Critical current anisotropy in Nd-1111 single crystals and the infuence of neutron irradiation
M. Eisterer, V. Mishev, M. Zehetmayer, N. D. Zhigadlo, S. Katrych, J. Karpinski
aa r X i v : . [ c ond - m a t . s up r- c on ] N ov Critical current anisotropy in Nd-1111 single crystals and theinfluence of neutron irradiation
M. Eisterer, V. Mishev, and M. Zehetmayer
Atominstitut, Vienna University of Technology,Stadionallee 2, 1020 Vienna, Austria
N. D. Zhigadlo
Laboratory for Solid State Physics, ETH Zurich, CH-8093 Zurich, Switzerland
S. Katrych and J. Karpinski
Laboratory for Solid State Physics, ETH Zurich, CH-8093 Zurich, Switzerland andInstitute of Condensed Matter Physics,EPFL, CH-1015 Lausanne, Switzerland
Abstract
We report on angle-resolved magnetization measurements on NdFeAsO . F . (Nd-1111) singlecrystals. The field dependence of the critical current density, J c , is non-monotonous in these crystalsat all orientations and temperatures due to the fishtail effect, which strongly influences the angulardependence of J c . The currents decrease as the field is tilted from the crystallographic c -axis at lowfields, but increase at high fields. A peak occurs in the angular dependence of J c at intermediatefields. The critical currents are significantly enhanced after irradiation with fast neutrons and thefishtail disappears. The different current anisotropies at low and high fields, however, persist. Wediscuss the data in the framework of the anisotropic scaling approach and propose a transitionfrom dominant pinning by large defects of low density at low fields to pinning by small defects ofhigh density at high fields in the pristine crystal. Strong pinning dominates at all fields after theirradiation, and the angular dependence of J c can be described by anisotropic scaling only after anappropriate extension to this pinning regime. . INTRODUCTION The pinning properties of iron-based superconductors have been in the focus of intensiveresearch since the discovery of superconductivity in these compounds.[1] Many similaritiesto the cuprates were found. The critical currents in single crystals often show a fishtaileffect, which disappears after the introduction of an efficient pinning landscape, for instanceby irradiation techniques.[2–7] In thin films on the other hand, pinning is much strongerand the currents decrease monotonously with field.[8–23] Angle-resolved measurements ofthe pinning properties are very efficient for studying the pinning landscape and anisotropyeffects of the vortex lattice. They were performed nearly exclusively on films so far, inwhich growth-related and often correlated defects dominate the properties, which are notrepresentative for the defects prevailing in bulk materials such as single crystals or grainsin wires or tapes. Angle-resoved measurements on crystals are thus highly desirable tocomplement the film data. Thin films are widely available only of the Ba-122 (BaFe As )[8–15] and 11 (FeSe − x Te x ) [16–20] families and only a few data exist for the 1111 (LaFeAsO)family.[21–23] The latter has the highest anisotropy among them, [24] which makes it thebest candidate for studying anisotropy effects. Anisotropy is considered as a key parameterfor applications, since it enhances the harmful thermal fluctuations. In this study we reporton the anisotropy of the in-plane critical currents of Nd-1111 single crystals by angle-resolvedmagnetization measurements. The results are discussed in the framework of the anisotropicscaling approach.[25] After the characterization of the pristine crystals the defect structurewas changed completely by irradiation with fast neutrons to assess changes in the pinningproperties arising from the introduced pinning centers. II. EXPERIMENTAL
The NdFeAsO . F . single crystals were prepared by a high pressure technique.[26]Two crystals were studied, whose geometries were determined in two steps. First, an opticalmicroscope was used to establish the lateral surface area. A subsequent mass measurementenabled the calculation of the volume and the thickness of the samples from the theoreticalmass density.[27] The results are listed in Table I. The transition temperature ( T c ) wasmeasured in a 1 T SQUID by applying an AC field of 0.3 mT. The reported transition tem-2erature refers to the onset of superconductivity, where the susceptibility starts to deviatefrom its behavior in the normal conducting state. Sample a (mm) b (mm) c (mm)Nd1111
Magnetization loops were recorded on crystal c -axis of the sample. The critical currentdensity, J c , along the ab -planes was evaluated from the irreversible magnetic moment m irr .A self-field correction was applied for the calculation of the average magnetic field B withinthe crystal.[28]Sample E > . . · m − and 1 . · m − , respectively. The fluence was determined from the radioactivity of a nickelfoil which was placed in the same quartz tube as the sample during the irradiation. Fastneutron irradiation is known to result in a variety of defects, ranging from single displacedatoms to spherical defect cascades of about 5 nm in diameter.[3, 29–31]Angle-resolved magnetization measurements were performed on crystal ab -planes (the large surface). This conditionwas verified from the orientation of the magnetic moment, which is available in a vectorVSM. The currents inside the sample were found to remain parallel to the large surface (andto the ab -planes) up to an angle of at least 80 ° , which is a consequence of the large aspectratio of the crystal. Only data within this angular range will be considered in the following inorder to avoid problems with currents flowing in arbitrary directions and the resulting changein geometry of the current loops. However, not all currents flow under Maximum LorentzForce (MLF), when the sample is inclined from one of its main orientations, and the currentsflowing under Variable Lorentz Force (VLF) potentially change the angular dependence of J c .[16] Whenever the VLF-currents may influence the behavior in a qualitative way, it will3 J ab c ( A m - ) B(T)
10 K 20 K 30 K0 1 2 3 4 5 610 J ab c ( A m - ) B(T)
FIG. 1. Critical current densities of the Nd-1111 single crystal B k c ). The open and solid symbols refer to the pristine andthe neutron irradiated crystal, respectively. be noted explicitly. We will also restrict our considerations to 15 K where the VSM signalis sufficiently large ( > − Am ), the self-field is comparatively small and the peak of thefishtail is visible in a wide angular range. At higher temperatures, the signal of the tinycrystals was too small for a careful analysis, at lower temperatures the self field increasesand the fishtail moves out of the accessible field range ( < III. RESULTS
The irradiation slightly reduces the transition temperature from 39.9 K to 39.3 K in crystal . · m − ) and from 39.3 K to 39.1 K in crystal . · m − ). These findingsare consistent with previous reports on Sm-1111 bulk samples [3] or Ba-122 single crystals.[2]The modest decrease in T c is also comparable with that in the cuprates [34, 35]. A smallneutron fluence does not harm the transition temperature significantly, but improves pinning.(Note that superconductivity is totally suppressed after irradiation to a neutron fluence ofthe order of 10 m − .[36].)Figure 1 shows the changes in critical current density upon neutron irradiation at var-4 J c ( A m - ) B(T) J c ( A m - ) B(T)
FIG. 2. Field dependence of the critical current density in crystal c -axis. Left panel: pristine crystal.Right panel: after irradiation to a fast neutron fluence of 1 . · m − ious temperatures for the magnetic field applied parallel to the crystallographic c -axis. Astrong increase in J c , the disappearance of the fishtail (or second peak) effect and a shiftof the irreversibility field at high temperatures are observed. This behavior resembles thecorresponding changes in cuprate superconductors,[35, 37, 38] Sm-1111 bulk samples,[3] andSm-1111 crystals irradiated with heavy ions.[39] In the latter case, the enhancement as wellas the resulting currents are much higher, because this irradiation technique introduces largerdefects and because of the higher transition temperature of those 1111 crystals, which weremuch closer to optimal doping than the crystals of our study. In Co-doped Ba-122 singlecrystals on the other hand, the irreversibilty fields tend to decrease at high temperaturesafter fast neutron irradiation, while similar J c -enhancements were found.[2]Next, we consider the anisotropy of the critical currents including the influence of disorder.The field dependence of J c at 15 K and varying crystal orientation is shown in Fig. 2. α denotes the angle between the applied magnetic field and the crystallographic c -axis, thus α = 0 refers to H k c . In the left panel (pristine crystal), the position of the “fishtail”-peakshifts to higher magnetic fields at larger α and the peak value of J c grows for α > ∼ ° . Belowthe peak field, the currents decrease with α , in contrast to expectations for uncorrelatedpinning centers in an anisotropic superconductor. At high fields, the “usual” behavior, i.e.5
15 30 45 60 75 901x10 J c ( A m - ) ((cid:176)) J c ( A m - ) ((cid:176)) FIG. 3. Angular-dependence of the critical currents (crystal growing currents with increasing α , is found. The angular dependence of J c is plotted inFig. 3 for a better illustration of the change in behaviour. A peak occurs in J c ( α ) at 3and 4 T, because these fields are above and below the position of the “fishtail”-peak at low( < ∼ ° ) and high angles ( > ∼ ° ), respectively.Although J c becomes monotonous with field after irradiation, a similar transition fromthe “unusual” behavior at low fields to the expected behavior at high fields is observed (rightpanel in Fig. 3), since the J c ( B ) curves cross each other (right panel in Fig. 2). IV. DISCUSSION
The current standard approach for modelling anisotropy effects in superconductors wasproposed by Blatter et al. more than two decades ago.[25] The main idea of this approachconsists of scaling all relevant superconducting properties by functions of ǫ ( α ), which is givenby ǫ ( α ) = q γ − sin ( α ) + cos ( α ) (1)The anisotropy parameter γ originally refers to the anisotropy of the effective mass of thecharge carriers but is usually determined by the anisotropy of the upper critical field (i.e. γ = B ab c2 /B c c2 , where the indices ab and c refer to the crystallographic ab -planes and c -axis,6espectively). In particular, the angular dependence of the upper critical field becomes B c2 ( α ) = B c c2 /ǫ ( α ), as predicted by anisotropic Ginzburg-Landau theory, thus motivatingthe anisotropic scaling approach. This behavior is widely observed in many classes of su-perconductors, although multi-band [40, 41] or two-dimensional [42] superconductivity maycause deviations. Available data on the iron based superconductors [2, 43] suggest its valid-ity also in this new family. The irreversibilty fields are expected to share the same angulardependence ( B irr ( α ) = B c irr /ǫ ( α )), if pinning is not too anisotropic. Since B irr defines thefield where J c becomes zero, it is obvious that the angular dependence of J c at high fields(close to B irr ) has to be dominated by the behavior of B irr itself. This is indeed observed inboth the pristine and irradiated crystal.The scaling law for J c is less obvious because J c is given by the (extrinsic) pinningproperties. The original prediction of the anisotropic scaling approach is based on thecollective pinning theory, which was proposed for a high density of weak pinning sites. Inthis case and if the currents flow parallel to the ab -planes, only the field has to be scaled: J c ( B, α ) = J c ( Bǫ ( α ) , ° . If the currents decrease with field (as usual), they increase with α . Due tothe fishtail effect in the pristine samples of our study the currents increase with field in acertain field range, where the scaling approach results in decreasing currents at increasing α . However, this does not explain all features of the angular dependence observed in theunirradiated crystal, as discussed in the following.The data of Fig. 2 are replotted as a function of the scaled field ( Bǫ ( α )) in Fig. 4 inorder to sort out the effect of field scaling. If the scaling approach works properly, we expectthat J c ( Bǫ ) in the right panel has the same slope at all angles, which is indeed obtained for γ = 3 .
5. This value also seems realistic in view of the available data, i.e. γ is 5-8 near T c and decreases with temperature.[21, 44, 45]Although the field scaling brings the minima and maxima of J c close together, the curvesdo not collapse (left panel in Fig. 4). The positions of the maxima do not coincide, whichcould be caused by a higher anisotropy in the unirradiated crystal. It also seems that thevalue of J c at the second maximum increases at large angles, but this might be an artifactof the measurement method (VLF currents). On the other hand, the decrease of the J c -minimum with α cannot be caused by VLF currents and agrees with the overall behavior ofthe angular dependence of J c in the irradiated crystal.7 J c ( A m - ) B(T) J c ( A m - ) B(T)
FIG. 4. Same data as in Fig. 2 but with field scaling assuming an anisotropy γ of 3.5. Scaling of J c in the irradiated crystals can be performed by J c ( B, α ) = A J ( ǫ ( α )) J c ( Bǫ ( α ) , A J ( α ) (or A J ( ǫ ( α ))). (Note that this scaling fails at verylow fields, where the self field rotates B within the sample toward the c -axis. This is anartifact of our evaluation, because the applied self field correction only calculates the abso-lute value of B . Although correcting for α was possible, it would impede plotting J c ( B, α )without interpolation between measurements at different angles.) A J ( α ) is expected to beconstant [25] within the single vortex pinning regime of collective pinning theory, wherethe defects are assumed to be smaller than the coherence length ξ . In a simple model,the pinning energy of a single defect becomes proportional to E c r , with the condensationenergy density E c and the defect radius r d . Therefore, the pinning energy does not dependon α . If the defects are larger than the coherence length, the pinning energy becomesproportional to E p ∝ E c r d ξ ab ξ ( α ) = E c r d ξ ab ǫ ( α ), thus decreases with α . This qualitativelyexplains our data on the irradiated crystal, although a direct scaling with pinning energy A J ( α ) ∝ E p ( α ) is not consistent with our data, when assuming a realistic systematic errorcaused by the VLF currents. However, a direct proportionality between pinning energyand critical current density is not expected from most pinning models, in particular in viewof the changing elastic properties of the vortex lattice when the field orientation changes.Scaling by the square root of the pinning energy leads to reasonable agreement of all data,but a quantitative analysis of the angular dependence of A J is not meaningful because of8he systematic error of angular resolved magnetization measurements.The angular dependence of A J should not be related to a particular superconductor, butshould result from large pinning centers. Indeed, a decreasing J c with increasing α was alsoobserved in neutron irradiated coated conductors [46] before the intrinsic peak close to H k ab occurs and only if the field is significantly below B irr .The fishtail effect induces additional complexity into the angular dependence of J c (e.g.left panel of Fig. 3, which can be understood by field scaling (see above).) However, we finda crossover in A J ( α ), which decreases with α at low fields, but increases at higher fields, inparticular near the second peak. The behavior near and above the second peak is essentiallyconsistent with the predictions of the anisotropic scaling approach,[25] if one assumes theanisotropy to be a little higher and relates the slightly different currents at the peak to thepeculiarities of the measurement method. At low fields on the other hand, the currentsdecrease with α , as in the irradiated crystal. The crossover suggests that pinning in thepristine crystals is dominated by comparatively large defects of low density at low fields andby small defects of high density at high magnetic fields. V. CONCLUSIONS
The angular dependence of the critical currents was derived from magnetization mea-surements of Nd-1111 single crystals. The fishtail effect and the introduction of disorderby neutron irradiation were shown to change the current anisotropy significantly. It wasdemonstrated that the originally proposed pure field scaling resulting from collective pin-ning theory is valid only in a limited field range. However, the concept can be extended toother pinning regimes by introducing an additional J c -scaling, which was motivated by theexpected anisotropy of the pinning energy. This extension is mandatory for J c at low fieldsin the unirradiated sample and in the whole field range after fast neutron irradiation, sincepinning is dominated by large defects in both these cases. ACKNOWLEDGMENTS
We wish to thank H. W. Weber for fruitful discussions. This work was supported by theAustrian Science Fund (FWF): P22837-N20 and by the European-Japanese collaborative9roject SUPER-IRON (No. 283204). [1] Kamihara Y., Watanabe T., Hirano M., and Hosono H. 2008
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