Effect of controlled point-like disorder induced by 2.5 MeV electron irradiation on nematic resistivity anisotropy of hole-doped (Ba,K)Fe 2 As 2
M. A. Tanatar, Erik I. Timmons, M. Ko'nczykowski, O. Cavani, Kyuil Cho, Yong Liu, T. A. Lograsso, R. Prozorov
EEffect of controlled point-like disorder induced by 2.5 MeV electron irradiation onnematic resistivity anisotropy of hole-doped (Ba,K)Fe As M. A. Tanatar,
1, 2
Erik I. Timmons,
1, 2
M. Ko´nczykowski, O. Cavani, Kyuil Cho, Yong Liu, T. A. Lograsso,
1, 4 and R. Prozorov
1, 2 Ames Laboratory, USDOE, Ames, Iowa 50011, USA Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA ∗ Laboratoire des Solides Irradis, CEA/DRF/lRAMIS, Ecole Polytechnique,CNRS, Institut Polytechnique de Paris, F-91128 Palaiseau, France Department of Material Science and Engineering, Iowa State University, Ames, Iowa 50011, USA (Dated: September 16, 2020)In-plane anisotropy of electrical resistivity was studied in samples of the hole-dopedBa − x K x Fe As in the composition range 0 . ≤ x ≤ .
26 where anisotropy changes sign. Low-temperature ( ∼
20 K) irradiation with relativistic 2.5 MeV electrons was used to control the levelof disorder and residual resistivity of the samples. Modification of the stress-detwinning techniqueenabled measurements of the same samples before and after irradiation, leading to conclusion ofanisotropic character of predominantly inelastic scattering processes. Our main finding is that theresistivity anisotropy is of the same sign irrespective of residual resistivity, and remains the same inthe orthorhombic C phase above the re-entrant tetragonal transition. Unusual T -linear dependenceof the anisotropy ∆ ρ ≡ ρ a ( T ) − ρ b ( T ) is found in pristine samples with x =0.213 and x =0.219,without similar signatures in either ρ a ( T ) or ρ b ( T ). We show that this feature can be reproducedby a phenomenological model of R. M. Fernandes et al. Phys. Rev. Lett. ,217002 (2011). Wespeculate that onset of fluctuations of nematic order on approaching the instability towards there-entrant tetragonal phase contributes to this unusual dependence.
I. INTRODUCTION
Studies of in-plane anisotropy of electrical resistivityin iron-based superconductors are performed on stress-detwinned samples [1, 2] creating preferential orienta-tion of orhthorombic domains [3]. The resistivities forprincipal orthorhombic directions, a and b , ρ a ( T ) and ρ b ( T ), and their difference ∆ ρ ≡ ρ a − ρ b referred to asanisotropy, reveal several unusual features. The resis-tivity of the parent BaFe As is lower for the long a − axis, ρ a < ρ b , corresponding to the antiferromagneticchains in the stripe magnetic structure. The anisotropyincreases with electron doping [and suppression of theorthorhombic distortion δ = ( a − b ) / ( a + b )], taking max-imum near optimal doping on electron-doped side [2].The anisotropy changes sign on the hole-doped side [4],with ρ a > ρ b , see phase diagram, Fig. 1. The mechanismof this sign change in the electronic transport attracts no-table interest, since contributions from both elastic scat-tering due to impurities/defects [5, 6] and inelastic scat-tering on magnetic excitations [7, 8] and phonons can beanisotropic.The magnitude of the anisotropy strongly depends onsample residual resistivity, as found in the study on theannealed samples [9–11]. It was argued [8] that the signchange of the resistivity anisotropy can be caused bydramatic difference in the levels of disorder scatteringon the electron-doped side in Ba(Fe − x T M x ) ( T M =Co, Ni, Rh, Ir [12, 13]) and the hole-doped side in ∗ [email protected] Ba − x K x Fe As [14–17], as summarized in the bottompanel of Fig. 1. Indeed, substitution in the electron-ically active Fe sites introduces high level of scatter-ing, with residual resistivity extrapolating to 100 µ Ω cm or so close to optimal doping. The K-substitution inBa − x K x Fe As proceeds in electronically inactive Basite and the residual resistivities are typically close to30 µ Ω cm . This difference may imply that the sign maybe the same for all the phase diagram.Another consideration regarding the origin of the signchange is related to approaching the composition rangeof the re-entrant tetragonal C phase [15, 18, 19]. Atambient pressure for compositions x < ∼ .
24 the sam-ples of Ba − x K x Fe As undergo simultaneous structural(tetragonal to orthorhombic) and magnetic (paramag-netic to stripe antiferromagnetic) transition below T C (see phase diagram Fig. 1). For x > .
24 a sequenceof phase transitions is observed, with re-entrance of thetetragonal phase below T C with complicated antiferro-magnetic structure [20]. This phase was not known atthe time of resistivity anisotropy study [4].We have recently succeeded controlling the residualresistivity of the iron-based superconductors using low-temperature electron irradiation with relativistic 2.5MeV electrons [21–23] and achieving residual resistivitylevels comparable to the electron-doped side, as shown inFig. 1 with open dots for x =0.20 [21], solid red circlesand magenta stars ( x =0.213 and x =0.260, respectively,this study). Disorder introduced by irradiation does notchange carrier density and enables disentangling effectsof doping and of the substitutional disorder, which are in-tertwined in the electron-doped Ba(Fe − x T M x ) . We usethis development to study electrical resistivity anisotropy a r X i v : . [ c ond - m a t . s up r- c on ] S e p - 0 . 2 - 0 . 1 0 . 0 0 . 1 0 . 2 0 . 30 . 00 . 20 . 40 . 60 . 8- 1 . 0- 0 . 50 . 0
05 01 0 0 - 0 . 2 - 0 . 1 0 . 0 0 . 1 0 . 2 0 . 3 T C 2 T (K) T C 2 T N T C 4
O , S t r i p e A FO T e t , P M T e t , A FS C S C r / r (300K) Dr / r FIG. 1. (Color online) Top panel. Summary phase diagramof electron-, Ba(Fe − x Co x ) As , and hole-, Ba − x K x Fe As ,doped iron based superconductors. Red, blue and magentapoints are T C , T c and T C of the pristine samples x =0.213,0.219 and 0.260 respectively, used in this study. Middle panelshows composition dependence of the low-temperature resis-tivity anisotropy, ∆ ρ/ρ , where ∆ ρ = ρ a − ρ b . Black solidsymbols in the middle and bottom panels show effect of resid-ual resistivity on resistivity anisotropy at low temperatures inparent BaFe As , squares after [1], triangles after [11] and cir-cles after [9]. Red, blue and magenta symbols are from thisstudy. Bottom panel shows evolution of the resistivity ra-tio, ρ (0) /ρ (300 K ) taken as a proxy of the residual resistivity.Open black circles are for the samples with x =0.20 subjectedto electron irradiation [21], red and magenta symbols from thesamples studied in this article, x =0.213 and x =0.260, in thesign reversal composition range. Blue is for the sample with x =0.219 studied only in the pristine state. in the sign change composition range 0 . ≤ x ≤ . x =0.213 and x =0.260. The first sample was on theorthorhombic, C , side of the composition boundary, thesecond one x =0.260 was in the re-entrant range. Ourmain finding is that the resistivity anisotropy is of the same sign irrespectively of residual resistivity, and re-mains the same in C phase range above the re-entranttetragonal transition. II. EXPERIMENTAL
Single crystals of Ba − x K x Fe As were grown as de-scribed in detail in Ref. 16. Large, above 5 × sur-face area crystals were cleaved on both sides to a thick-ness of typically 0.1 mm to minimize the variation ofthe K-content with thickness. The crystals from twodifferent batches were used in this study with averagecompositions x av =0.22 and 0.25, as determined from theelectron-probe microanalysis with wavelength dispersivespectroscopy (WDS). The large slabs were cut using wiresaw along the tetragonal [110] direction. Several cutswere made side by side to achieve the closest similar-ity of the sample properties. Multiple samples cut weremounted for four probe resistivity measurements. Con-tacts to the samples were tin-soldered [24, 25]. Thesecontacts are strong enough to withstand multiple irradia-tion measurements [22] and the applications of stress [26].Samples were pre-characterized by the electrical resistiv-ity measurements, to ascertain reproducible properties.Despite identical WDS composition, samples revealedsome variation in positions of features in ρ ( T ) curves atthe concomitant structural/magnetic transition T C andsuperconducting T c . We account for this variation us-ing polynomial fits of T C ( x ) and T c ( x ) [27]. This wasparticularly important for samples from the batch with x av =0.25, as these show some variation of the positionsof T C and T C features in ρ ( T ) even between the crystalscut from the same slab. Samples selected for irradiationin this study had x =0.213 and x =0.260 ( ± . x =0.219, allcompositions determined from the T C ( x ) formula [27].Use of T c ( x ) gave similar composition differences.Due to high probability of formation of cracks duringstress application, we prepared two samples of each com-position. Only one sample of each composition eventuallysurvived irradiation cycles without crack formation. Thesilver wires of potential contacts were used both for re-sistivity measurements and for stress application [1, 28].We used a specially designed device enabling easy sam-ple mounting/dismounting and controllable applicationof the tensile stress, shown in inset of the left panel inFig. 3 below. Four-probe resistivity measurements wereperformed in a Quantum Design
PPMS.The low-temperature 2.5 MeV electron irradiation wasperformed at the SIRIUS Pelletron linear accelerator op-erated by the
Laboratoire des Solides Irradi´es (LSI) atthe
Ecole Polytechnique in Palaiseau, France [29]. Thesamples for resistivity measurements during and afterelectron irradiation were mounted on a thin mica platein a hollow
Kyocera chip, so that they could be movedbetween the irradiation chamber (in LSI) and the de-twinning resistivity setup (in Ames laboratory) withoutdisturbing the contacts. The
Kyocera chip was mountedinside the irradiation chamber and was cooled by a flowof liquid hydrogen to T ≈
22 K in order to remove ex-cess heat produced by relativistic electrons upon colli-sion. The flux of electrons amounted to about 2.7 µ Aof electric current through a 5 mm diameter diaphragm.This current was measured with the Faraday cup placedbehind a hole in the sample stage, so that only trans-mitted electrons were counted. The irradiation rate wasabout 5 × − C / (cm · s) and large doses were accumu-lated over the course of several irradiation runs. The pen-etration depth of electrons in the hole-doped iron basedsuperconductors is estimated as 1.3 mm [30], tin and sil-ver used in the contacts have similar values, so that forsamples of our dimensions the irradiation is homogeneousand there should be no shadow on the samples under thecontacts. To stay on a safe side, though, the samples werepositioned with electron beam incoming from the oppo-site to the contacts side of the samples. Throughout themanuscript we use “pristine” and “unirradiated” inter-changeably to describe samples that were not exposed toelectron irradiation.Irradiation of a dose 1 C/cm with 2.5 MeV results inabout 0.07% of the defects per iron site [23]. The Frenkelpairs are created at about the same density in all sub-lattices. It is well known that in metals, self-diffusion ofinterstitials is much higher than that of vacancies, espe-cially warming up above roughly 100 K or so and thatthey mostly diffuse out and disappear at various sinks,like extended defects (dislocations/disclinations) and sur-faces [31]. A much slower to relax population of vacanciesremain in the crystal in a quasi-equilibrium (metastable)state controlled by the highest temperature reached. Re-sistivity measurements in situ at 22 K during irradiationin Ba − x K x Fe As with close composition x =0.20 [21]show linear increase with irradiation dose at a rate ∼ µ Ωcm per 1 C/cm , decreasing to ∼ µ Ωcm uponwarming to room temperature due to defect annealing[21]. The dose of defects created by electron irradiationis negligible compared with electron and hole densitiesin a good metal like Ba − x K x Fe As , as verified experi-mentally by Hall effect measurements [21]. III. ELECTRICAL RESISTIVITY
In Fig. 2 we show evolution of the temperature-dependent resistivity of Ba − x K x Fe As , x =0.213, withelectron irradiation. Measurements were done in stress-free conditions in the twinned state, with resistivity de-noted as ρ t . The evolution is consistent with our previousstudies [21, 22], with suppression of the superconducting T c (inset in left panel) and of the temperature of thestructural/magnetic transition, T C , as seen in resistiv-ity derivative plots (right panel). The increase of theresistivity is not constant in temperature and it is no-tably larger on T →
0, revealing notable Matthiessen ruleviolation. The residual resistivity increases more than by r t ( mW cm) T ( K ) x = 0 . 2 1 35 . 6 C2 . 6 C0 C d r /dT ( mW cm/K) FIG. 2. (Color online) Temperature-dependent electri-cal resistivity of stress free twinned samples, ρ t ( T ), ofBa − x K x Fe As , x =0.213, with composition in the nematicanisotropy sign reversal range (left panel). Inset shows zoomof the superconducting transition. Black curves show datafor sample before irradiation (0 C/cm ), blue and red curvesafter irradiation with 2.6 C/cm and 5.6 C/cm , respectively.Right panel shows temperature-dependent resistivity deriva-tive for the data in the left panel revealing clear anomalies atthe tetragonal to orthorhomic structural transition coincidingwith the antiferromagnetic ordering, T C . Electron irradia-tion monotonically increases ρ (0) from ∼
30 to ∼ µ Ωcmand suppresses both T c and T C at approximately the samerate. a factor of 3, from ∼
30 to ∼ µ Ωcm.On application of tensile stress using hook horseshoedevice [26] sample goes into the detwinned state with pre-dominant orientation of domains with the orthorhombic a -axis along the stress direction. The resistivity increaseswith stress and saturates once detwinning action of stressis complete. The resistivity in this state, ρ a , is shown inFig. 3 with grey, cyan and magenta lines for 0, 2.6 and5.6 C/cm samples. The bottom curves show resistivityalong b direction in the plane (black, blue and red curvesfor 0, 2.6 and 5.6 C/cm respectively). Resistivity along b direction was determined assuming equal population ofdomains in the stress-free sample, ρ t = ( ρ a + ρ b ) /
2, and ρ b = 2 ρ t − ρ a .The in-plane resistivity anisotropy, ∆ ρ ≡ ρ a − ρ b isshown in the right panel of Fig. 3. The anisotropy signremains the same for all irradiation doses with ρ a > ρ b .The anisotropy in pristine sample (black curve in theright panel of Fig. 3) reaches broad maximum at about ∼
70 K and then decreases approximately linearly downto the superconducting transition. With 2.6 C/cm ir-radiation, an increase of the residual resistivity from ∼
30 to ∼ µ Ωcm and shift of T C from 94 to 91 K, themaximum in ∆ ρ ( T ) shifts to ∼
60 K and some curva-ture starts to develop above T c . The anisotropy above T c notably increases compared to the pristine sample,from ∼ ∼ µ Ωcm. Finally, with 5.6 C/cm irradi-ation, increase of the residual resistivity to ∼ µ Ωcmand T C suppression to 88 K, the maximum transformsinto a plateau, starting somewhat below 60 K and con-tinuing down to T c . This ∆ ρ ( T ) for 5.6 C/cm irradiated FIG. 3. (Color online) Temperature-dependent electrical re-sistivity of Ba − x K x Fe As sample with x =0.213. Twosets of curves for each irradiation dose represent resistivityalong a − , ρ a (gray, cyan and magenta, top curves in thepair), and b − , ρ b (black, blue and red, bottom curves inthe pair), directions in the conducting plane. Right panelshows temperature-dependent in-plane resistivity anisotropy,∆ ρ ≡ ρ a − ρ b , and its evolution with irradiation. Inset in theleft panel shows hook device used for detwinning experimentswith multiple mounting/dismounting cycles [26]. Sample isirradiated with 2.5 MeV electrons to introduce disorder in acontrolled way between stress application runs. Open darkyeallow circles show temperature dependence of the nematicorder parameter, δ = ( a − b ) / ( a + b ), left axis in the rightpanel, in sample with x =0.22 in thermal expansion measure-ments [18]. sample resembles temperature evolution of the nematicorder parameter δ = ( a − b ) / ( a + b ), shown with dots (leftscale in the right panel) from thermal expansion data ofB¨ohmer et al. [18] for close x =0.22.In the left panel of Fig. 4 we show evolution of the tem-perature dependent resistivity in Ba − x K x Fe As samplewith x =0.260. Measurements in stress-free conditions(black curve for pristine sample, blue and red for samplesafter irradiation with 2.35 and 7.98 C/cm , respectively)show monotonic increase of the resistivity. Note a fea-ture at ∼
30 K in the ρ ( T ) curve for the sample with 7.98C/cm under stress (magenta line in Fig. 4) marked withthe star. Here the sample partially cracked on cooling,with the stress release. Since this crack happened afterthe resistivity data were taken, we were able to determinethe resistivity anisotropy as shown in the right panel 0fFig. 4. However in the analysis below we use the datafor 2.35 C/cm sample. The features at T C (small in-crease on cooling below 60 K) and T C (small resistivitydecrease below 35 K) are very sensitive to stress, whichleads to sharp anomalies in the anisotropy plot in theright panel. With irradiation the T C is suppressed to atleast below onset of the superconducting transition whilethe feature at T C is nearly unaffected.Evolution of the in-plane resistivity anisotropy in thesample x =0.260 is quite remarkable. The stress-inducedanisotropy in the tetragonal phases above T C and below T C is notably larger than in the orthorhombic phase. x = 0 . 2 6 07 . 9 8 C2 . 3 5 C0 C r a r t, r a ( mW cm) T ( K ) r t * d Dr = r a- r b ( mW cm) d ( 1 0 - 3 ) FIG. 4. (Color online) Temperature-dependent electrical re-sistivity of Ba − x K x Fe As sample with x =0.260. Two setsof curves for each irradiation dose represent resistivity instress free twinned state, ρ t ( T ), (black, blue and red for 0,2.35 and 7.98 C/cm respectively) and detwinned by appli-cation of tensile stress, ρ a ( T ) (gray, cyan and magenta for0, 2.35 and 7.98 C/cm , respectively). Star marks partialcracking of the 7.98 C/cm sample leading to a stress release.Right panel shows temperature-dependent in-plane resistivityanisotropy, ∆ ρ ≡ ρ a − ρ b , and its evolution with irradiation.For reference we show temperature evolution of nematic or-der parameter, δ = ( a − b ) / ( a + b ), (open dark yellow circles,left axis in the right panel), measured with thermal expansiontechnique in the sample with x =0.262 [18]. The overall magnitude of the anisotropy is about 2 timessmaller than in x =0.213 sample. The temperature de-pendence of anisotropy has little resemblance to that in x =0.213, with anisotropy remaining nearly temperature-independent.In Fig. 5 we show evolution of the resistivity and of theresistivity anisotropy at characteristic temperatures withirradiation dose. For sample with x =0.213 these tem-peratures were selected as T =60 K (in the vicinity of themaximum of anisotropy), at T =22 K (above onset of thesuperconducting transition) and in T → x =0.20composition. Interestingly, resistivity in T → T c initially rises, then seems to saturate.For sample with x =0.260 (bottom panel in Fig. 5) theresistivity increase for all temperatures has a tendencyto downward deviation. One possibility is that this isan artefact of incorrect dose determination. Big dosesare accumulated over several irradiation runs (during aperiod up to three years) and partial defect annealing canbe happening over these long periods.To check for systematics of the results, we measuredone more pristine sample of Ba − x K x Fe As from the
05 01 0 0 x = 0 . 2 1 3 r ( mW cm) Dr ( mW cm) x = 0 . 2 6 0 r ( mW cm) D ( C / c m ) Dr ( mW cm) FIG. 5. (Color online) Irradiation dose dependence of re-sistivity (left axes, black symbols) and resistivity anisotropy(right axes, red symbols) in samples of Ba − x K x Fe As with x =0.213 (top panel) and x =0.260 (bottom panel). In thetop panel solid black down triangles and open red up-trianglesare for T =60 K, at about maximum of anisotropy, solid up-triangles and open circles for T =22 K, just above T c , andblack solid circles in T → T =55 K, slightly below the T C , solid black up-triangles andopen red circles are for T =38 K above T C , and solid blackcircles for T =0 extrapolation. same batch as sample x =0.213, however, with some-what different composition, x =0.219. The temperature-dependent electrical resistivity of the stress-detwinnedsample with x =0.219 for measurements along principalin-plane directions, ρ a and ρ b , is shown in Fig. 6. Thesample is characterised by somewhat lower T C comparedto sample x =0.213 (inset in left panel of Fig. 6, 90.6 Kvs 94 K) and higher T c , 21.3 K vs 19.8 K. The resistiv-ity curves show the same tendency as found in pristinesample with x =0.213, with two curves converging oncooling above T c . In the right panel of Fig. 6 we show∆ ρ ( T ) for sample with x =0.219 (red line) in comparisonwith samples x =0.213 (black top curve) and x =0.260(bottom blue curve). We can clearly see two trends withincreasing x , the decrease of the maximum anisotropyand decrease of the slope of the linear portion of ∆ ρ ( T )(highlighted by lines serving as guides for eyes). r b r ( mW cm) T ( K ) B a K x F e A s x = 0 . 2 1 9 r a r a -r b ( mW cm) d r t/dT FIG. 6. (Color online) Temperature-dependent electricalresistivity of Ba − x K x Fe As sample with x =0.219 formeasurements along a − , ρ a (top curve), and b − , ρ b (bot-tom curve), directions in the conducting plane (left panel).Inset shows zoom of the structural/magnetic transition.Right panel shows temperature-dependent in-plane resistiv-ity anisotropy, ∆ ρ ≡ ρ a − ρ b . For reference we show simi-lar measurements in samples x =0.213 (black top curve) and x =0.260 (bottom blue curve). Dashed lines are guides foreyes. IV. DISCUSSION
There are two main groups of theories explaining ne-matic resistivity anisotropy, see [33] for the review. Thefirst group is relating the nematic anisotropy to theDrude term, n/m ∗ , reflecting anisotropy of the bandstructure. The other group of theories is relating ∆ ρ to the anisotropy of scattering, both elastic and inelas-tic. In all theories the anisotropy should be proportionalto the nematic order parameter, δ = ( a − b ) / ( a + b ), asfound in scattering [19] and thermal expansion measure-ments [18] , the later shown in Fig. 3 and Fig. 4 for sam-ples with x =0.22 and x =0.262, respectively. It is alsopossible to have a temperature dependent pre-factor Υ,coming, for example, from temperature dependent scat-tering in which case it should be proportional to ρ . Theanalysis of nematic resistivity anisotropy using this ap-proximation, ∆ ρ = ρ t δ , was very successful in FeSe [34],giving quite good description of the data. We need tokeep in mind though, that the situation in FeSe is sim-pler than in the hole doped Ba − x K x Fe As . Nematicorder is not accompanied by the long range magnetic or-dering in FeSe, and thus no Fermi surface folding effectsare involved [35, 36]. On the contrary, the Fermi sur-face changes at the transition are important for the holedoped compositions studied here.We start with analysis of the heavily irradiated sam-ples, as shown in the left panel of Fig. 7. Here we com-pare directly ∆ ρ ( T ) of the sample with x =0.213 irra-diated with 5.6 C/cm (black line) with δ ( T ) measuredby B¨ohmer (dark yellow circles) and a product of resis-tivity in the twinned state ρ t ( T ) and δ ( T ) (dark yellowline). For reference we show ∆ ρ ( T ) for 2.35 C/cm ir- Dr = r a- r b ( mW cm) r t * dd d r t * dD rD r Dr = r a- r b ( mW cm) T ( K ) d (10-3) r t , in * d r t * d D r FIG. 7. (Color online) Left panel. Comparison of thein-plane resistivity anisotropy in samples of Ba − x K x Fe As with x =0.213 (5.6 C/cm ) and x =0.260 (2.35 C/cm ) withthe degree of orthrhombic distortion, δ = ( a − b ) / ( a + b ), asdetermined in thermal expansion measurements by B¨ohmer etal. [18] (open yellow circles) and a product ρ t δ (red and ma-genta lines for 0.213 and 0.260, respectively). Right panel.Comparison of ∆ ρ ( T ) in the pristine sample of x =0.213(black line) with a product ρ t × δ (red line) and of the inelas-tic part of resistivity, ρ t,in = ρ t − ρ t, , and the orthorhombicorder parameter, ρ t,in × δ (cyan line). radiated sample with x =0.260 (blue line) and δ ( T ) forsample with x =0.262. First, we can clearly see thatthe magnitude of the resistivity anisotropy scales withthe degree of the orthorhombic distortion δ , in sharpcontrast with the electron-doped side [2]. Second, theproduct δρ t gives quite good description of the data for x =0.22 sample (red vs black curve) below approximately60 K. The difference at higher temperatures is quite no-table, however, it is natural that ∆ ρ ( T ) has a contri-bution from temperature dependent folding gap open-ing. In the right panel of Fig. 7 we perform the sameanalysis for sample x =0.213 in pristine the state. Theresistivity anisotropy ∆ ρ ( T ) (black line) shows close to T − linear dependence. The product ρ t δ (we use the same δ ( T ) as shown in the left panel) captures this T − lineardependence, despite neither ρ t ( T ) (black line in Fig. 2)nor δ ( T ) showing T − linear dependence. The differencewith irradiated case is quite notable, since ∆ ρ ( T ) de-creases notably faster than the ρ t δ product in the rangewhere the temperature-dependent folding gap openingshould have minor effect. The match becomes signifi-cantly better if we use only inelastic part of the resistiv-ity, ρ t,in = ρ t ( T ) − ρ t (0), as shown with cyan line.As a general remark, we should point out, that elec-tron irradiation at the doses used in this study does notintroduce variation of carrier density sufficient to haveany noticeable impact. This was verified through Halleffect measurements on samples with x =0.20 [21] andis in line with common expectations for metals [37]. Sofor our discussion we can consider effect only throughscattering rate.The results of this study are in general agreement withthe previous studies using annealing to control residual
051 01 5 0 . 0 0 . 5 1 . 00 . 00 . 51 . 0 0 . 0 0 . 5 1 . 0 r a- r b ( mW cm) x ( - 1 / 4 ) x ( - 1 / 3 ) r t / r (Tsm) T / T s m FIG. 8. (Color online) Comparison of the temperature-dependent electrical resistivity anisotropy for clean samples(left top panel) and dirty (top right) samples of various ironbased superconductors. The data are presented vs normal-ized temperature scale,
T /T C . Blue curve is for annealedparent BaFe As [9], the data are divided by 4, green for FeSe[34], black and red are for Ba − x K x Fe As samples x =0.213and x =0.260, respectively (this study). Yellow curve in thetop right panel is for Ru-substituted BaFe As [11] and isdivided by 3. Red line is for the x =0.213 irradiated with5.6 C/cm , magenta line is for x =0.260 sample irradiatedwith 2.35 C/cm . The bottom panels show the temperaturedependent resistivities of the same compounds, plotted usingnormalized ρ ( T ) /ρ ( T C ) and T /T C scales. resistivity or the samples with naturally low residual re-sistivity. For example, the decrease of anisotropy from alarge value below T C on cooling to low temperatures isfound in perfectly annealed BaFe As [9] (blue curve inFig. 8) and in very clean samples of FeSe [34] (green curvein Fig. 8). We explicitly compare the anisotropy found inthese compounds with Ba − x K x Fe As samples x =0.213and x =0.260 in the pristive state. It was argued [9, 11]that the decreasing anisotropy on cooling is determinedby contribution of light carriers [38–42], strongly sup-pressed by disorder scattering. In this respect, close to T − linear dependence of ∆ ρ ( T ) in the pristine sampleswith x =0.213 and 0.219 may suggest that this groupof carriers suffers critical scattering on approaching C q =0 componentshould have notably bigger effect on small pockets of theFermi surface.Strikingly, the increase of residual resistivity with irra-diation does not increase anisotropy beyond its maximumvalue in the clean samples. This fact suggest that ρ (0)does not contribute much to the anisotropy, at least onthe hole doped side close to C ( x ) phase boundary.Interestingly, while T − linear dependence is a hallmarkof a quantum critical point in the phase diagram of iso-valently substituted BaFe (As,P) [43, 44] and partiallyelectron-doped Ba(Fe, T M ) As [45], the temperature-dependent resistivity in Ba − x K x Fe As does not revealit [16]. Our observation may be suggesting that the rea-son for this may be phase competition. Indeed, the re-sistivity in the C phase in the sample with x =0.260is close to linear, though in a very limited temperaturerange. V. CONCLUSIONS
The sign reversal of resistivity anisotropy in the sam-ples of hole-doped Ba − x K x Fe As on approaching thereentrant tetragonal phase is insensitive to disorder, op-posite to some theory suggestion [8]. The anisotropy at high temperatures does not depend on the residual resis-tivity, the anisotropy of clean samples with x =0.213 and0.219 notably decreases on cooling in the pristine sam-ples and stays constant in the samples with high residualresistivity. This study suggests that inelastic scatteringresponsible for the temperature-dependent part of resis-tivity is anisotropic, while elastic scattering responsiblefor residual resistivity is notably less anisotropic. Thetemperature dependent anisotropy in pristine samplessuggests contribution of high mobility carriers subject toscattering on nematic fluctuations. ACKNOWLEDGMENTS
This research was supported by the U.S. Department ofEnergy, Office of Basic Energy Sciences, Division of Ma-terials Sciences and Engineering. Ames Laboratory is op-erated for the U.S. Department of Energy by Iowa StateUniversity under Contract No. DE-AC02-07CH11358. Ir-radiation realized on SIRIUS platform was supported byFrench National network of accelerators for irradiationand analysis of molecules and materials EMIR&A underproject 18-5354. [1] M. A. Tanatar, E. C. Blomberg, A. Kreyssig, M. G. Kim,N. Ni, A. Thaler, S. L. Bud’ko, P. C. Canfield, A. I.Goldman, I. I. Mazin and R. Prozorov. Phys. Rev. B ,184508 (2010).[2] J-H. Chu, J. G. Analytis, K. De Greve, P. L. McMahon,Z. Islam, Y. Yamamoto, and I. R. Fisher. Science ,824 (2010).[3] M. A. Tanatar, A. Kreyssig, S. Nandi, N. Ni, S. L.Bud’ko, P. C. Canfield, A. I. Goldman, and R. Prozorov,Phys. Rev.B , 180508 (R) (2009).[4] E.C.Blomberg, M.A.Tanatar, R.M.Fernandes, I.I.Mazin,B.Shen, Hai-Hu Wen, M.D. Johannes, J. Schmalian, andR. 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