Introduction

Fe-based superconductors (FBS)1 have been intensely studied in the last years because of the unique physics of their pairing mechanism2,3 and their potential for applications due to their high critical temperature Tc (up to 55 K)4,5 and high upper critical field Hc2 (estimated beyond 100 T)6,7,8,9. Studies of their critical current density Jc have been also of particular interest because of its weak field dependence and the varieties of properties discovered in the different compounds. BaFe2As2 (Ba122) thin films were widely investigated because of their high density of self-assembled or artificially introduced pinning centres that are able to significantly enhance Jc while also suppressing the effective anisotropy10,11,12,13,14. Further pinning improvements were obtained when combining artificially introduced defects with point defects generated by CaF2 substrate-induced strain15. No evidence of intrinsic pinning was observed in Ba122; however, enhancements in Jc(H//ab) due to extended correlated planar defects were found16. Fe(Se,Te) films, despite their much lower Tc, revealed a high Jc17,18,19 with a low Jc anisotropy18,19 and surprisingly showed signs of intrinsic pinning below 8 K20. The intrinsic pinning properties of SmFeAs(O,F) and LaFeAs(O,F) single crystals were studied by Moll et al.21 by measuring the angular dependence of the vortex dynamics in the flux-flow regime at high current density: they found that a sharp peak appears at low temperature for fields applied parallel to the ab-planes. This phenomenon is related to the relatively large intrinsic electronic anisotropy of these materials (γ = (M/m)1/2 ∼ 4–6, where M and m are the effective masses along the c-axis and parallel to the ab-plane, respectively)7 that induces a modulation of the order parameter along the c-direction. For these anisotropy values, the coherence length ξc falls below the interlayer distance d with decreasing temperature and the vortices undergo a transformation from 3D Abrikosov to 2D Josephson vortices22.

The purpose of this paper is to investigate how the layered structure of NdFeAs(O,F) (Nd1111) influences its vortex dynamics and Jc, considering also the multiband effects and the existence of different anisotropy parameters. In fact, differently from single-band superconductors that have a single temperature-independent anisotropy parameter (γ = γξ = ξab/ξc = γλ  = λc/λab = γHc2 = Hc2,ab/Hc2,c with γξ, γλ and γHc2 being the coherence length, the penetration depth and the Hc2 anisotropy, respectively), in multiband materials γξ and γλ differ from each other, are temperature-dependent and typically show an opposite temperature dependence merging at Tc23. Moreover in FBS, because of possible paramagnetic pair-breaking, γHc2 at low temperature may differ from γ and γξ24,25,26. Here we studied the pinning properties of a 60 nm-thick Nd1111 thin film deposited on MgO(100) substrate by molecular beam epitaxy (MBE) (see Methods). This film, whose Tc,90% is ∼47.1 K (Tc,0 ∼ 42.5 K), was characterized over a wide temperature range and in high magnetic fields up to 35 T at the National High Magnetic Field Laboratory. We found that surface and point defects independently act as pinning centres for H//c with two distinct field ranges of effectiveness, whereas for H//ab the intrinsic pinning induced by the layered structure of Nd1111 clearly plays a determining role. In this respect, we were able to identify H-T-θ regions where the vortices are trapped in a staircase structure or locked between the layers22.

Results and analysis

The high crystalline quality of the Nd1111 thin film was verified by X-ray diffraction with narrow full width at half maximum (FWHM) of the 003 rocking curve (Δω = 0.62°) and of the 102 ϕ-scan (Δϕ = 1.26°) (see Supplementary and Fig. S1). Field and angular dependence of the critical current density Jc was measured up to 35 T at 4.2 K and up to 16 T at higher temperatures (see Methods). Figure 1 shows how Jc and the pinning force density Fp evolve with temperature for the two main orientations (H//c and H//ab). At 4.2 K the self-field Jc reaches ∼3.3 MA/cm2. The field dependence is very weak in the ab-configuration with Jc(35 T,4.2 K) exceeding 1 MA/cm2 and Fp(35 T,4.2 K) larger than 400 GN/m3. For H//c Jc is clearly more strongly field dependent but still reaches ∼4.8×104 A/cm2 at 35 T and 4.2 K. Angular dependences were performed up to 35 K (see Supplementary and Fig. S2): in order to identify pinning contributions originating from random uncorrelated defects, correlated defects and intrinsic pinning, the Jc(θ) curves were analysed using the anisotropic Ginzburg-Landau scaling approach of Blatter et al.27 as shown in Fig. 2. This scaling approach is widely used to investigate the angular dependence of either YBa2Cu3O7-δ (YBCO)28,29,30 or FBS thin films31,32 and shows that those parts of the Jc(θ) curves that are affected by small random defects alone collapse onto a single trend line when plotted as a function of the effective field (with θ being the angle between the applied field and the ab-planes). To properly rescale the data, an increasing Jc anisotropy parameter has to be used with decreasing temperature. This behaviour was also observed in the Fe(Se,Te) thin film of ref. 20, which also showed intrinsic pinning. Clear deviations from the main trend approaching the ab-direction become more and more obvious at lower temperatures and increasing field (a few examples are marked by black arrows on the 4.2 K data). The increasing amplitude of the ab-peak with decreasing temperature also excludes significant effects of vortex interactions with the surface (which should induce an opposite temperature dependence because of the increasing d/λ ratio at high temperature)33. A much weaker deviation due to correlated defects is also noticed for the data near the c-axis at intermediate and high temperatures in the low-field region (few examples are marked by coloured arrows on the 25 K data).

Figure 1
figure 1

Field dependence of critical current density Jc and pinning force density Fp of a NdFeAs(O,F) thin film.

The film was measured with field parallel to the c-axis (a,b) and the ab-plane (c,d) up to 16 T in the 35-10 K temperature range and in high-field up to 35 T at 4.2 K. The red lines in panel (b) are fitting curves obtained with eq. (1) as described in the text.

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Figure 2
figure 2

Blatter’s rescaling of the angular dependence Jc(θ).

The curves were measured up 16 T in the 35-10 K range and up to 35 T at 4.2 K. Black arrows along the 4.2 K data indicate deviations from the rescaling due to ab-correlated pinning, whereas coloured arrows along the 25 K data point to deviations related to c-axis correlated pinning. Inset: temperature dependence of the anisotropy as obtained from the rescaling.

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In order to investigate the nature of the different pinning mechanisms in the two principal field configurations, two different approaches have been followed. For the c-axis pinning, the shape of the Fp(H//c) curves has been analysed by a modified Dew-Hughes model34, but we did not follow a similar approach for Fp(H//ab) because it is unable to reveal a possible 3D/2D transition of the vortices. Moreover, since the Josephson vortices, unlike the Abrikosov vortices, have no normal cores, they have little interaction with pinning defects. In order to reveal the nature of the ab-pinning, we instead performed an analysis of the n-values of the I-V curves in the flux-creep regime (n ∼ Up/kBT, where Up is the pinning potential and kB is the Boltzmann constant, in the case of logarithmic current density dependence of Up)22,35.

Fitting Fp(H//c) in Fig. 1 with a function with 4 free parameters (p, q, A and HIrr)34 generates unphysical p and q values because of the superposition of different pinning mechanisms. However, using constant p and q according to different possible pinning scenarios does not reproduce the curves well either, although the best fits were obtained with (p,q) = (0.5,2) at low temperature and (p,q) = (1,2) at high temperature. According to ref. 34, these parameters correspond to surface pinning [(0.5,2)] and point defect (PD) pinning [(1,2)]. However, vortex shearing generates the same functional dependence as surface pinning and its possible effect has to be considered and will be discussed ahead (surface pinning or vortex shearing contribution will be marked by S in the following)36,37. Considering that this is a thin film, the surface contribution could be provided by planar defects parallel to the c-axis such as domain, antiphase/twin boundaries or dislocation array, whereas PD pinning is probably induced by atomic defects such as vacancies or disorder. To reproduce the experimental data taking into account the superposition of two contributions, we used the expression

with 4 free parameters: Fp,S, Fp,PD, HS, HPD [only one contribution is considered for H > min(HS, HPD)]. The first two parameters represent the amplitudes of the PD and S contributions, while the latter two describe the maximum fields of their effectiveness. As shown in Fig. 1, this equation well reproduces the Fp(H//c) data at all temperatures. In all cases HS > HPD implying that HS actually corresponds to the experimental irreversibility field. The fitting parameters reported in Fig. 3(a) reveal a crossover in the dominant mechanism at about 20 K: the S contribution dominates at low T, whereas PD pinning is stronger at high T. Figure 3(b) also shows that the S contribution has a wider in-field effectiveness with HS exceeding 50 T at 4.2 K whereas PD pinning is limited to ∼20 T.

Figure 3
figure 3

Surface and point defects pinning contributions to Fp(H//c).

Fitting parameters of the curves in Figure 1(b) according to eq. (1) showing the temperature dependence of (a) the S and PD amplitudes and (b) their effectiveness field range.

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The I-V characteristics, from which Jc was determined, are well-described by the power-law relation V ∼ In in the entire field and temperature range, and the n-value, carrying information about the pinning potential, was determined (exemplary I-V curves are reported in the Supplementary, Fig. S3). In general, in case of random isotropic pinning, n scales with Jc, as experimentally shown in many compounds (YBCO38,39, MgB240, Nb3Sn41,42,43, Nb-Ti43), independently of temperature, field or angle. A relation of the type n ∼ Jcα was suggested and means that an increase of Jc leads to an increase in the n-value. As a consequence the Jc(H,θ) and n(H,θ) plots usually have similar trends. This is roughly the case observed in Fig. 4 at 30 K (and above, not shown) where n presents a maximum along ab. However, this trend changes with decreasing temperature. A small dip in n-value starts forming at 25 K (it is more visible for increasing field) revealing an inverse n-Jc correlation. At 20 K the dip becomes deeper and wider, but there is a point exactly at 180° where the n-value peaks with respect to its neighbouring angles. At 15 K both the dip and the peak become more marked and visible over a wider angular range. At 10 K, because of the increasing intensity of the emerging peak, the dip substantially disappears leaving just a flattened region at intermediate angles next to the increasingly emergent peak. At 4.2 K there is no longer any obvious trace of the dip and n(θ) just shows a sharp peak along the ab-planes. Even though at any fixed temperature part of the n(Jc) data lie on a single curve showing n ∼ Jcα (Fig. 5), clear deviations from this curve occur at higher Jc values, i.e. when the ab-direction is approached. At 25 K, where the dip in n(θ) starts to appear, the data deviate downward from the n ∼ Jcα trend-line and Jc increases despite the n-value drops. This initial behaviour is visible also at 20, 15 and 10 K but the emerging peak inside the dip of n(θ) produces a second deviation toward high n-values. Although less evident, a similar double-deviation behaviour is also observed at 4.2 K.

Figure 4
figure 4

Angular dependence of the n-value in the 30-4.2 K temperature range.

Magnetic field was applied up to 16 T in the 30-10 K temperature range and in high-field up to 35 T at 4.2 K.

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Figure 5
figure 5

n-value as a function of Jc in the 30-4.2 K temperature range.

Magnetic field was applied up to 16 T in the 30-10 K temperature range and in high-field up to 35 T at 4.2 K. The black lines are linear eye-guides and the red arrows emphasize the trend followed by the data approaching the ab-direction.

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Discussion

The critical current density and the pinning properties of the Nd1111 thin film can be compared with other films of the same family. Of particular interest is the comparison with Sm1111 which has the same structure but higher Tc. The self-field Jc(4.2 K) of this Nd1111 film, ∼3.3 MA/cm2, is more than 2.6 times larger than in Sm1111 thin films, despite its lower Tc (Tc,90% ∼ 47.1 K in Nd1111 versus 54.2 K in Sm1111)44. These compounds also show a quite different in-field pinning behaviour. In fact for H//c, despite a similar maximum value, Fp of Nd1111 peaks at about 10 T, whereas Sm1111 has a wide plateau between 20 and 35 T. This suggests both a strong difference in the irreversibility field, as expected because of the difference in Tc and in Jc(4.2 K,35 T) (3.5 times smaller than in Sm1111), and a different type of active pinning landscape. For H//ab, Jc(4.2 K,35 T) in the Nd1111 sample is still larger than in the Sm case, suggesting either a larger anisotropy or a more effective pinning mechanism.

Although Blatter’s rescaling was developed for anisotropic single-band superconductors, it has been successfully applied also to multiband materials like FBS20,31,32. However, similarly to what was previously reported for the other compounds, this rescaling reveals a peculiar temperature dependence of the effective Jc anisotropy (inset of Fig. 2): increases quite sharply with decreasing temperature down to 20 K but it flattens out at lower temperatures. Temperature dependence of anisotropy parameters is typically found in multiband compounds45, and this was verified also for FBS23. In Nd1111 single crystals the Hc2 anisotropy (related to γξ as long as Hc2 is not affected by the paramagnetic limitation at low temperature)24,25,26 decreases with decreasing temperature whereas the penetration depth anisotropy γλ increases (the two merging at ∼5–7 near Tc). In our film initially increases below Tc similarly to γλ, as already reported for Fe(Se,Te) films20. However, the magnitude of is clearly smaller than γλ, suggesting that both intrinsic and extrinsic factors affect it. The Jc rescaling also highlights the presence of ab- and c-axis-correlated pinning. The analysis of the Fp(H//c) curves shows the superposition of two independent contributions, PD pinning and either surface pinning or vortex shearing. At high temperature the S contribution with (p,q) = (0.5,2) can be easily ascribed to surface pinning because of the c-axis-correlated Jc enhancement revealed by Blatter’s rescaling. At lower temperature such enhancement becomes less obvious and vortex shearing may partially determine the S contribution. In either case it is interesting to notice that the PD and S contributions have different field ranges of effectiveness (Fig. 3). Although the superposition of different mechanisms is common (e.g. refs 46 and 47), their independence as revealed by different effective fields is unusual (one example is given by ref. 48, where, however, the high and low field regions were separately fitted using all exponents as free parameters). In our case the lack of interaction can be explained at high temperature by the specific geometry and the type of pinning centres involved. In fact, in an epitaxial thin film the main defects acting as surface pinning are parallel to the c-axis. PDs are on the other hand typically related to the presence of vacancies or atomic disorder located in the grains. As a consequence, in the H//c configuration the vortices are either intragrain and pinned on PD or intergrain and pinned on the planar defects parallel to the c-axis. Only when the field forms a high angle with the c-axis can the vortices interact with both PD and planar defects. It is also interesting that the cross-over between the PD and S contributions occurs at ∼20 K [Fig. 3(a)], the same temperature at which changes its trend (inset of Fig. 2). PDs generate isotropic random pinning that affects Jc at every field angle: the stronger temperature dependence of in the range dominated by PD (>20 K) suggests that there Blatter’s rescaling more strongly probes the temperature dependence of the intrinsic anisotropy γλ. At lower temperature both Fp,PD and flatten out and the PD contribution becomes less important, suggesting that is affected by factors other than the intrinsic anisotropy γλ. For instance, in YBCO samples the microstructure and the effect of strong pinning can generate ∼1.5–329,30, significantly lower than the intrinsic value of ∼5–6 found in samples with weak pinning28. Similarly, strong pinning can be responsible for the low effective Jc anisotropy found in our Nd1111 sample.

Figures 4 and 5 clearly show that for Nd1111 the n ∼ Jcα relation does not hold in the whole T-H-θ range and that two drastic changes in the n-Jc trend indicate two different pinning regimes. The n(Jc) plots are particularly helpful in determining the angles from the ab-plane at which these deviations occur, and these transition angles are reported in Fig. 6. The suppression of the n-value, which starts to be visible at 25 K, affects an angular region up to an angle φT (trapping angle) either side of the ab-plane (φT is defined as the angle at which the data clearly deviate from the trend line in Fig. 5). This behaviour was previously observed in high-Tc superconductors like YBa2Cu3O7-δ (YBCO)49,50 and more recently in other FBS like Sm111144 and Fe(Se,Te)20 where it has been ascribed to the formation of a staircase structure in which segments of vortices are trapped in the ab-plane and connected by vortex kinks as sketched in Fig. 6(a). With the current parallel to the planes and perpendicular to H, the Lorentz force on the vortices is directed along the c-axis for the portion trapped between the ab-planes but it is mostly along the ab-planes for the kinked segments51. This induces motions of the kinks and suppression of the n-value. Up to 20 K, the field dependence of φT approximately follows the φT ∼ H−3/4 relation [Fig. 6(a)] as theoretically predicted by Blatter et al.22, whereas at 25 K it has a weaker field dependence probably due to the proximity to the 2D/3D transition. The 2D/3D transition occurs at a temperature Tcr between 25 and 30 K: knowing the layer spacing in the Nd1111 sample (d = 0.856 nm determined by XRD), ξc(0) can be calculated by the relation (ref. 22.) to be 0.36–0.41 nm. Since the in-plane coherence length ξab(0) (estimated from the Hc2 slope at Tc and the WHH formula52 is about 1.93 nm, the intrinsic anisotropy γ = γξ = ξab/ξc lies between 4.7 and 5.4. These anisotropy and coherence length values are consistent with those previously reported7,53. It is important to notice however that the relations in ref. 22 assume a temperature independent anisotropy but, since this is not the case for FBS23, the γ value estimated here should be ascribed to the temperature range for which it was calculated (25–30 K). It is also interesting to notice that Tcr/Tc is about 0.6, indicating that Nd1111 is an intermediate case with respect to La1111 (Tcr/Tc ∼ 0.5) and Sm1111 (Tcr/Tc ∼ 0.8)21 as already suggested from Hc2 characterizations7.

Figure 6
figure 6

Field dependence of the trapping, φT, and lock-in, φL, angles.

The angles were obtained from Figs 4 and 5. The insets represent the sketches of the arrangement of vortices (red lines) in the trapping (a) and lock-in (b) regimes in a layered superconductor.

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Figure 6(b) shows the field dependence of φL (lock-in angle, φL < φT): this is the maximum angle from the ab-plane at which the vortices are completely locked parallel to the layers, as sketched in Fig. 6(b) (φL is defined as the angle at which n increases again from the dip or plateau in Fig. 5). Since in this case the whole vortex is parallel to the ab-planes, the Lorentz force is always directed along the c-axis. This generates very strong pinning and an increased n-value (Figs 4 and 5). φL seems to have a weaker dependence (∼H−1/2) than the theoretical prediction (φL ~ φT/H)22 and an amplitude larger than previously observed in YBCO (0.1–1°)22,51 which has a slightly higher intrinsic anisotropy. However, here the reduced temperature is much lower than for YBCO and the multiband nature of FBS and the temperature dependence of the superconducting parameters could also play a role in determining the vortex lock-in. Another factor to take into account is the sample mosaicity: despite the high crystalline quality, the vortex lock-in likely occurs over the domain-size, not the entire sample, enhancing φL. Awaji et al.50 characterized YBCO films down to 4.2 K and observed that the n-value for H//ab first increases on going below Tc, has a plateau from 70 to 40 K and then increases again below 20 K. The authors explained this behaviour by vortex kink excitation in the plateau region, followed by its suppression below 20 K. In our Nd1111 sample we observed the same trend when the reduced temperature is taken into account. Clear evidence of locked-in vortices have never been reported before for FBS, however Iida et al.20 did observe a small peak emerging from the n-value dip at 4 K in Fe(Se,Te). It is quite striking that even a material with such a low Tc reveals itself to have such strong intrinsic pinning.

To conclude, in this paper we investigated the intrinsic and extrinsic pinning properties of an epitaxial NdFeAs(O,F) thin film by measuring the field and angular dependence of Jc up to 35 T. We found that both intrinsic and extrinsic pinning contributions affect the Jc performance. Jc(H//c) is dominated by extrinsic pinning properties determined by the sample microstructure, and Fp can be described at every temperature by the superposition of surface and point pinning contributions or vortex shearing acting in different field ranges. More striking is the clear evidence of intrinsic pinning below 25–30 K induced by the layered structure of Nd1111when the ab-planes are approached. In fact, when the magnetic field forms an angle smaller than φT from the ab-plane for T < 30 K, a staircase structure of vortices is created that produces an inverse correlation between Jc and n because of the movement of kinked vortex segments. At lower temperature (T ≤ 20 K) and angles smaller than φL(<φT), the vortices are locked between the strong pinning layers, greatly increasing the n-value. These results make clear that the 1111 phase has intrinsic properties more similar to the high-Tc superconductors like YBCO than to low-Tc materials, an important factor to be taken into account when considering these compounds for possible applications.

Methods

NdFeAs(O,F) epitaxial thin films have been prepared on MgO(100) single crystal substrates by molecular beam epitaxy (MBE) using solid sources of NdF3, Fe, As and Ga and a gas source of O2. Here Ga works as F getter as the following reaction occurs: Ga + 3F → GaF3. A first deposition at 800 °C yielded the mother compound of NdFeAsO with a thickness of about 75 nm. Subsequently, the NdOF cap layer was deposited on the NdFeAsO at 800 °C, followed by annealing at the same temperature for 0.5 h. During the NdOF cap layer deposition and annealing processes, F diffuses into the NdFeAsO layer. The detailed fabrication process was reported in ref. 54. In order to remove the NdOF caplayer, the resultant film was covered by photolithography, followed by ion-beam etching. After the etching process the NdFeAs(O,F) film thickness was about 60 nm.

Transport characterizations were performed on 45 μm wide and 1 mm long bridges fabricated by laser cutting. The I-V curves were obtained at varying field, temperature and field orientation but always while maintaining the maximum Lorentz force configuration. Data were measured up to 16 T in a physical property measurement system (PPMS) and up to 35 T in the 35 T DC magnet at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee. The critical current was determined by a 1 μV/cm criterion.

Additional Information

How to cite this article: Tarantini, C. et al. Intrinsic and extrinsic pinning in NdFeAs(O,F): vortex trapping and lock-in by the layered structure. Sci. Rep. 6, 36047; doi: 10.1038/srep36047 (2016).

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