As has smaller quadrupole splitting and isomer shift in comparison 2 2 with CaKFe As and CaFe As . Its QS decreases slightly on cooling that dif- 4 4 2 2 fers from the generic behavior observed in many non-cubic metals. The Debye temperatures evaluated from the temperature dependent IS and spectral area are ∼474 K and ∼325 K respectively, these values being ∼100 K higher than those for CaKFe As . 4 4 Acknowledgments This work was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. The research was performed at the Ames Laboratory. Ames Laboratory is operated for the 7 U.S. Department of Energy by Iowa State University under Contract No. DE- AC02-07CH11358. In addition, W. R. M. was supported by the Gordon and Betty Moore Foundations EPiQS Initiative through Grant GBMF4411. References References [1] Y. Kamihara, T. Watanabe, M. Hirano, H. Hosono, J. Am. Chem. Soc. 130 (2008) 3296. [2] P.C.CanfieldandS.L.Bud’ko,Annu.Rev.Condens.MatterPhys.1(2010) 27. [3] D. C. Johnston, Adv. Phys. 59 (2010) 803. [4] G. R. Stewart, Rev. Mod. Phys. 83 (2011) 1589. [5] N.-L. Wang, H. Hosono and P.-C. Dai (eds.), Iron-based Superconductors. 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