Critical current density and mechanism of vortex pinning in KxFe2-ySe2 doped with S
aa r X i v : . [ c ond - m a t . s up r- c on ] A ug Critical current density and vortex pinning mechanism of K x Fe − y Se with S doping Hechang Lei and C. Petrovic
Condensed Matter Physics and Materials Science Department,Brookhaven National Laboratory, Upton, NY 11973, USA (Dated: April 23, 2017)We report critical current density J c in K x Fe − y Se − z S z crystals. The J c can be enhancedsignificantly with optimal S doping (z = 0.99). For K . Fe . Se . S . the weak fishtaileffect is found for H k c. The normalized vortex pinning forces follow the scaling law with maximumposition at 0.41 of reduced magnetic field. These results demonstrate that the small size normalpoint defects dominate the vortex pinning mechanism. PACS numbers: 74.25.Sv, 74.25.Wx, 74.25.Ha, 74.70.Xa
I. INTRODUCTION
Since the discovery of LaFeAsO − x F x (FeAs-1111type) with T c = 26 K, intensive studies have been carriedout in order to understand the superconducting mecha-nism, explore new materials and possible technical ap-plications. Among discovered iron-based superconduc-tors, FeAs-1111 materials and AFe As (A = alkalineor alkaline-earth metals, FeAs-122 type) exhibit high up-per critical fields ( µ H c ) and good current carrying abil-ity which are important for energy applications. − Onthe other hand, even though FeCh (Ch = S, Se, andTe, FeCh-11 type) materials have nearly isotropic high µ H c and considerable critical current density, , theirrelatively low T c when compared to FeAs-1111 and FeAs-122 superconductors is a serious disadvantage. Recently,A x Fe − y Se (A = K, Rb, Cs, and Tl, AFeCh-122 type)materials attracted much attention due to rather high T c,onset ( ∼
32 K), and µ H c ( ∼
56 T for H k c at 1.6 K). , However, preliminary studies indicate that the criticalcurrent density in K x Fe − y Se is lower than in other ironbased superconductors. , Therefore, it is important toexplore pathways for the critical current density J c en-hancement in AFeCh-122 compounds.In present work, we report the enhancement of crit-ical current density and vortex pinning mechanism inK x Fe − y Se − z S z single crystals. Point defect pinningdominates the vortex pinning mechanism whereas crit-ical current density is maximized for z = 0.99(2). II. EXPERIMENT
Details of crystal growth and structure characteriza-tion were reported in previous work. , Crystals werepolished into rectangular bars and magnetization mea-surements were performed in a Quantum Design Mag-netic Property Measurement System (MPMS-XL5) up to5 T. The average stoichiometry and homogeneity of sam-ples were determined by examination of multiple pointsusing an energy-dispersive x-ray spectroscopy (EDX) ina JEOL JSM-6500 scanning electron microscope.
FIG. 1. (a) Magnetization hysteresis loops ofK x Fe − y Se − z S z at 1.8 K for H k c. (b) Superconduct-ing critical current densities J abc ( µ H ) determined frommagnetization measurements using the Bean model. III. RESULTS
Fig. 1(a) shows magnetization hysteresis loops(MHLs) of K x Fe − y Se − z S z at 1.8 K for H k c with fieldup to 5 T. The shapes of MHLs for all of samples aretypical of type-II superconductors. However, for differ-ent S doping, they exhibit different flux pinning behavior.For low S doping (z = 0 and z = 0.32), the MHLs areasymmetric. This asymmetry suggests that the bulk pin-ning is small and that the influence of the surface barrieris important. , On the other hand, for higher S dop-
FIG. 2. EDX mapping of K . Fe . Se . S . .(Scale bar is 0.1 mm.) ing (z = 0.99 and z = 1.04), the shapes of MHLs aresymmetric indicating that the bulk pinning is dominant.For K . Fe . Se . S . crystal, a small fish-tail hump appears at 0.8 T, similarly to FeAs-122 singlecrystals. , − We determine the critical current densityfrom the Bean model. , For a rectangularly-shapedcrystal with dimension c < a < b, when H k c, the in-plane critical current density J abc ( µ H ) is given by J abc ( µ H ) = 20∆ M ( µ H ) a (1 − a/ b ) (1)where a and b (a < b) are the in-plane sample size incm, ∆ M ( µ H ) is the difference between the magnetiza-tion values for increasing and decreasing field at a par-ticular applied field value (measured in emu/cm ), and J abc ( µ H ) is the critical current density in A/cm . FromFig. 1(b), it can be seen that the J abc ( µ H ) shows smallincrease at high field region for z = 0.32 when comparedto z = 0 sample. On the other hand, it is enhancedabout one order of magnitude for z = 0.99 in the wholemagnetic field range. For higher S content, the J abc (0)is still much larger than in pure K . Fe . Se . ,but the J abc ( µ H ) at high fields is smaller. It should benoted that the T c decreases significantly when z > T c,onset = 33.0 K), z = 0.99crystal has T c,onset = 24.6 K, whereas z= 1.04 has T c,onset = 18.2 K. Therefore, sample with z = 0.99 exhibits thebest performance and we studied its field dependence ofmagnetization and critical current density in detail. K,Fe, Se and S are uniformly distributed in z = 0.99 crystal(Fig. 2), as is the case with all crystals we investigated.Fig. 3 shows the MHLs of crystal with z = 0.99for both field directions. The fishtail effect is only ob- -5 -4 -3 -2 -1 0 1 2 3 4 5-35-30-25-20-15-10-505101520253035-5 -4 -3 -2 -1 0 1 2 3 4 5-4-3-2-101234
T=1.8K T=4K T=6K T=8K T=10K T=12K T=14K T=16K T=18K M ( e m u / c m ) H (T) H//c(a)(b) M ( e m u / c m ) H (T) H//ab
T=2K T=4K T=6K T=8K T=10K T=12K T=14K T=16K T=18K
FIG. 3. MHLs of K . Fe . Se . S . for (a) H k cand (b) H k ab. served for H k c. It diminishes gradually with increas-ing temperature. Similar behavior has also been seen inBaFe − x Co x As , suggesting anisotropic flux pinning. On the other hand, linear M ( µ H ) background existsfor both field directions, being more obvious for H k ab.This is also observed in pure K . Fe . Se . . The slope of this background for crystal with z = 0.99is nearly the same as in pure material, suggesting thathigh temperature magnetism changes little with z for z M ( µ H ) background has no effect onthe calculation of ∆ M ( µ H ), and is due to incompletesuperconducting volume fraction of the crystals used inthis study. We will discuss the effects of electromagneticgranularity in the next section.The J abc ( µ H ) is calculated using eq. (1) for H k c andshown in Fig. 4(a)The evaluation of critical current den-sity becomes more complex for H k ab, since there are twodifferent contributions. One is vortex motion across theplanes, J cc ( µ H ), and the other is vortex motion parallelto the planes, J k c ( µ H ). Usually, J k c ( µ H ) = J abc ( µ H ).Assuming a, b ≫ c/ · J k c ( µ H ) /J cc ( µ H ), we obtain J cc ( µ H ) ≈ M ( µ H ) /c . The calculated J cc ( µ H ) isshown in Fig. 3(b).The J abc (0) and J cc (0) are 7.4 and 8.4 × A/cm at 1.8 K and 2 K, respectively. Even though theyare still smaller than in other iron pnictide super-conductors (where critical current densities are usuallyabove 10 A/cm at 5 K), , S doping significantly T=1.8K T=4K T=6K T=8K T=10K T=12K T=14K T=16K T=18K J c ab ( A / c m ) H//c(a)
T=2K T=4K T=6K T=8K T=10K T=12K T=14K T=16K T=18K J cc ( A / c m ) H (T)H//ab(b)
FIG. 4. Magnetic field dependence of superconducting crit-ical current densities (a) J abc ( µ H ) and (b) J cc ( µ H ) forK . Fe . Se . S . . enhances the critical current density when comparedto pure K . Fe . Se . . , It suggests that Sdoping introduces effective pinning center and there-fore enhances the J c for both field directions. On theother hand, the ratio of J cc ( µ H )/ J abc ( µ H ) is approxi-mately 1 and is smaller than in BaFe − x Co x As . Thefield dependence of J cc ( µ H ) is somewhat weaker than J abc ( µ H ). This could be related to the layered structureof K x Fe − y Se − z S z . IV. DISCUSSION
In order to gain more insight into the vortex pin-ning mechanism in K . Fe . Se . S . , weplot the normalized vortex pinning force f p = F p /F max p as a function of the reduced field h = H/H irr at vari-ous temperatures for H k c (Fig. 5). The pinning force F p was obtained from the critical current density us-ing F p = µ HJ c , and F max p corresponds to the maxi-mum pinning force. The irreversibility field µ H irr isthe magnetic field at which J abc ( T, µ H ) is zero. It canbe clearly seen that the f p vs h curves exhibit scalingbehavior, independent of temperature, suggesting dom-inance of single vortex pinning mechanism. Scaling law f p ∝ h p (1 − h ) q explains well our data. The obtainedparameters are p = 1.10(1) and q = 1.64(2). The value of h fit max (= p/ ( p + q )) ≈ h exp max ≈ f p vs h curvesat various temperatures. According to the Dew-Hughes f p = F p / F p m a x h=H/H irr
6K 8K 10K 12K 14K 16K F p m a x ( N / m ) H irr (T) FIG. 5. Normalized flux pinning force f p = F p /F max p as a function of reduced field h = H/H irr forK . Fe . Se . S . . Solid line represents the fit-ting curve using f p = Ah p (1 − h ) q . Inset shows F max p as afunction of µ H irr . Solid line shows the fitting result obtainedby using F max p = A ( µ H irr ) α . model for pinning mechanism, the h max = 0.33 with p = 1 and q = 2 corresponds to small size normal pointdefects pinning. Our results indicate that small normalpoint defects pinning dominates vortex pinning mech-anism. These defects could be related to distributionof S ions on a submicron scale, similarly to FeAs-122system. , , Moreover, the F max p can be fitted using F max p = A ( µ H irr ) α and we obtain α = 1.94(3). This isconsistent with the theoretical value ( α = 2). Since our crystals are rather homogeneous (Fig. 2), theshape of M(H) for z = 0 and z = 0.32 suggests some elec-tromagnetic granularity similar to SmFeAsO . F . . Since we used the full sample dimensions in J abc and J cc calculation, the values we obtained represent the lowerlimit of bulk superconducting crystals. Indeed, very re-cently Gao et al. reported the J c of K x Fe − y Se can beenhanced significantly (about 1.7 × A/cm at 5 K) us-ing one-step technique. It implies that with S doping,the J c of AFeCh-122 might increase further if preparationprocess can be optimized. V. CONCLUSION
In summary, we show an order of magnitude increasesin J c by S doping in K x Fe − y Se . The optimum S con-tent in K x Fe − y Se − z S z single crystals is z = 0.99. Forthe optimally doped sample, the weak fishtail effect isobserved when H k c. The analysis of vortex pinning forceindicates that the dominant pinning sources are small sizenormal point defects which could originate from distribu-tion of doped S. The results demonstrate that by furtheroptimizing the vortex pinning force, higher values of J c could be achieved, raising the prospects for technical ap-plications of AFeCh-122 compounds. VI. ACKNOWLEDGEMENTS
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