Low field anomaly in the critical current of Ba1− x K x Fe2As2 tapes

Ba1−x K x Fe2As2 superconductors have strong potential for magnet applications through their very high upper critical field, relatively high superconducting transition temperature and manufacturability through the powder-in-tube (PIT) route. However, the critical current density in PIT tapes is still low compared to the incumbent technologies, so a greater understanding of the limiting factors is required. We have measured the in-field critical currents (I c) of stainless steel and silver double-sheathed monofilament Ba0.6K0.4Fe2As2 superconductor tapes at elevated temperatures from 15 K to 35 K. At 20 K, the critical current density is up to 140 kA cm−2 in low (optimal) field and 22 kA cm−2 in 8 T. In the low-field region we observe an anomalous and sharp suppression of I c centred at the zero field. This feature is non-hysteretic for lower temperatures and perpendicular fields, but becomes hysteretic for higher temperatures in perpendicular fields and for all temperatures in parallel fields. The low-field suppression is also reflected in the n-values which can otherwise be very high, in excess of 100 in the optimal field. Magnetic-field hysteresis of I c is generally attributed to flux exclusion/flux trapping in granular superconductors and this is likely to be the case also in the present conductors. The low-field I c anomaly also likely has its origin in planar granularity, while magnetic phases in grains or grain boundaries may also play a role.


Introduction
Iron-based superconductors have been developed towards commercial applications since their discovery in 2008 [1].The 122-derived compounds such as (Ba,K)Fe 2 As 2 and (Sr,K)Fe 2 As 2 identified very soon after [2,3] have been a particular focus due to their promising properties including a relatively high superconducting transition temperature, comparable to that of MgB 2 , and a very high upper critical field [4], Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
putting it into a similar category as REBa 2 Cu 3 O 7 for highfield magnet applications.Unlike REBa 2 Cu 3 O 7 though, there exists the possibility to make tapes by the powder-in-tube (PIT) route [5][6][7][8][9][10], giving potential for cheaper manufacturing and higher fill factors than the coated conductor type tapes.On the other hand, the PIT method gives somewhat less control over grain alignment, grain orientation and the formation of pinning centres, requiring some ongoing development work to achieve competitive engineering current densities.
In recent progress, the critical current density (J c ) of PIT (Ba,K)Fe 2 As 2 tapes have been improved through control of the pressing or rolling process, the preparation of precursor materials and the choice of sheath materials [11][12][13][14][15][16][17][18][19][20][21].For example, J c exceeding 10 5 A cm −2 has been achieved through a flat-rolled double sheath material with the superconductor encased first in silver or silver-tin alloy and then in stainless steel [16], where silver provides chemical compatibility with the superconductor and the stainless steel is a hard outer sheath that transfers the pressure of the rolling process while minimizing the sausaging effects of the softer silver sheath.
In this work, we have investigated critical currents in a recent stainless steel/silver sheathed Ba 0.6 K 0.4 Fe 2 As 2 tape.We have highlighted detailed temperature-, field-and angulardependent measurements in medium-to-high temperatures and low-to-medium magnetic fields.In part, this will inform future AC loss simulations.

Samples
The stainless-steel/Ag/Ba 0.6 K 0.4 Fe 2 As 2 tapes were fabricated by the PIT method from metallic precursors.Precursor powders of Ba, K, Fe and As were used in the ratio 0.6:0.5:2:2giving a slight K excess to account for evaporation.BaAs and KAs intermediates were prepared first by ball milling and sintering at 400 • C-600 • C.These powders were then mixed with Fe and As powder, ball milled again and sintered at 900 • C.This precursor powder was packed into an Ag tube, swaged, drawn and rolled.For the outer sheath, the stainless-steel tube with outer diameter 2.5 mm and inner diameter 1.5 mm was flat rolled to 1.7 mm thickness and the packed Ag tape was then inserted into this flat tube and further flat rolled to the final dimensions of 4.15 mm × 0.80 mm.The tape was further sintered in short pieces at 750 • C.These tapes are nominally very similar to other monofilament tapes produced at the Chinese Academy of Sciences and described in the literature [11][12][13][14][19][20][21].
A cross-section micrograph of the final tape is shown in figure 1.The Ba 0.6 K 0.4 Fe 2 As 2 superconductor cross-sectional area is 0.13 mm 2 , with a fill-factor of approximately 4.3%.
Detailed microstructures of the granular superconducting core have been shown in similar tapes without a stainless-steel outer sheath [14,22,23], revealing a planar granular structure where grains are about 5-10 µm long and 1-2 µm thick and have a strong c-axis alignment.Given the similarity of preparation processes and the high-field I c data reported herein and therein, it is likely that the microstructure in the samples presented here are very similar to those in the previous reports.

Critical current measurement
The critical current was measured over a range of temperatures, magnetic fields and magnetic field angles on a SuperCurrent four-probe transport measurement system [24].The system controls the temperature with a cold helium gas flow and a heater on the current leads.Currents of up to 1200 A, sample temperatures below 15 K, magnetic fields up to 8 T and full angle dependences in the maximum Lorentz force configuration can be measured with this system.The system allows for relatively rapid measurements and for batch-based automated measurements, which has allowed  us to explore the field, angle, and temperature dependence in some detail.In particular, the field-reversal region has shown some surprising results.We measured two samples from the same tape with identical results to show that the results are reproducible.60 mm long samples were cut for testing.Because stainless steel is difficult to solder, 12 mm long silver shims were soldered to one face at each end of the sample with Sn-Pb electronic solder and a ZnCl-based flux.The stacked sample was then soldered silver-shim side down onto copper current contacts with a low-temperature In-Bi solder.A small silver shim was also soldered near the centre of the sample to maintain direct thermal contact with a cernox temperature sensor.Voltage probes were soldered with low-temperature solder on the top (reverse-side) of the sample with 5 mm spacing.This arrangement was chosen to achieve sufficient current transfer into the superconductor while minimizing heating, within the constraints of the apparatus.The critical current I c and n-value were obtained by fitting voltage-current (V-I) characteristics to a power law With this system, we also measured the superconducting transition temperature by the current transport method, giving 37.7 K for the appearance of dissipation as shown in figure 2. This was measured with a fixed transport current of 10 mA and voltage tap spacing of 5 mm.Note that the resistance above the transition mainly reflects that of the silver sheath rather than the normal state of the superconductor.

Field and temperature dependence of critical current
The magnetic field dependence of I c is shown in figure 3(a) for fields applied normal to the tape (perpendicular field) and figure 3(b) for fields applied in the plane of the tape (parallel field), and for several temperatures between 15 K and 30 K. The material critical current density, based on the crosssectional area of the superconducting material only, is shown on the right axis.
The maximum critical current was 260 A at 15 K in low, but non-zero, perpendicular field.This corresponds to a material critical current density of 195 kA cm −2 .At 20 K, 8 T, maximum I c is 29.2 A, extrapolating to 25.0 A at 10 T giving J c of 18.8 kA cm −2 (20 K, 10 T).
Both ascending-field and descending-field measured data are shown for fields below 3 T and there is a clear degree of hysteresis below about 1 T.

Hysteresis and low-field anomaly
The hysteresis effect is clarified in more detailed field dependences of I c as shown in figure 4. Here, we expand the low-field region and sweep the field in both polarities with both ascending and descending sweeps.In addition to a marked hysteresis, we also uncover a remarkable 'dip' or sharp minimum of I c at or close to zero field.In perpendicular field and low temperatures (figure 4(a)) this I c dip is centred at zero field and is almost completely non-hysteretic, with only a slight hysteresis in the positive-peak shoulders of this dip.The hysteretic asymmetry of the shoulders increases with temperature.At the highest temperature of 30 K (figure 4(d)), the I c dip begins to shift slightly from zero field and becomes slightly hysteretic.In a parallel field, on the other hand, the I c dip is offset from zero and again, therefore hysteretic right from the lowest temperatures (figure 4(e)) and the degree of hysteresis reduces with increasing temperature (figures 4(f)-(h)).The shoulders are also asymmetrical at all temperatures.
The observation of an I c minimum near zero field in this material qualitatively confirms previous observations [20,21].In those reports, only unipolar fields were applied, but there was a clear low I c region for very low fields as well as hysteresis.Such low-field minima are highly unusual.'Fish-tail' effects involving a second peak have long been seen in magnetization data [25] especially of single-crystal or sinteredpowder cuprate superconductors [26,27] and only occasionally observed in transport measurements [28].The effect tends to be increased in measurements across low-angle grain boundaries on a bi-crystal [29].However, the behaviour we note here is somewhat different in that the zero-field peak is missing entirely; we have two peaks, one each in positive and negative fields, whereas in the classic fish-tail effect there are three peaks at positive, zero and negative fields.
The possibility of a zero-field minimum of I c has been described as a consequence of magnetic granularity [27,30] in which the grain boundaries can form a continuous percolative path for vortices to traverse the sample.At low fields, vortices in the grain boundaries are weakly pinned and limit the transport J c to a level below the intra-grain J c .As the field increases, strongly pinned vortices also appear in the grains and magnetic interactions between vortices lead to collective pinning and increasing transport J c .Eventually, the flux pinning limit of the intra-grain vortices is reached and the decreasing-I c regime in higher fields is limited by intra-grain pinning.The magnetic granularity described in these works corresponds well to the planar granular structure reported in (Ba,K)Fe 2 As 2 tapes [14,22,23].
Magnetic granularity also explains the I c hysteresis [31].Best illustrated by figures 4(c) and (d), in the descending-field leg approaching the first (positive-field) I c maximum, flux is trapped by closed current loops circulating within the grains, giving a higher density of vortices in the grain than was present at the same field in the ascending leg.Strong collective pinning therefore extends to lower fields until the reverse flux from intra-grain current loops cancels the applied field in the grain boundaries and the flux again starts to flow now in the opposite direction (though still in a positive applied field).
In parallel fields (figures 4(e)-(h)) the relative importance of hysteresis versus the low-field I c dip changes as the dimensionality of the grain-boundary network changes.At higher temperature, 30 K, the I c dip and hysteresis look quite similar for perpendicular and parallel fields (figures 4(d) and (h)), but as temperature reduces the hysteresis becomes more dominant for parallel fields rather than less dominant for perpendicular fields.The details of this behaviour are not yet fully explained, but are related to the dimensions of the grains which are long and flat due to the rolling process.In parallel fields the grains are side-on to the field but may also be better linked to adjacent grains.
The magnetization of a short sample of this tape, shown in figure 5 may also play a role as suggested in [20].The overall shape shown in the inset has a large positive slope associated with weak ferromagnetism of the stainless-steel sheath induced through the mechanical deformation process.This background slope has been subtracted to show the underlying magnetism in the main figure.There remains a second significant ferromagnetic or superparamagnetic component that saturates at quite low magnetic field, around 0.5 T. This feature also appears in tapes without a stainless steel outer sheath [20] and most likely originates from iron particles in the (Ba,K)Fe 2 As 2 material [32].Given the range of fields that this appears at there is a possibility that this feature may also contribute to the I c dip or the details of the hysteresis.There may be a flux concentration/diverting effect at low fields depending on whether these phases appear within grains or in the grain boundaries.The transport data at 15 K, perpendicular field, suggests that this effect then saturates at around 200 mT.
Below T c the magnetization curve is hysteretic due to the macroscopic circulating supercurrents, and we also observe a small inflection close to zero field which appears to mimic, at  least qualitatively, the I c dip that we observe in the transport data.

Angle dependence of critical current
The field-angle dependence of the critical current is shown over a range of temperatures and magnetic fields in figure 6. θ = 0 • is defined as the perpendicular field and θ = 90 • as the parallel field.The transport current is always perpendicular to the applied magnetic field.We show in this figure fields of 2 T and above at which hysteresis is negligible.All data in figure 6 show I c measured in both angle ascending and angle descending sweeps.The curves are indistinguishable confirming that angular hysteresis is negligible in this range.
We observe here an interesting reversal in the anisotropy, as has previously been noted for (Sr,K)Fe 2 As 2 PIT tapes [15].The anisotropy is in any case low compared to the high-T c cuprates.Approaching T irr the anisotropy tends towards  the 'expected' sense with J c para > J c perp , but as temperature reduces the anisotropy reverses to give the opposite sense by 20 K at the fields available here.
The reversal of anisotropy has been explained as a natural consequence of pinning by spherical defects with radii somewhat larger than the in-plane coherence length [21].When the field is parallel to the tape, the vortex core becomes elliptical with the c-axis coherence length smaller by the effective mass anisotropy (γ ∼ 2).The smaller vortex has a correspondingly smaller elementary pinning force relative to the spherical pin.The cross-over field is temperature dependent, as shown in figure 7.Over the limited range shown here, the cross over field appears to be diverging as the temperature is reduced, in contrast to the trend observed for (Sr,K)Fe 2 As 2 tapes [15].
At fields below 2 T we observed the onset of hysteresis in the field dependence of I c (figure 3) and this carries across into the angle dependences.In figure 8 we show an example of this at 25 K and a low field of 0.02 T. Measurements taken in ascending-or descending-angle order show a large hysteresis effect, symmetrical about the 0 • and 90 • principal axes of the tape.This complex behaviour makes modelling for this wire, for DC or AC magnet applications for example, challenging until intrinsic field/angle dependences and the mechanism for hysteresis are determined.

N-values
The n-values, the index of the power law current-voltage characteristic, is also important for modelling for applications.These vary strongly with temperature, field and angle and values can be over 100 at low field, down to around 10 at 8 T (figure 9).The n-values are hysteretic and also show a lowfield minimum, qualitatively following the trends of I c values.The fields at which minima occur closely follow those of the  I c values for both perpendicular and parallel fields, while the shapes of the shoulder peaks are rather broader than I c values.An example of the n-value hysteresis, taken at 20 K and parallel applied field, is shown in figure 10; the minima occur at ±70 mT similar to I c and the maxima at around 200 mT-300 mT.Note that the maxima are rather poorly determined since the large n-values over about 50 could not be determined accurately.

Conclusion
We have investigated transport I c (T,B,θ) measurements over a range of temperatures and magnetic fields suitable for applications.Of particular note, we have observed an anomalous dip in the field-dependence of I c occurring at or near zero field.It is especially clear in perpendicular fields and low temperatures  where hysteresis is small, in which case the dip is located at zero field.This differs from the usual 'fish-tail' effects (which are in themselves rare in transport measurements) in that those usually still have a local maximum at zero field accompanied by extra peaks at positive and negative fields.This effect could arise from the granularity associated with planar grains, where initially weakly-pinned vortices in grain boundaries become more strongly pinned by collective pinning with vortices in the grains at moderate field strength.Beyond the in-field peak, I c becomes limited by the usual intra-grain pinning.
In parallel fields, hysteresis becomes more predominant and the dip shifts with field sweep sense to occur after sweeping through zero in either direction.The positive-peak 'shoulders' are asymmetric with the highest I c occurring before sweeping through zero in either direction.
These anomalous low-field I c characteristics have not been reported in this form previously, however this is partly because much of the literature has focused on performance in high magnetic fields.Given that our samples do not appear to be very different from literature reports in terms of their preparation or high-field I c behaviour, it is likely that this low-field behaviour is common, if not universal, in granular PIT 122type superconducting tapes.Further work will be required to establish this.

Figure 1 .
Figure 1.SEM cross sectional image of the tape sample.The outer dimensions of the tape are 0.8 mm thick by 4.15 mm wide.The superconducting fill fraction is 4.3%.

Figure 2 .
Figure 2. The resistance of the tape as function of temperature, showing the superconducting transition.The conduction in the normal state is dominated by the silver sheath.

Figure 3 .
Figure 3. Field dependence of critical current (left axis) and critical current density (right axis) for (a) perpendicular applied field and (b) parallel applied field, at a range of temperatures.

Figure 4 .
Figure 4. Bipolar field dependence of the critical current for ascending and descending sweeps of the magnetic field, for different temperatures and for (a)-(d) perpendicular applied field or (e)-(h) parallel applied field.

Figure 5 .
Figure 5. Magnetization hysteresis at T = K of a small 2.4 mm long sample of the tape with cross section shown in figure 1.The inset shows the full magnetization curve while the main figure shows the curve with the main linear component subtracted, highlighting a superparamagnetic component and circulating-current hysteresis with small inflection near zero field.

Figure 6 .
Figure 6.Field-angular dependences of Ic at magnetic fields of (a) 2.0 T, (b) 4.0 T and (c) 8.0 T and at a range of temperatures.All curves include both ascending-angle and descending-angle sweeps.

Figure 7 .
Figure 7. Temperature dependence of the cross-over field between conventional anisotropy (Jc para > Jc perp ) and reversed anisotropy (Jc para < Jc perp ).

Figure 8 .
Figure 8.An example of the hysteresis of the field-angular dependence of Ic at 25 K and 0.02 T.However, the hysteretic angle dependences are dependent also on past field excursions as well as the sweep direction.

Figure 9 .
Figure 9. Field dependence of n-values at a range of temperatures for (a) perpendicular, and (b) parallel applied field.

Figure 10 .
Figure 10.Field-sweep hysteresis of the n-value at 20 K, parallel applied field.