Introduction

The intermetallic Fe-based superconductors (FBS) of ThCr2Si2-type crystal structure, such as electron or hole-doped AEFe2As2 (AE alkali earth metal), are characterized by a low Ginzburg number 1,2, high upper critical fields, 3 and very low anisotropies, 4,5, which tend to approach 1 at low temperatures. Although the in-plane coherence length, , is similarly small as in YBa2Cu3O7−δ (YBCO), grain boundaries (GBs) are slightly less detrimental to the current flow than in high cuprates6. The reason is mainly a difference in order parameter symmetry, being predominantly d-wave in YBCO but of s-wave type (presumably with a sign change, s±)7 in FBS. All these properties make FBS materials interesting for high-field applications at low temperatures since they combine advantageous properties of the low-temperature superconductors (narrow in-field transition, low Gi, low anisotropy) and high- cuprates (high upper critical fields ). Indeed, first prototypes of Co-doped BaFe2As2 (Ba-122) coated conductors8,9 and K-doped Ba-122 powder-in-tube wires10,11 have been reported.

A well-investigated member of this family is Co-doped Ba-122 due to its relatively easy preparation as thin films by pulsed laser deposition and stability at ambient conditions12. Furthermore, Co-doped Ba-122 proved to be very susceptible to a high density of artificial pinning centers and record values of the maximum pinning force density, , of around 70 GN/m3 for at 4.2 K have been reported for films on CaF2 substrate13. Lee et al. demonstrated that Co-doped Ba-122 films grown at relatively high O2 partial pressure14 or with oxygen-containing targets15 develop correlated c-axis-oriented columnar oxide defects. These defects lead to a huge contribution to pinning for fields applied parallel to the c-axis16. Katase et al. found similarly high Jc values for Co-doped Ba-122 on (La,Al)(Sr,Ta)O3 (LSAT)17. In most of these pinning-improved Co- or P-doped18,19 Ba-122 samples, a large density of c-axis correlated or extended random defects is introduced. This paper investigates the high-field transport properties of Co-doped Ba-122 thin films with several different natural growth defects, such as small-angle grain boundaries and stacking faults. It will be shown how these defect populations, in combination with the multi-band superconductivity, influence the vortex matter and the pinning properties in different regions of the H-T phase diagram.

Results and Discussion

Microstructure

The film investigated grew phase-pure and highly textured with in-plane and out-of-plane full width at half maximum, FWHM, of = 0.74° and = 0.9°, Suppl. S1. The sample, however, does contain a large density of ab-planar defects, as revealed by transition electron microscope (TEM) images of focused ion beam (FIB) cuts near the microbridges, Fig. 1. These defects are presumably stacking faults (i.e. missing FeAs layers)20. The reason for this defect formation (also observed on technical substrates)21 is not fully understood. Possible reasons are a partial As loss during deposition22 and relaxation processes in combination with the Fe buffer layer23. Estimating the distance between these intergrowths leads to values varying between 5 and 10 nm. Between the planar defects, an orientation contrast is visible in TEM (inset Fig. 1b), i.e. the brighter crystallites are slightly rotated either around (010) (out-of-plane spread, ) or around (001) (in-plane spread, ) and enclosed by dislocation networks or small-angle GBs. Since the crystallites are sandwiched between planar defects, an in-plane misorientation is most likely. The out-of-plane misorientation, on the other hand, is visible as a slight tilt of the ab-planar defects with respect to each other, especially in the upper part of the sample. No globular or columnar precipitates were found.

Figure 1
figure 1

(a) Bright field TEM image of the lamella showing a large number of stacking faults parallel to the ab-plane. (b) High-resolution TEM image of two stacking faults, i.e. missing FeAs layers. The inset (bright field) shows the diffraction contrast image of a tilted grain (in-plane) between two stacking faults which strongly suggests the existence of c-axis correlated defects.

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Upper critical field Hc2

To determine the nature of the superconducting transition, the temperature dependent resistance has been measured in static magnetic fields up to 35 T for both major directions, and , Fig. 2a, as well as in pulsed fields up to 65 T (Suppl. S2). was estimated from the experimental data using a constant 95% criterion (upper dashed line in Fig. 2a). A of 25.8 K in absence of an applied magnetic field was recorded. The temperature dependence of , Fig. 3, shows different behavior for and . Both directions differ clearly from the single-band WHH model for orbital limitation (dashed lines). For , can be fitted well by the single-band WHH model including paramagnetic limitation and spin-orbital effects. Best fits were achieved with a Maki parameter  = 1.25 and a spin-orbit scattering term  = 0.5. Conversely, for a two-band approximation is necessary since the orbital is lower than the measured values. The data were analyzed using the WHH approach for two-band superconductors in the dirty24 and the clean limit25,26. In the dirty limit, a reasonable description of the experimental data was achieved with the diffusivity, scattering parameters and coupling constants given in Fig. 3a. Similar fits have been shown for single-crystal data5.

Figure 2
figure 2

Resistive transitions R(T) measured in static magnetic fields up to 35 T for both major directions (left) and (right).

(a) linear representation. The broken lines indicate criteria for determining the upper critical field (95) and irreversibility field (1), respectively. (b) Arrhenius plots.

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Figure 3
figure 3

Temperature dependence of the upper critical field Hc2.

It was determined with a criterion of 95% Rn of resistance curves in pulsed (HZDR and IFW) and static magnetic fields (NHMFL). The dashed lines are fits near with single-band orbital limitation. shows clear indication of paramagnetic limitation, of two-band behavior, which can reasonably be fitted both in the dirty (a) and the clean limit (b). Insets: Temperature dependence of the respective anisotropies .

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However, as pointed out by Gurevich, most of iron-pnictide superconductors should be in the clean limit (electron mean free path ) due to low Fermi velocities25,26. The observed scaling behavior of the slope of at , , for many iron pnictides supports this assumption27. Applying the two-band description in the clean limit including paramagnetic effects leads to reasonable fits for the temperature dependencies of for both crystallographic directions, Fig. 3b and angular dependencies at constant temperature, Fig. 4b. For the calculations, we used moderate values of the coupling constants () consistent with the case of -wave superconductivity in this compound. Also, we used values of the Fermi velocities in agreement with average values obtained from ARPES data for the BaFe2As2 system28. Paramagnetic effects for both directions were taken into account by introducing small values of the Maki parameters. Here, we assumed that the anisotropy of the Maki parameters is given not only by the an-isotropy of the Fermi velocities but also by the anisotropy of the spin susceptibilities. This was taken into account by introducing the anisotropy of the magnetic moments in plane and out of plane. Reasonable agreement of the calculations with experimental data were obtained for .

Figure 4
figure 4

Angular dependence of the upper critical field Hc2 at 18 K and 4 K.

(a) The blue dashed line shows the result of a linearization of the one-band AGL formula (Eq. 2, =2), inset. Deviations near and are clearly visible. Red line: phenomenological approximation of with Eqs 1,2 (). (b) Solid green lines: calculations using the clean-limit two-band WHH model with the same parameters as shown in Fig. 3. For 4 K, a fit according to Eqs 1,2 (full black line, → ) and a one-band AGL dependency (dashed) are also shown.

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The clean- and dirty-limit anisotropies, , insets Fig. 3, are increasing almost linearly from 1.2 near 0 K to 1.85 close to . This is a combined effect of multi-band superconductivity and paramagnetic limitation. The sample investigated here shows at all temperatures a slightly lower anisotropy than microstructurally clean films of similar nominal composition29. Whether this effect is a direct consequence of the defect structure or caused by a slightly different doping state due to e.g. As disorder or differing Co content could not been clarified completely.

The angular dependence of the upper critical field, , shown in Fig. 4a at 18 K, cannot be described in the full angular range by the Anisotropic Ginzburg Landau (AGL) formalism for one-band 3D superconductors. This is illustrated by a linearization method of the AGL dependency as proposed by Tarantini et al.30 [inset Fig. 4a]. The resultant anisotropy curve at 18 K, shown as blue dashed line in Fig. 4a, deviates from the measured values for field directions close to and . The deviation for seems to be marginal in . It is, however, not negligible for a correct determination of the (AGL) anisotropy parameter, as evidenced by the linearization method.

For (single-band) dirty limit, Takezawa et al. showed that periodic structures of superconducting and non-superconducting layers can lead to intermediate functions between 3D AGL and pure 2D behavior31. This effect had also been reported by Ghosh et al. for CaAlSi single crystals with planar defects similar to the ones seen in our sample32. This can be explained by a modification of the coherence length via a reduction of the mean free path 33. Both kinds of defects in our sample, GB network and -planar intergrowths, would lead to different angular dependencies of resulting in a modified dependency. It is feasible that in dirty limit both effects, multi-band superconductivity and extended defects, together determine the exact dependence.

Alternatively, the dependencies can be explained solely by a combination of multi-band and paramagnetic effects, assuming that the film is in the clean limit. In Fig. 4b, the result of the two-band calculation with the same parameters as given in Fig. 3b are shown for 18 K and 4 K. For 18 K, the deviation between fit and data especially around compared to the AGL fit is decreased considerably. For 4 K, a small secondary peak around for the clean-limit is observed, which is a consequence of the anisotropic paramagnetic effects. Which scenario, clean or dirty limit, holds for this sample is not possible to determine at the present stage since both yield fits of with similar accuracy and the dependencies are expected to be similar as well. Future experiments regarding coherence length and mean free path in samples with and without extended defects should clarify this issue.

For further investigations of the anisotropy, see below, it is helpful to describe with some well-behaved analytical function. One possibility is:

where is a free parameter close to 2 and . With δ →2, Eq. 1 goes back to the usual AGL dependency. The full red line in Fig. 4a is a fit to this function with δ = 1.77 and = 1.65. Also the clean-limit dependence at 4 K can be approximated reasonably with this function, Fig. 4b full black line.

Thermal activation

Arrhenius plots, ln R (1/T), Fig. 2b, show the typical linear behavior of thermal activation of flux motion. The activation energy for vortex motion can be estimated under the assumption of linear temperature dependence, , which leads to ln and ln, where is a prefactor. The data were refined by evaluating and from linear fits of ln and by fixing the crossing point of the linear fits in the Arrhenius graphs, Fig. 2b. This method yields a value of 25.8 K, corresponding to = 95% ( normal state resistance) in accord with the criterion used for evaluating .

The field dependencies of for both major directions, Fig. 5, are best described by

Figure 5
figure 5

Magnetic field dependence of the pinning potential

U0. Full lines are fits to Eq. 3 for H ≥ 5 T.

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This functionality was first proposed for the case of MgB2 by Thompson et al.34 who argued that the exponents should be similar to the exponents in the field dependence of the pinning force density. As will be shown later, this is, interestingly, not the case for in our sample. Eq. 3 can further be explained by statistical considerations. A statistical distribution of pinning energies in the sample and the principle of entropy maximization also lead naturally to this dependency. In that case, it takes the form of a beta-distribution, i.e. the maximum-entropy distribution over a finite range (here magnetic field range)35 because has to go to zero near , i.e. . The data are well fitted above 5 T with exponentsα = 0.72 and 0.5 for and , respectively and β = 1.0 for both field directions. was varied independently, best fits were achieved with (461) T and (56±0.4) T for and , respectively. At low fields, the data differ from fits to Eq. 3 because of the crossover to the regime of single vortex pinning where is constant. Similar dependencies have recently been found for polycrystalline MgB2, NbSe236 and FeSe37,38, as well as LiFeAs single crystals39.

Critical Current Density Jc

The angular dependencies of the critical current density at low fields reveal a strong influence of the c-axis correlated defect structures, Fig. 6a–c. All curves show a maximum at (θ = 90°). Additionally, there is a broad maximum visible at ( = 0°) for the respective lowest fields. The -axis peak vanishes at all temperatures around ( being the irreversibility field determined from fits) and grows with decreasing at a given magnetic field. The curve for = 1 T at 12 K represents the lowest value of 0.06 in the data set of Fig. 6a–c and shows the highest -axis peak [ at 1 T, 8 K was not measureable due to current limitation]. A similarly broad -axis peak related to threading dislocations has recently been found in P-doped Ba122 thin films by Sato et al.19 This increasing c-axis pinning for lower T is in contrast to the behavior in cuprates such as YBCO where the c-axis peak has been observed to disappear at low T40. This striking difference has two reasons: Firstly, the mass anisotropy in YBCO is much larger and so the ab-peak is growing disproportionately with decreasing temperature, hiding a minor c-axis peak. Secondly, Ba-122 is a multi-band superconductor in contrast to YBCO. Therefore, the anisotropy of the penetration depth, , does not equal the anisotropy, . With , as for Ba-122, any strong pinning contribution at large random defects will lead to a maximum in the pinning potential for 41. The larger the distance to the irreversibility line (i.e. the lower the flux creep processes), the stronger this contribution is and the better it can compete with the ab contribution.

Figure 6
figure 6

Angular dependence of Jc.

(a) 8 K, (b) 12 K, (c) 16 K showing a -axis peak at low magnetic fields besides the always present peak. (d) at 4.2 K for several fields up to 30 T in logarithmic representation. The full and broken lines in (d,e) represent the “random-pinning contribution”, Eq. 6 and are the same for all three types of scaling. (e) scaling applying scaling function (Eq. 2, full black lines) as well as scaling function (Eq. 5, identical to , broken red and blue lines). The upper (black line) and lower data sets (red line) are shifted in and for clarity. Inset: , 4.2 K, 5 T) in linear representation.

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As shown in refs 42 and 43 Jc of microstructurally clean samples (i.e. containing very few defects of size larger than the coherence length) of multi-band superconductors is scalable on an effective magnetic field

with a single, yet temperature-dependent scaling parameter , which was identified as . This approach follows the Blatter-Geshkenbein-Larkin (BGL) scaling for anisotropic single-band superconductors and can be understood as transformation of the anisotropic superconductor into an equivalent isotropic one44. Commonly, the envelope function of the scaled Jc data is associated with pinning at isotropic and random defects45. Fig. 6d displays the angular dependence of Jc at 4.2 K for several magnetic field strengths between 5 and 30 T. The same data are scaled according to Eq. 4 in Fig. 6e (lower data sets, dashed lines). The envelope and simultaneously the corresponding random-pinning contributions in Fig. 6d, was fitted using an empirical function46 which can be understood as combination of the modified Kim model47 and the generalized Kramer model48.

by independently varying the parameters , and . The parameters and were fixed at 0.5 and 2, respectively. These values correspond to the fit parameters , of the pinning force density discussed below, Fig. 7 and Eq. 7 and are well justified for pinning at small random defects43. is related to the self-field49 and/or the accommodation field for single vortex pinning50. Good fits were achieved with parameters MA/cm2 (slightly larger than the measured value), mT, T (in good agreement with the value determined by resistive measurements at 4.2 K, Fig. 8) and , which is slightly larger than .

Figure 7
figure 7

(a) Pinning force density at 4.2 K for three magnetic field directions in linear and logarithmic field scale. The lines are functions according to Eq. 7 with parameter sets for (c), (0.5,1.45) for 55° and (0.5,1) for . Below 5 T, (a) -axis contribution is visible. (b) Magnetic field dependence of the pinning force density and of the resistance illustrating the region of very weak pinning at high magnetic fields. The dashed line is a low-field fit with similar to high as well . (c) Temperature dependence of and the parameters and : comparison between and , was fixed at 2.

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Figure 8
figure 8

H-T phase diagram of a Co-doped Ba-122 thin film with extended defects for and .

Squares: upper critical field , triangles: resistive irreversibility field , stars: pinning-force irreversibility field , balls: (cf. Fig. 5a). Different symbol fillings indicate different measurements (pulsed (open and half symbols) or static fields (full symbols)), green lines: clean-limit two-band fits.

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The data above 10 T can be well scaled in the vicinity of the -direction using this formalism. However, there is a large intermediate angular range which neither follows the scaling nor really belongs to the sharp -peak due to correlated -planar defects. This region can be scaled if one takes again into account the altered angular dependency of . If, instead of , Eq. 5, , Eq. 2, with found for (clean-limit two-band approximation, Fig. 4b) is used for the scaling, nearly the full angular range of can be scaled for high fields, as illustrated in Fig. 6e upper data sets (full line, data shifted for clarity) and Fig. 6d (full lines). One has to keep in mind, however, that both parameters (which still differs from ) and are purely phenomenological here. The scaling merely shows that Jc at high fields is determined by the angular dependence of since in this region correlated defects play a minor role. The sharp extra peak near ab at fields below 20 T is mainly due to correlated pinning at the planar defects visible in TEM and, therefore, not following either scaling.

Whereas for high fields the modified scaling according to gives the better scaling results, the usual BGL scaling is better at low fields, as illustrated in Fig. 6d for 10 T. In fact, for 5 T, results in near perfect scaling behavior for intermediate angles, Fig. 6d,e (red dashed line and inset). For , the angular dependence of plays a minor role and the contributions of random and correlated pinning can, with necessary care, be distinguished in the common way. The difference between measured Jc and scaling curve at 5 T near is again due to the dislocation networks and disappears between 5 and 10 T, i.e. at , cf. the disappearance of the c-axis peak in Fig. 6a–c.

Pinning Force Density Fp and Phase Diagram

The field dependence of the pinning force density depends strongly on temperature and field orientation, Fig. 7. All data for and between 4.2 and 16 K as well as for = 55° at 4.2 K were fitted with the empirical formula51:

For , was fixed at 2.0 to minimize fit ambiguity and was slightly lower than 0.5 for all temperatures due to the correlated -axis defects active at low fields. In Fig. 7a, the difference between the fit function with parameter set and the values illustrates this influence at low fields, as emphasized in logarithmic scale. In contrast to , the parameter is lower than 2 for = 55° ( = 1.45) and ( = 1.0) at 4.2 K. Below 5 T, for exceeds the = 55° data, again a consequence of the -axis correlated defects.

As summarized in Fig. 7c, is around 2 at high temperatures and decreases roughly linearly to 1 below 12 K for . This matches the temperature where the irreversibility field , determined from the dependence, shows a sharp kink. Below 12 K, T is distinct from the values determined resistively for , Fig. 8. A parameter set as determined for 4.2 K is typical for core pinning at extended planar defects52. A matching field of 35-37 T corresponds to a defect distance of around 7.5 nm, which is in good agreement with the distance of the -planar defects estimated by TEM (5–10 nm), Fig. 1. Vortices at higher magnetic flux densities are only pinned very weakly. A fit with leads to unreasonably high values (dashed line Fig. 7b). In comparison, a clear change in pinning mechanism at low temperatures is hard to observe in cuprates due to the high irreversibility fields. Nevertheless, it can be assumed that these effects may be present in cuprates with similar microstructures.

The magnetic field-temperature phase diagram, Fig. 8, shows clear differences for (left) and (right): For , the irreversibility field can be well described by a simple power law of the form with 4/3 (red line). Similar power laws for at high temperatures have been measured for Co-doped Ba-122 single crystals by resistive53 and AC susceptibility measurements54. In contrast, seems to be strongly influenced by the temperature dependence of as well as the extended planar defects. It was fitted empirically as with = 1.2 and = 1.08. For both directions, is distinct from the upper critical field at zero temperature, . That means the sample investigated shows a clear and relatively wide vortex-liquid region at zero temperature despite the relatively low Ginzburg number of Ba-122 compounds (). The origin of this broad region of the vortex-liquid phase is unclear and has to be clarified in further investigations.

Conclusion

The electrical transport properties of a superconducting Co-doped Ba-122 thin film with a large density of -planar defects (stacking faults or intergrowths) were measured in high magnetic fields. Between these planar defects, a dense network of small-angle grain boundaries parallel to is formed. Both types of defects contribute to strong pinning in such films, indicated by the presence of a clear -axis peak in in fields up to around 5 T and a sharp peak above the random-pinning curves up to around 20 T. The angular dependence of was found to be influenced by the multi-band superconductivity and/or the extended defects. This, in consequence, strongly influences the angular dependence of the critical current density,. can be scaled very effectively by a modified Anisotropic Ginzburg-Landau approach which takes into account the actual dependence of . The vortex-matter phase diagram down to lowest temperatures was evaluated for both major directions, and , from resistive measurements in magnetic fields up to 62 T. was measured in the complete superconducting region, revealing a surprisingly large vortex-liquid phase at zero temperature. follows a simple power law whereas is influenced by the temperature dependence of as well as the presence of planar defects. At fields above the matching field of the planar defects ( T), the vortices are only weakly pinned at random disorder. All data were analyzed self-consistently: Arrhenius derivation of the pinning potential and determination of used the same value. Furthermore, corresponds to .

Methods

Thin film preparation

Co-doped Ba-122 thin films of 170 nm thickness were grown by pulsed laser deposition under UHV conditions (base pressure mbar) from a stoichiometric sintered target of Ba(Fe0.92Co0.08)2As2 using a KrF excimer laser ( = 248 nm). The energy density of the laser beam at the target was around 4 J/cm2, the repetition rate 10 Hz, the substrate temperature 750 °C. As substrate, we used single-crystalline (001) MgO covered by an epitaxially grown 20 nm thick (001) Fe layer. The Fe layer was grown at room temperature and 5 Hz repetition rate and subsequently heated to the deposition temperature of Ba-122 (750 °C) to ensure a smooth surface55.

Microstructural Analysis

Crystal structure, texture and phase purity were measured by x-ray diffraction (XRD) in parallel-beam geometry with Co radiation ( = 1.78897 Å) on a Bruker D8 Advance and in Bragg-Brentano geometry on a Phillips X’pert goniometer with an Euler cradle using Cu radiation ( = 1.54056 Å). The microstructure was further investigated by transmission electron microscopy (TEM) on an FEI Tecnai T20 (LaB6, 200 kV) and an FEI Titan 80–300, operating at 300 kV with an image corrector. The lamella was prepared with the in-situ lift-out method in a focused ion beam (FIB) device56.

Electrical transport properties

Resistance and critical current density in dependence of temperature, T, magnetic field, H and its orientation, θ, were measured on microbridges in four-point geometry in maximum Lorentz force configuration. The angle θ is measured between the magnetic field and the crystallographic -direction. The microbridges, fabricated by Ar ion etching and laser cutting, had widths between 50 and 250 μm and lengths between 0.5 and 1 mm. PPMS devices with fields up to 9 T and 16 T, a Florida NHMFL Bitter magnet up to 35 T and the Dresden pulsed field facilities at IFW Dresden57 (45 T) and HZDR Rossendorf 58 (62 T) were used for these measurements. The upper critical fields as well as the critical temperature were determined at several constant levels around 90% of the normal-state resistance at 35 K of the Fe/Ba-122 bilayer and checked for plausibility regarding curvature of near and regarding values determined from thermal activation of flux motion and scaling of in the vicinity of a hypothetical glass-liquid transition (not discussed in this paper). A value of 95% showed consistency. This is slightly higher than the usually applied 90% due to the conducting Fe interlayer, as described in ref. 59. The irreversibility field was estimated from the field dependence of the pinning force, in combination with a plausibility check of the -value (exponent in the electric field-current density characteristics near : 1 for ). The critical current density was determined with a constant electrical field criterion of 1 μV/cm from characteristics. The validity of the 95% criterion for as well as the phenomenological fit function Eqs. 1 and 2 was further checked by rescaling at several angles θ to , Suppl. S3.

Additional Information

How to cite this article: Hänisch, J. et al. High field superconducting properties of Ba(Fe1−xCox)2As2 thin films. Sci. Rep. 5, 17363; doi: 10.1038/srep17363 (2015).