c -axis charge gap and its critical point in the heavily doped Ba(Fe 1−x Co x ) 2 As 2
M. A. Tanatar, N.Ni, A. Thaler, S. L. Bud'ko, P. C. Canfield, R. Prozorov
aa r X i v : . [ c ond - m a t . s up r- c on ] J un c -axis charge gap and its critical point in the heavily doped Ba(Fe − x Co x ) As M. A. Tanatar, ∗ N. Ni,
1, 2
A. Thaler,
1, 2
S. L. Bud’ko,
1, 2
P. C. Canfield,
1, 2 and R. Prozorov Ames Laboratory, Ames, Iowa 50011, USA Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA (Dated: October 31, 2018)Temperature-dependent inter-plane resistivity, ρ c ( T ), was used to characterise the normal stateof the iron-arsenide superconductor Ba(Fe − x Co x ) As over a broad doping range 0 ≤ x < . ρ a ( T ), and magnetic susceptibility, χ ( T ), takenin H ⊥ c , as well as Co NMR Knight shift, K , and spin relaxation rate, 1 /T T . The inter-planeresistivity data show a clear correlation with the NMR Knight shift, assigned to the formationof the pseudo-gap. Evolution of ρ c ( T ) with doping reveals two characteristic energy scales. Thetemperature of the cross-over from non-metallic, increasing on cooling, behavior of ρ c ( T ) at high-temperatures to metallic behavior at low temperatures, T ∗ , correlates well with an anomaly in allthree magnetic measurements. This characteristic temperature, equal to approximately 200 K inthe parent compound, x =0, decreases with doping and vanishes near x ∗ ≈ x ≥ . T ∗ , with metallic behavior of ρ c ( T ) found above thelow-temperature resistivity increase. The characteristic temperature of this charge-gap formation, T CG , vanishes at x CG ≃ T -linear, ρ c ( T ) close to x CG and super-linear T -dependence for x > x CG . None of these features are evident in the in-plane resistivity ρ a ( T ). For doping levels x < x CG , χ ( T ) shows a known, anomalous, T -linear dependence, whichdisappears for x > x CG . These features are consistent with the existence of a uniaxial charge gap,accompanying formation of the magnetic pseudogap, and its critical suppression with doping. Theinferred c -axis charge gap reflects the three-dimensional character of the electronic structure and ofthe magnetism in the iron arsenides. PACS numbers: 74.70.Dd,72.15.-v,74.25.Jb
The metallic state of the, until recently, only knownhigh temperature superconductors, the compounds basedof Cu-O elements and frequently referred to as thecuprates [1], is characterized by a plethora of anomalies.At low doping levels, anomalous behaviours are foundin the temperature-dependent resistivity, magnetization,NMR Knight shift and relaxation rate, as well as in spec-troscopic data [2]. These behaviours are consistent witha decrease in the density of states at low temperatures,usually assigned with pseudogap formation. The phe-nomenology and k -space distribution of the pseudogapin the cuprates is now well established [3], however, itsmicroscopic origin is still debated [4]. Main theories andexperiments link it to two neighboring phases, an antifer-romagnetic Mott-insulator, with pseudogap arising dueto exotic magnetism [5], or to a superconducting phase,as an effect of the preformed superconducting pairs [6].The pseudogap is universally observed in both hole andelectron [7] doped cuprates, though it is much more pro-nounced in the former.Discovery of superconductivity with high critical tem-peratures in FeAs-based materials [8], breaking themonopoly of the cuprates, naturally raises the questionabout the common features of the two families [9]. Itfuels the hopes that one day the enigmatic mechanism ofhigh temperature superconductivity will be understood.One of the important features to understand from suchcomparison, is a possible link between superconductivityand the pseudogap. Features consistent with pseudogap are indeed ob-served in the hole doped RFeAsO [10–14] (R= rare earth,1111 compounds in the following). A clearly decreaseddensity of states is found in ARPES measurements in(Ba,K)Fe As (BaK122 compounds in the following) [15].Because the parent compounds of iron pnictides are met-als, the pseudogap here is believed to arise from nestinginstability [16].On the contrary, the experimental situation in electrondoped Ba(Fe − x Co x ) As (BaCo122 in the following) isless clear. NMR studies suggest the existence of a pseu-dogap over the whole doping range, from magneticallyordered parent compound to overdoped superconductor,with a characteristic temperature of 560 K ±
150 K at op-timal doping [17]; ARPES found a tiny feature just abovethe superconducting T c [18], whereas the in-plane resis-tivity does not reveal any pseudogap-like features [19]and is well described in a broad composition range by asum of T -linear and T -contrinutions [20].We have recently undertaken extensive anisotropicelectrical resistivity measurements on parent and opti-mally doped Ba(Fe − x Co x ) As [21–23]. In addition toa small ac -anisotropy, we found different temperature de-pendencies of the in-plane and inter-plane electrical re-sistivity. Here we report a systematic study of the evolu-tion of the inter-plane resistivity with doping. We showthat the anomalies in the inter-plane resistivity reflect theexistence of the enigmatic pseudogap state in BaCo122.Clear correlation with NMR measurements in BaCo122as a function of doping, [24] and the lack of any associ-ated features in the in-plane transport, suggest uniaxialsymmetry of the pseudogap.Tracking the evolution of the characteristic featuresof the temperature-dependent inter-plane resistivity withdoping we found a critical concentration, x CG ≈ T -linear increase at high tempera-tures. At the critical concentration, the ρ c ( T ) is veryclose to linear. This evolution of the inter-plane electri-cal resistivity suggests a (quantum) critical point [20, 25]on the edge of the pseudogap state. EXPERIMENTAL
Single crystals of BaFe As doped with Co were grownfrom a starting load of metallic Ba, FeAs and CoAs, asdescribed in detail elsewhere [19]. Crystals were thickplatelets with sizes as big as 12 × × and large facescorresponding to the tetragonal (001) plane. The actualcontent of Co in the crystals was determined with wave-length dispersive electron probe microanalysis and is the x -value used throughout this text.In our study of resistivity anisotropy inBa(Fe − x Co x ) As , undoped x =0 [22] and opti-mally doped x =0.074 [21], we have found that specialcare must be taken for measurements in configurationswith current along the tetragonal c -axis so as to avoideffects associated with the exfoliation of the samples.Cutting and shaping into transport samples inevitablyintroduces cracks, which affect the effective geometricfactors of the samples and, in case the cracks aredeep, can produce admixture of the in-plane resistivitycomponent. A strong tendency to exfoliate prevents thecutting of samples with c ≫ a . This limitation putssevere constraints on the measurement technique.Samples for electrical resistivity measurements withcurrent flow along the tetragonal c axis ( ρ c ) were cutinto (0.3-0.7) × (0.3-0.7) × (0.1-0.5)mm ( a × b × c ) slabs.All sample dimensions were measured with an accuracyof about 10%. Contacts to the samples were made byattaching silver wires using ultrapure tin, resulting inan ultra low contact resistance (less than 10 µ Ω) [26].Measurements of ρ c were made in the two-probe sam-ple configuration. Contacts were covering the whole ab plane area of the c -axis samples. A four-probe schemewas used to measure the resistance down to the contactto the sample, i.e. the sum of the actual sample resistance R s and contact resistance R c was measured. Taking intoaccount that R s ≫ R c , contact resistance represents aminor correction of the order of 1 to 5%. This can bedirectly seen for superconducting samples [21, 26, 27] attemperatures T < T c , where R s =0 and the measured resistance represents R c .The drawback of the measurement on samples with c ≫ a is that any inhomogeneity in the contact resis-tivity or internal sample connectivity admixes in-planecomponent due to redistribution of the current. To min-imize this effect, we performed measurements of ρ c on atleast 5 samples of each compositions. In all cases we ob-tained qualitatively similar temperature dependences ofthe electrical resistivity, as represented by the ratio of re-sistivities at room and low temperatures, ρ c (0) /ρ c (300).The resistivity value, however, showed a notable scatterand at room temperature was typically in the range 1to 2 mΩcm. For the sake of comparison we selected thesamples with the temperature dependence of resistivityleast similar to that of ρ a ( T ). The value of resistivity forthese samples at room temperature is shown as a func-tion of doping in the top panel of Fig. 1. Typically, thesesamples had the lowest value of electrical resistivity, asdescribed in detail in Ref. 21. This is important sincepartial exfoliation increases resisitivity values [21]. Asa best demonstration of the correctness of our measure-ments, thermal conductivity measurements in the normalstate for samples with x =0.127, accessed by the applica-tion of magnetic field, found Wiedemann-Franz law tobe obeyed in T → quantitative coinsid-ence of two independent measurements is very important,because cracks can be partially transparent for phononsand thus affect thermal and electrical transport in a dif-ferent way, leading to gross extrinsic Wiedemann-Franzlaw violation [29]. The evolutions of the inter-plane resis-tivity at room temperature, ρ (300 K ), and of the residualresistivity ratio, ρ c (0) /ρ (300 K ), with doping are summa-rized in Fig. 1. The resistivity value at room temperaturefor most compositions stays in the range 1 to 1.5 mΩcm,with doping it decreases to approximately 0.5 mΩcm. Forseveral x compositions we were not able to find crystalswith resistivity values lower than 2 mΩcm, despite thefacts that (1) the evolution of the temperature-dependentresistivity for these samples followed the general trend,(2) close in x compositions show usual resistivity values.This limits the accuracy of the absolute ρ c value deter-mination by approximately a factor of two.Samples for electrical resistivity measurements withcurrent flow along the [100] a -axis in the tetragonal plane( ρ a ) were cut into bars of (2 − × (0 . − . × (0 . − . ( a × b × c ). Measurements of ρ a were made in bothstandard 4-probe and 2-probe configurations and gaveidentical results, see Ref. [26 and 27]. Electrical resis-tivity of the samples at room temperature is shown as afunction of doping in Fig. 2. Error bar represent statis-tisal standard deviation for at least 5 samples of eachcomposition. The in-plane resistivity monotonically de-creases from 270 µ Ω.cm in the parent compound to about100 µ Ω.cm in the heavily overdoped composition with x =0.48. The magnitude of ρ a (300) is in good agreementwith previous report over a narrower doping range [30]. c ( K ) [ m c m ] X WDS c ( ) / c ( K ) FIG. 1. Room-temperature inter-plane resistivity, ρ c (300 K ),of Ba(Fe − x Co x ) As as a function of doping (top panel).Lower panel shows doping dependence of the ratio of re-sistivities at low temperatures and at room temperature, ρ c (0) /ρ c (300 K ). Residual resistivity ratio shows a rapid increase in therange where the Fermi surface topology change (Lifshitstransition) happens (at x ≈ x =0.05 and then decreases towards minimumclose to x =0.1. With further doping the ratio increases,the effect which mainly comes from a decrease of resis-tivity at room temperature.The magnetization measurements were performed oncleaved samples to minimize the risk from small amountof surface flux. Samples typically had total mass of 10to 20 mg. Measurements were performed in a standardMPSM SQUID magnetometer in a field of 5 T. Unlessspecially mentioned, magnetization measurements wereperformed in configuration H ⊥ c . For a composition x =0.325 measurements were also performed with H k c .They found essentially no anisotropy, similar to our pre-vious study [19]. a ( K ) [ m . c m ] Ames Orsay X WDS a ( ) / a ( K ) FIG. 2. Room-temperature in-plane resistivity, ρ a (300 K ),of Ba(Fe − x Co x ) As as a function of doping (top panel).Red stars show resistivity values taken from Ref. 30. Lowerpanel shows doping dependence of the resistivity ratio, ρ a (0) /ρ a (300 K ). RESULTS
In Figs. 3 and 4 we present evolution of thetemperature-dependent resistivity with doping. Theinter-plane resistivity (top panel, Fig. 3) of the par-ent compound decreases sharply below T SM , similar tothe in-plane resistivity (bottom panel, Fig. 3). In theinter-plane resistivity the decrease at T SM =135 K is pre-ceded with resistivity maximum at T ∗ ≈
200 K (shownwith arrow in Fig. 3). With doping, the decrease of ρ c ( T ) below T SM turns into an increase (as seen forsamples with x =0.038 to 0.058), similar to the behav-ior of ρ a ( T ), which shows two anomalies due to splitstructural/magnetic transition [19]. This change near x ≈ ρ c ( T ) at T ∗ remains ofthe same crossover type and does not follow resistivity x =0.166 x =0.00 T [K] c / c ( K ) a / a ( K ) x =0.166 x =0.00 T [K]
FIG. 3. Temperature dependence of the inter-plane resistivity, ρ c , normalized by its value at room temperature ρ c (300 K ), forsamples of Ba(Fe − x Co x ) As with x ≤ .
166 (slightly abovethe concentration boundary for the superconducting dome)as shown in the figure (top panel). The curves are offset toavoid overlapping. Arrows show a position of the resistivitymaximum, presented as a function of dopant concentrationin the T − x phase diagram (see Fig. 5 below), cross-arrowsshow position of the resistivity minimum, T CG , appearing athigh doping levels. Bottom panel shows doping evolution ofthe temperature-dependent in-plane resistivity, ρ a , normal-ized by room-temperature value ρ a (300 K ). Arrows show po-sitions of T ∗ and T CG as determined from ρ c ( T ), revealing nodiscernible features in the in-plane resistivity. behavior below T SM (either increase or decrease), sug-gesting that it is an independent feature. At dopingclose to optimum, x opt ≈ ρ a ( T ) and ρ c ( T )], and the temperature dependenceof the inter-plane resistivity is dominated by the maxi-mum at T ∗ and superconducting transition.At the highest doping shown in Fig. 3, x =0.166, whenthe superconductivity is suppressed, a new feature ap-pears in the temperature-dependent interplane resistiv-ity: a shallow resistivity minimum appears at T CG > T ∗ .In Fig. 4 we present the evolution of the resistivity forhigher Co concentrations, starting from those on the x =0.475 x =0.127 c / c ( K ) T [K] x =0.475 x =0.127 a / a ( K ) T [K]
FIG. 4. Temperature dependence of the inter-plane resistivity, ρ c , normalized by its value at room temperature ρ c (300 K ),for samples of Ba(Fe − x Co x ) As with high doping levels x ≥ T CG , and maxi-mum, T ∗ , respectively. Bottom panel shows evolution of thetemperature-dependent in-plane resistivity, ρ a , normalized byroom-temperature value ρ a (300 K ). Arrows show positions of T CG and T ∗ as determined from the inter-plane resistivitytemperature dependence, revealing no discernible features inthe in-plane resistivity. over-doped side of the superconducting dome, x =0.127.The top panel shows the inter-plane resistivity, the bot-tom panel shows the in-plane resistivity, which showsmetallic behavior for all compositions. Cross-arrows inthe top panel show the position of the high-temperaturecross-over from the metallic to non-metallic temperaturedependence of the inter-plane resistivity at T CG . Cross-arrows in the bottom panel show the same characteristictemperatures with respect to the temperature-dependentin-plane resistivity finding no discernible features in the ρ a ( T ) curves.We summarize the doping evolution of the main fea-tures of the temperature-dependent resistivity in thephase diagram, Fig. 5. The lines of the superconduct-ing, T c , structural, T S and magnetic, T M transitions are T CG T*T S T M T c X WDS [Co, %] T [ K ] FIG. 5. Temperature-doping phase diagram ofBa(Fe − x Co x ) As as determined from inter-plane re-sistivity measurements. Inset shows comparison of T ∗ and T CG , corresponding to the maxima amd minima in ρ c ( T ),with T PG as found in NMR study by fiting the temperature-dependent Knight shift [24, 33]. Arrow in the inset showsa minimum estimate for T CG for the border composition x =0.127. discernible in both in-plane [19] and inter-plane resistiv-ity. The lines corresponding to maxima, T ∗ , and minima T CG of the temperature-dependent inter-plane resistivityfind no correspondence in the temperature dependenceof the in-plane transport.This phase diagram suggests existence of a critical con-centration, at which charge gap vanishes. Interestinglyenough, at the concentration close to critical, x CG ≃ x =0.313 (red curve in the top panel of Fig. 4)for T >
20 K. For higher x , the temperature-dependentresistivity develops positive curvature, and can be reason-ably described by a sum of T -linear and T contibutions, ρ c ( T ) = ρ + AT + BT , similar to in-plane transport[20], as shown in the top panel of Fig. 3 for samples with x =0.343 and x =0.370.In Fig. 6 we compare the inter-plane resistivity withearlier evidence of the pseudogap in the electron-dopediron arsenides: the temperature dependence of the CoNMR Knight shift K and T -normalized NMR relaxationrate, T T , as measured in Ref. 24. We recall that, ina simple metal, both K and T T should be tempera-ture independent. In contrast, both Knight shift andrelaxation rate data in Ba(Fe − x Co x ) As are stronglytemperature-dependent. In the parent compound, x =0, Co x=0% c / c ( K ) Co x=4% NMR x=4.2% c Co x=8% NMR x=7.4% c T [K]
Co x=10.5% NMR x=10.8% c K K K [ % ] K K T 1/T T T T / T T [ s - K - ] FIG. 6. Comparison of the temperature-dependent in-terplane resistivity ρ c (solid lines, left scale) with thetemperature-dependent Co NMR Knight shift K ( T ) (solidsymbols) and relaxation rate, 1 /T T , (open symbols) fromRef. [24] (two right scales) for BaFe As (top left panel) andBa(Fe − x Co x ) As with x=0.04 (top right panel), x=0.074-0.08 (bottom left panel) and x=0.105-0.108 (bottom rightpanel). A broad maximum in the temperature dependenceof the inter-plane resistivity clearly correlates with pseudogapfeatures in NMR measurements: a crossover slope change in K ( T ) and the onset of a low-temperature rapid rise in 1 /T T . K ( T ) shows an increase with temperature (seen in allcompositions), with a mild slope change around 210 K.On the other hand, T T slightly increases on cooling be-low 200 K on approaching the temperature of the coupledstructural-magnetic transition, T SM = 135 K. These twofeatures in K ( T ) and T T vs T are close in temperatureto a shallow maximum in ρ c ( T ) at around 200 K, pre-ceding a sharp drop of resistivity at T SM .This correlation between the features in thetemperature-dependent NMR Knight shift and theinter-plane electrical resistivity becomes clearer withincreasing Co doping. The slope change in the Knightshift becomes more pronounced and, for a compositionwith x =0.105, it shifts down to ∼
100 K. In both NMRmeasurements and in the inter-plane resistivity thefeatures remain of a broad crossover type, with difficultto define characteristic temperatures. The resistivitymaximum is a better defined feature, though it is stillbroad and its location for several samples studied foreach composition could be slightly affected by theadmixture of the in-plane resistivity. This admixturemay affect the ρ c ( T ) for the x =0.108 sample in Fig. 6, assuggested by its slight deviation from the series evolutionwith doping, top panel in Fig. 3. (Small jumps in thetemperature dependence are extrinsic and are caused by m o l [ - e m u / O e ] T [K]
Co-doping 0 0.038 0.114 0.135 0.238 0.270 0.290 0.313 0.343 0 fit d m o l e / d T ( K ) [ e m u / O e K ] x WDS [Co, %]
FIG. 7. (Color online) Top panel. Temperature-dependentmolar magnetic susceptibility, χ mole ( T ), measured in mag-netic field H ⊥ c = 5 T. The data for low dopings are fromRef. 19. On doping increase the slope of the T -linear increasein χ ( T ) (shown with orange line for pure composition x =0at T =250 K) decreases and for x =0.313 the dependence be-comes flat at T > ∼
150 K. Bottom panel. Doping evolutionof the slope of χ mole ( T ), dχ mole ( T ) /dT , at T =250 K. sample cracking during thermal cycle.)The linearly increasing NMR Knight shift [34] reflectsan unusual linear temperature-dependent static magneticsusceptibility, χ ( T ), [35–37]. This anomalous linear χ ( T )dependence was shown to go away at high doping levels,being replaced by a Curie-Weiss behavior of susceptibil-ity [35]. The magnitude of the Knight shift variation alsodiminishes for over-doped compositions, and it was sug-gested that the pseudo-gap feature disappears at criticalconcentration for superconductivity x SC ≈ < x ≤ .
166 was studied system-atically by Ni et al. [19] for both orientations of mag-netic field parallel and perpendicular to the tetragonal c -axis and found small anisotropy. Our new measure-ments for x ≥ H ⊥ c . We performed mea-surements with H k c only for sample x =0.343 and foundno anisotropy. As can be seen from Fig. 7, the slope ofthe T -linear portion in χ ( T ) gradually diminishes with x . The χ mole ( T ) curve for x =0.290 shows very smallbut still clearly discernible increase with T , though withthe slope notably smaller than the slope for x =0.270. For x =0.313 the increase of magnetic susceptibility with tem-perature is completely gone. Instead, χ ( T ) becomes tem-perature independent above 150 K. The Curie-Weiss in-crease of χ ( T ) on cooling at low temperatures for samplewith x =0.313 is most likely extrinsic, it is not observedfor samples with lower and higher doping, x =0.290 and x =0.343. On the other hand, the χ mole ( T ) dependencedoes not reveal any increase at high T for both x =0.313and two different samples of x =0.343.To quantify this evolution, in the bottom panel ofFig. 7 we show a slope of χ mole ( T ) at T =250 K as afunction of x . The dependence shows a dramatic changebetween x =0.290 and x =0.313, the same concentrationas x CG determined from inter-plane resistivity. We notethat since the crystals used in the inter-plane resistiv-ity and magnetization measurements are from the samebatches, there is minimal uncertainty in the concentra-tion comparison. Both inter-plane resistivity and mag-netic susceptibility show pronounced changes of behaviorbetween x =0.290 and x =0.313. For x > χ ( T ) for heavily dopedcompositions is similar to the early report [35], thoughwith notable difference in the concentration boundaries( x =0.125 in our notations vs 0.30). This discrepancymay be a result of poor composition control in earlycrystals. We would like to point out that at similar con-centration ∼ DISCUSSIONDoping evolution of the anisotropy
The electronic structure of Co-doped BaFe As is nowwell established to be three-diemnsional by various tech-niques [39–43]. However, evolution of the anisotropy withdoping was never studied in a systematic way. FromFig. 2 we can see that doping in the range from x =0to x =0.48 leads to an approximately 3 times decrease ofthe in-plane resistivity at room temperature, agreeing,within error bars, with the previous measurements [30].For ρ c , Fig. 1, the variation is approximately of the samemagnitude, keeping in mind an uncertainty of the factorof 2 for ρ c values. This suggests that the evolution ofthe anisotropy in a broad doping range is very gradual,and puts an upper bound of about a factor of two for theanisotropy change. Comparison of these numbers withthe existing band structure calculations [21, 22, 44–47]should be taken with a grain of salt, since variation ofthe position of the As atom in the lattice from the oneobtained in experiment to the one calculated from totallattice energy minimum [21, 22] brings the effect which byfar exceeds the total anisotropy variation. A general de-crease of both in-plane and inter-plane resistivities withdoping is suggestive that charge is actually donated intothe system, which does not go in line with suggestionsthat all doping can be treated as additional scattering[47].The anisotropy at low temperatures, important for theanisotropy of the upper critical field in the superconduct-ing state, is heavily affected by the structural/magnetictransition and by the pseudogap. We will discuss theseeffects in the next sections. Structural/magnetic ordering and inter-planeresistivity
Magnetic ordering below T SM , presumably of spin den-sity wave (SDW) nature [48], reconstructs the Fermi sur-face, opening a superzone gap on electron and hole pock-ets. This is seen as an increase of the in-plane resistivityin BaCo122 with x =0.025 to 0.058. The parts of theFermi surface which are not affected by the superzone(SDW) gap, enjoy a notably reduced inelastic scatteringin the magnetically ordered phase [23, 30, 49]. In the par-ent compound, in which elastic scattering is small, thisdecrease of scattering overcomes the loss of the carrierdensity so that the total conductivity increases below T SM . Since the inter-plane transport is determined bythe warped parts of the Fermi surface [21], least affectedby the SDW superzone gap, the inter-plane resistivityshould be affected much less by the SDW gap openingthan ρ a . This is indeed seen, in BaCo122, most clearlyfor sample with x =0.012. Here, the in-plane resistivityshows an intermediate behavior between pure and heav-ier doped compositions: whereas ρ a ( T ) increases imme-diately below T SM and then shows a shallow decrease toa much higher residual value than in pure samples, theinter-plane resistivity does not manifest a local maximumbelow T SM and the resistivity decrease is almost as steepas in pure crystals. The features in the temperature-dependent resistivity upon crossing structural and mag-netic transitions [19, 50] can be similarly resolved in in-plane and inter-plane transport, though structural tran-sition is always less pronounsed in ρ c ( T ). Maximum in the temperature-dependent inter-planeresistivity at T ∗ The decrease of the inter-plane resistivity below T ∗ shows a clear correlation with the NMR Knight shift,therefore we need to look for a common origin. Animportant observation is that in BaCo122 with x =0.08,Fig. 6, both the Knight shift and the inter-plane resistiv-ity at low temperatures, T < T ∗ , follow expectations ofa metal with temperature-independent density of states:the resistivity shows metallic decrease on cooling, andthe Knight shift is temperature-independent. Simultane-ously, the T T increase indicates slowing down of mag-netic fluctuations. This suggests that magnetic correla-tions may play an important role in the anomalies in allthree measurements. Same trend hold for sample with x =0.105, however, the features in NMR measurementsfade away with overdoping.In the NMR study of Ref. 17, the temperature-dependent Knight shift was fit using a two-componentmodel, with K = A + B ∗ exp ( − T P G /T ). At tem-peratures T ≪ T P G this crosses-over to a metallic be-havior with constant Knight shift detemined by the A term unaffected by the pseudo-gap. At T > T
P G bothterms become temperature-independent and we can ex-pect restoration of the metallic behavior with K = A + B .Fitting the temperature-dependent Knight shift, the au-thors determined T P G =560 K ±
150 K for optimallydoped BaCo122 samples, x =0.08 (with A=0.715% andB=0.244%), Ref. 17, and T P G =450 K for x =0.26 (withA=0.20% and B=0.23%). Assuming that the A and Bcoefficients represent partial DOS contributions of theungapped and gapped parts of the Fermi surface, respec-tively, we would expect that at temperatures of the orderof T P G /3 or so, which would give us a temperature in100 to 200 K range for optimal doping, we restore metal-lic resistivity temperature dependence, while resistivitydecrease with temperature would be observed at highertemperatures due to carrier activation. This is consistentwithin general trend in evolution of ρ c ( T ), but not ρ a ( T ).This would suggest that the pseudogap affects predomi-nantly the most warped parts of the Fermi surface.We need to notice though, that it is difficult to explainresistivity decrease above T ∗ solely by the existence ofa spin gap , as probed by NMR [34]. Activation of spinfluctuations in the metallic phase can only increase scat-tering of charge carriers, which is seen in in-plane trans-port. Decrease of the inter-plane resistivity, despite beingvery small, would require rather an increase of the carrierdensity by excitations over a charge gap . Minimum in the temperature-dependentinter-plane resistivity and charge gap
The importance of charge gap formation for non-metallic temperature dependence of ρ c above T ∗ is mostclearly seen from the temperature-dependent inter-planeresistivity for BaCo122 composition with 0 . ≤ x ≤ . T CG . The monotonic evolution of thecurves suggests that for lower dopings, x < T CG goes above the experimentally accessible range. Ifthis is true, the end of the temperature range of mono-tonic resistivity decrease on heating gives us an estimatefor a minimum value of charge gap for compositions with x ≤ T CG from the inter-plane re-sistivity measurements with T P G determined from fitting K ( T ) curves. Both measurements have very big errorbars, and yet they do not match well. This may suggestanother possibility, that a metallic temperature depen-dence of ρ c at high temperatures is only confined in somerange of dopings.The scenario with the existence of a semi-metalliccharge gap was invoked for an explanation of the T -linear magnetic susceptibility, with simultaneous strongtemperature-dependent Hall and Seebeck coefficients [30,31, 51]. In this model thermal activation of carriers overa narrow gap results in a carrier density increase withtemperature. This would naturally lead to a decrease ofthe inter-plane resistivity with temperature. We shouldnotice though that the magnitudes of the effects, nec-essary to explain temperature-dependent magnetization,by far exceed the magniture of the ρ c variation observedin our experiments. This is also true with respect to dop-ing evolution of the characteristic temperatures, T P G and T CG , Fig. 5, which do not connect gradually. Simultane-ously the linear rise in magnetization with temperaturedoes not coincide with resistivity maximum in our study,especially for pure BaFe As .Despite this clear discrepancy between the two sug-gested explanations for the temperature-dependent mag-netization and transport and our data, the effects inthe inter-plane resistivity and in the magnetization areclearly correlated. In addtion, determination of the char-acteristic pseudogap temperature T P G in NMR measure-ments is heavily model dependent, whereas the minimumin the temperature dependence of the inter-plane resistiv-ity, despite being boad, is rather well defined for x >
Critical concentration
We now turn to the evolution of ρ c ( T ) and magneticsusceptibility in the vicinity of x CG . The most remark-able observation here is that at x =0.313 the resistivityis faily linear over a broad temperature range from ap-proximately 400 K down to 20 K and saturates at lowertemperatures. For x =0.290 the dependence is also closeto T -linear with a shallow slope change at ∼
150 K. Fordoping with x > .
313 the ρ c ( T ) becomes superlinear,similar to ρ a ( T ), and its inelastic part can be reasonablydecribed as a sum of T -linear and T terms, as shownfor the curves x =0.343 and x =0.370. In general, evolu-tion of ρ c ( T ) with doping is reminescent of the one foundin systems on the verge of magnetic order and assignedto the existence of the magnetic quantum critical point.This observation suggests that the pseudogap is magneticin origin, and is accompanied by the charge gap, ratherthan the charge gap itself being responsible for anoma-lous electronic properties.On note, none of the anomalies in the magnetic prop-erties is clearly reflected in the in-plane transport. Thisunusual single-axis effect of the pseudogap on the resis-tivity suggests that the magnetic action is concentratedon a small fraction of the Fermi surface, and importantly,on the most warped part contributing mainly to the inter-plane transport. Origin of the pseudogap
The existence of two additional crossover lines in thephase diagram of Ba(Fe − x Co x ) As , as revealed bythe inter-plane resistivity, raises an interesting questionabout their origins. Strong anisotropy of the pseudogapmakes a scenario, in which the gap is due to supercon-ducting pairing of charge carriers, however without su-perconducting condensate formation, very unlikely. Wetherefore should consider the possibility that the pseu-dogap is arising due to either short range, or short-lived,magnetic correlations, or represents a partial gap in theelectronic structure.The magnetic structure of parent BaFe As is char-acterized by a stripe-type antiferromagnetic ordering, inwhich antiferromagnetic spin arrangement is typical fordirections both in the plane and between the planes,introducing three-dimensional magnetic Brillouin zone,poorly matching the Fermi surface. It is difficult to ex-pect pronounced anisotropy for this case. On the otherhand, if correlations seen by the inter-plane transportwere the same as those of the ordered phase, it would bedifficult to explain a pre-transition decrease of resistivitybelow T ∗ in Co-doped samples with x =0.037 to 0.058,with successive increase of resistivity below T SM . Thismay suggest that uniaxial anisotropy of the pseudo-gapcomes from magnetic fluctuations with a different char-acteristic wavevector. A situation like this, when fluc-tuations and ordering wavevector are not the same wasfound in some intermetallic and heavy fermion systems[52]. Indirect evidence for such a possibility comes fromthe fact that in a closely related EuFe As , antiferro-magnetic ordering of Eu moments happens between theplanes, while the Fe layer moments remain parallel in theplanes [53, 54]. Since this ordering is mediated by RKKYinteractions via conduction electrons, it suggests that thegeneralized spin susceptibility may have maxima, whichcorrespond to the existence of the inter-plane nesting.In closely related BaMn As , magnetism is of local mo-ment type, and the magnetic order is of usual AF G-type[55]. In EuRh As , commensurate and incommensuratespiral-like structures with propagation along the c -axisare found. [56] Although these compounds are differingin band structure and electron count, these observationsof different types of ordering may be suggesting that var-ious magnetic structures are not very different in energy.In the lack of any evidence for the existence of suchcorrelations in Co-doped BaFe As , we just speculatewhat consequences uniaxial character of the pseudogapmay have. This type of a pseudogap is impossible intwo dimensional cuprates, it is a direct consequence ofthe difference in the dimensionality of the electronic andmagnetic systems in the cuprates and in iron arsenides.If the link between the symmetry of the pseudogap andof the superconducting order parameter, as found in thecuprates [3, 57], is preserved in the iron arsenides, c -axispseudogap would correspond to a superconducting gaphaving maxima/minima at the poles. This scenario wasinvoked theoretically for explanation of unusual behaviorin the superconducting gap [58]. In experiment, varia-tion of the superconducting gap with polar angle is foundin inelastic neutron scattering in Ni doped compoundat optimal doping [59], with gap magnitude decreasingtowards the poles, and in penetration depth study ofBaNi122 [60]. It is directly revealed in the inter-planeheat transport study [28], as opposed to the in-planestudy [61].Finally we would like to point to a certain similarityin the critical behaviour of the inter-plane resistivity inBaCo122 and in CeCoIn . In CeCoIn , a true criticalbehavior at a field-tuned QCP [62, 63] with T -linear re-sistivity and violation of the Wiedemann-Franz law isobserved for transport along the tetragonal c -axis [64].Transport in the plane perpendicular to c -axis, despiteshowing unusual power law behavior, obeys the WF law[65]. CONCLUSION
Contrary to the in-plane electrical resistivity, whichaway from the domain of structural/magnetic order-ing shows monotonic metallic temperature dependence, inter-plane resistivity, ρ c ( T ), reveals anomalous fea-tures clearly correlating with features in the tempera-ture dependence of the the NMR Knight shift and spin-relaxation rate, assigned to the formation of the pseudo-gap. Evolution of ρ c ( T ) with doping reveals two char-acteristic energy scales, of the the resistivity maximum(seen for compositions 0 ≤ x < ∼ .
2) and resistivity min-imum at a tempearture T CG , seen for 0 . ≤ x < x c , x c ≈ ρ c is close to lin-ear close to x CG and super-linear for x > x CG . Noneof these features are evident in the in-plane resistivity ρ a ( T ). For doping levels x < x CG , χ ( T ) shows a known,anomalous, T -linear dependence, which disappears for x > x CG . These features are consistent with the exis-tence of a uniaxial charge gap, accompanying formationof the magnetic pseudogap, and its critical suppressionwith doping. This evolution suggests existence of criticalpoint for pseudogap order. The superconducting dome isconfined inside the pseudo-gap dome. ACKNOWLEDGEMENTS
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