Introduction

Among the recently discovered Fe-based superconductors1, the highest superconducting transition temperature Tc of 56 K has been reported in SmFeAs(O,F)2. This new class of material shows very high upper critical fields at low temperatures together with a moderate anisotropy ranging from 4 to 73, which is suitable for high-field magnet applications. Hence several attempts on wire fabrication using SmFeAs(O,F) by powder-in-tube technique (PIT) have already been reported4, despite the lack of information on the field and orientation dependence of intra-grain critical current density [i.e., Jc(H, Θ)]. In order to exploit this material class, the knowledge of these properties should be clarified.

Epitaxial thin films are favourable for electronics device applications and investigating transport as well as optical properties thanks to their geometry. Recent success in fabricating epitaxial Fe-based superconducting thin films opens a great opportunity for investigating their physical properties and exploring possible superconducting applications. To date, high-field transport properties of Co-doped SrFe2As2 (Sr-122) and BaFe2As2 (Ba-122) and Fe(Se,Te) epitaxial thin films have been reported by several groups5,6,7. For Co-doped Ba-122, Jc performance can be tuned by introduction of artificial pinning centers and proton irradiation8,9. Additionally, multilayer approaches that can tailor superconducting properties and their anisotropy have been reported by Lee et al10. Furthermore, epitaxial Co-doped Ba-122 and Fe(Se,Te) thin films have been realised on ion beam assisted deposition MgO coated conductor templates11,12,13 and the rolling-assisted biaxially textured substrate14, respectively. Similarly, high performance K-doped Ba-122 and Sr-122 wires by PIT have been reported by Weiss et al.15 and Gao et al16, respectively. These results are very promising for realising Fe-based superconducting high-field applications. However, transport critical current properties of high-Tc (i.e., over 50 K) oxypnictide thin films have not been reported before due to the absence of high quality films. Recently, in situ prepared LnFeAs(O,F) (Ln = Nd and Sm) epitaxial thin films with Tc exceeding 50 K have been realised by molecular beam epitaxy (MBE)17,18. These successes give many possibilities to explore electro-magnetic properties.

In this paper, we report on various in – plane (i.e., current is flowing on the crystallographical ab-plane) transport properties up to 45 T of epitaxial SmFeAs(O,F) thin films grown by MBE on CaF2 (001) single crystalline substrates and discuss their pinning properties. A high Jc of over 105 A/cm2 was recorded at 45 T and 4.2 K for both crystallographic directions, which is favourable for high-field magnet applications. By analysing pinning properties the dimensional crossover between the out-of-plane superconducting coherence length ξc and the Fe-As interlayer distance dFeAs was observed at 30–40 K. This indicates the possible intrinsic Josephson junction in SmFeAs(O,F) at low temperatures.

Results

Microstructural analyses

As verified by x-ray diffraction, the biaxially textured SmFeAs(O,F) film with a narrow full width at half maximum (FWHM) of less than 0.65° was obtained (See in Supplementary Fig. S1). As shown in Fig. 1a, trapezoid shaped Sm(O,F) cap layers, which are changed from SmF3, are aligned discontinuously. Additionally, a crystallographically disordered layer with around 20 nm thickness as indicated by the arrows is present between Sm(O,F) cap and SmFeAs(O,F) layers. Relatively dark particles are observed in the SmFeAs(O,F) matrix, which are identified as iron-fluoride, presumably FeF2, by elemental mappings shown in Figs. 1b and 1c. This is due to the excess of Fe supplied during the film growth.

Figure 1
figure 1

Microstructural analyses by TEM.

(a) Cross-sectional scanning TEM image of the SmFeAs(O,F) thin film. A crystallographically disordered layer as indicated by the arrows is present between Sm(O,F) cap and SmFeAs(O,F) layers. (b) Elemental Fe and (c) F mappings measured by energy dispersive x-ray spectroscopy. (d) High-resolution TEM image of the SmFeAs(O,F) thin film in the vicinity of the CaF2 substrate/SmFeAs(O,F) film interface.

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Compared to Fe(Se,Te)19 and Co-doped Ba-122 films20 grown by pulsed laser deposition, a relatively sharp and clean interface is observed between SmFeAs(O,F) and CaF2 substrate, as shown in Fig. 1d. Furthermore, SmFeAs(O,F) layers contained neither correlated defects nor large angle grain boundaries (GBs).

Resistivity measurements up to 45 T

The superconducting transition temperature Tc,90 defined as 90% of the normal state resistivity is 54.2 K in zero magnetic field. Figures 2a and 2b show the Arrhenius plots of resistivity for both crystallographic directions measured in static fields up to 45 T. For both directions the Tc,90 is shifted to lower temperature with increasing H, as shown in the inset of Fig. 2b. The respective Tc,90 at 45 T for H || c and || ab are 44.9 K and 49.9 K. Significant broadening of the transition is observed for H || c, which is reminiscent of high-Tc cuprates. Such broadening of the transition originates from enhanced thermally activated vortex motion for H || c. In contrast, the in-field Tc,90 as well as its transition width for H || ab are less affected by H than that for H || c.

Figure 2
figure 2

In-field resistivity (ρ) measurements of SmFeAs(O,F) film up to 45 T and the analyses of the activation energy of pinning potential (U0).

(a) Arrhenius plots of ρ at various magnetic fields parallel to the crystallographic c-axis and (b) ab-plane. The inset shows the μ0H − Tc,90 diagram of SmFeAs(O,F) film for both directions, which is the identical to the extracted temperature dependence of the upper critical fields by employing a 90% criterion of the normal state resistivity. (c) Field dependence of the activation energy for H || c and || ab. (d) Relationship between lnρ0 and U0 for H || c and || ab.

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The activation energy U0(H) for vortex motion can be estimated by the model of thermally activated flux flow21. On the assumption that U(T, H) = U0(H)(1 − T/Tc), we obtain lnρ(T, H) = lnρ0(H) − U0(H)/T and lnρ0(H) = lnρ0f + U0(H)/Tc, where ρ0f is the prefactor. In Figs. 2a and 2b, the slope of linear fits corresponds to the U0 for vortex motion. Figure 2c shows U0 as a function of H for both major directions. It can be seen that U0(H) shows a power law [i.e., U0(H) ~ H−α] for both crystallographic directions. In the range of 1 < μ0H < 8 T, α = 0.46 is observed for H || c, whilst a similar field dependence of U0(H) reaches 20 T for H || ab. In higher fields U0 for H || ab shows a weak H dependence. On the other hand, α = 1.2 is obtained for H || c in the range of 8 < μ0H < 45 T, which is close to 1, suggesting a crossover from plastic to collective pinning at around μ0H ~ 8 T22.

Figure 2d shows the relationship between lnρ0 and U0 for H || c and || ab. The linear fitting for H || c yields Tc = 53.4 ± 0.2 K, whilst the corresponding value for H || ab is Tc = 53.5 ± 0.2 K. Both Tc values are equal within error and close to Tc,90. This perfect linear scaling is due to the correct assumption that both U(T, H) = U0(H)(1 − T/Tc) and ρ0f = const. conditions are satisfied in a wide temperature range in Figs. 2a and 2b.

In-field Jc performance

The field dependence of Jc at 4.2 K for both principal crystallographic directions measured up to 45 T is displayed in Fig. 3a. Jc for is lower than that for , which is a consequence of moderate anisotropy of SmFeAs(O,F). This tendency is observed for all temperature regions (see Supplementary Fig. S2). It is worth mentioning that a of over 105 A/cm2 was recorded even at 45 T, which is favourable for high-field magnet applications.

Figure 3
figure 3

In-field critical current density (Jc) performance of SmFeAs(O,F) thin film at 4.2 K.

(a) Field dependence of Jc measured at 4.2 K up to 45 T for both crystallographic directions and (b) the corresponding exponent n values.A crossover from extrinsic to intrinsic pinning is shown by the arrow. (c) Scaling behaviour of the field dependent Jc. (d) The pinning force density Fp for both crystallographic directions at 4.2 K.

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is observed to decrease gradually with H and it shows an almost constant value of 7.4 × 105 A/cm2 for μ0H > 28 T. This behaviour can be explained by a combination of extrinsic (i.e., normal precipitates and stacking faults) and intrinsic pinning, which is a similar observation in quasi two-dimensional (2D) system YBa2Cu3O7−δ [i.e., , where ξc(0) is the out-of-plane superconducting coherence length at zero temperature and is the interlayer distance between CuO2 planes]23. SmFeAs(O,F) is an alternating structure of SmO and FeAs layers, similarly to high-Tc cuprates. Additionally, ξc(0) is shorter than the interlayer distance between Fe-As planes dFeAs. Hence, modulation of superconducting order parameter along the crystallographic c-axis (i.e., intrinsic pinning) is highly expected in SmFeAs(O,F). In fact the extrinsic pinning is dominant up to 28 T, whereas the intrinsic pinning overcomes the extrinsic one above 28 T. The estimation of ξc(0) and dFeAs in our SmFeAs(O,F) case will be discussed later.

By analysing the E-J curves from which Jc was determined, we obtain the information on the pinning potential. On the assumption of a logarithmic current dependence of the pinning potential Up for homogeneous samples, E-J curves show a power-law relation E~Jn (n ~ Up/kBT, where kB is the Boltzmann constant)24. Hence Jc scales with n and indeed the field dependence of n has a similar behaviour to Jc(H) for H || c, as presented in Fig. 3b. For H || ab, n decreases with H up to 28 T, similarly to the Jc(H) behaviour, whereas at larger field it suddenly increases due to the dominating intrinsic pinning. Hence a failure to scale Jc with n or deviations as shown in Fig. 3c indicates the presence of intrinsic pinning.

The field dependence of the pinning force density Fp for both crystallographic directions at 4.2 K is summarised in Fig. 3d. An almost field independent Fp above 10 T for H || c is observed, whereas Fp for H || ab is still increasing up to the maximum field available.

Angular dependence of Jc

In order to gain a deeper insight into the flux pinning, the angular dependence of Jc [Jc(Θ), where Θ is the angle between H and the c-axis] was measured and summarised in Fig. 4. Figure 4a presents Jc(Θ) at 30 K in three different magnetic fields. Almost isotropic Jc(Θ, 2.5 T) of around 0.14 MA/cm2 was observed at angles Θ up to 75°. Similar isotropic behaviour is seen at 6 T. These results suggest the presence of c-axis correlated defects. However, the presence of these defects is ruled out by TEM investigation, since only relatively large FeF2 particles are observed in the SmFeAs(O,F) matrix. Recently, van der Beek et al. pointed out that defects of size larger than the out-of-plane coherence length contribute to c-axis pinning in anisotropic superconductors25. Additionally, the intrinsic pinning is active below T = 30 ~ 40 K, as shown below. Hence the combination of large particles and the intrinsic pinning may be responsible for this isotropic Jc(Θ).

Figure 4
figure 4

Field and orientation dependence of critical current density (Jc) of SmFeAs(O,F) thin film.

(a) Angular dependence of Jc measured at 3 different applied magnetic fields at 30 K and (b) the corresponding exponent n values. (c) Jc(Θ, H) measured at 40 K under several magnetic fields (μ0H = 2.5, 4 and 6 T) and (d) the corresponding exponent n values. (e) Angular dependence of Jc at 4.2 K under various applied magnetic fields up to 40 T. (f) Scaling behaviour of the angular dependent Jc measurements. Below 17 T (i.e., by substituting μ0H = 32.5 T and Θ = 59° in H cosΘ) as indicated by the arrow, both curves overlap each other.

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For H || ab, a broad maximum of Jc is observed and this peak becomes sharper with increasing H (Fig. 4a). However, the corresponding n shows a broad minimum for H close to ab direction (Fig. 4b), which is opposite behaviour to Jc. This is due to the thermal fluctuation of Josephson vortices, which leads to flux creep. Here, the flux creep rate S = −dln(J)/dln(t) and the exponent n are related as S = 1/(n − 1)26. When the applied field is close to the ab-plane, a number of thermally fluctuated Josephson vortices are generated, leading to an increase in S. This could quantitatively explain a dip of n at around H close to ab. Similar behaviour has been observed in YBa2Cu3O7−δ thin films27,28,29 and Fe(Se,Te) thin films30. On the other hand, this dip of n disappears at 40 K, although the Jc still shows a broad maximum (Figs. 4c and 4d). Hence the activation temperature of the intrinsic pinning is between 30 and 40 K, which is in good agreement with the transition temperature between Abrikosov-and Josephson-like vortices in SmFeAs(O,F) single crystals31.

Figure 4e shows Jc(Θ) measured at 4.2 K in fields up to 40 T. A sharp peak is observed for H || ab with a Jc of around of 8 × 105 A/cm2. For 2D superconductors (e.g., Bi2Sr2CaCu2O8+x), the relation holds in the intrinsic pinning regime, whereas is field independent32,33. Thus, in this regime Jc(Θ, H) depends only on the field component along the c-axis. For our SmFeAs(O,F) thin film, the aforementioned condition is satisfied above 28 T at which the crossover field between extrinsic and intrinsic pinning is observed (see Fig. 3a). Hence, for Θ > 59° (sinΘ = 28/32.5 = 0.86, Θ = sin−1(0.86) = 59°) the ab component of the applied fields exceed 28 T, entering in the field-independent region. It means that both angular–Jc curves measured at 32.5 and 40 T rescale with H cosΘ, as shown in Fig. 4f.

Discussion

We estimate the ξc(0) by using Tcr = (1 − τcr)Tc, where Tcr is the dimensional crossover temperature and is the dimensionless ratio characterising the crossover from quasi-2D layered to continuous 3D anisotropic behaviour34. By substituting Tcr = 30–40 K and dFeAs = 0.858 nm from the x-ray diffraction shown in Supplementary Fig. S1, is calculated to 0.3~0.4 nm. The ratio ξc(0)/dFeAs = 0.35 ~ 0.47 explains the intrinsic pinning related to a quasi 2D system observed in this film. The relation yields ξab(0) = 1.7 ~ 2.2 nm, where γ is the effective-mass or resistivity anisotropy, which is about 30 at T = 0 K from measurements of the c-axis plasma frequency using infrared ellipsometry35. The evaluated superconducting coherence lengths for both crystallographic directions are in very good agreement with single-crystals values reported by Welp et al36.

The presence of a dimensional crossover indicates a possible intrinsic Josephson junction in SmFeAs(O,F), which can be used in superconducting electronics applications such as a terahertz radiation source and a superconducting Qubit37,38. Indeed, the intrinsic Josephson junction was reported for a PrFeAsO0.7 single crystal, where an s-shaped stack junction in c-direction was prepared by focused ion beam39.

For high-field magnet applications, a high Jc together with a low Jc anisotropy () in the presence of magnetic field is necessary. The present results are promising, since Jc is over 105 A/cm2 at 45 T for both crystallographic directions. Further increasing in Jc is possible, since the only appreciable defects in our SmFeAs(O,F) films are large FeF2 particles. Improved pinning performance and, as a consequence, larger Jc could be realised by incorporating artificial pinning centres similarly to Co-doped Ba-122 thin films reported by Tarantini et al8. Albeit the Jc anisotropy is increasing with H, this value is still low compared to high-Tc cuprtaes. For instance, Jc anisotropy is about 3.6 at 30 T and 4.2 K in SmFeAs(O,F), whereas the corresponding value in YBa2Cu3O7−δ is over 7, albeit the latter shows higher Jc than the former40.

PIT is a more realistic process than MBE for high-field magnet applications. High temperature heat treatment in PIT leads to a loss of F, however, this problem can be solved by employing a low temperature synthesis and ex-situ process with SmF3 containing binder as explained in refs. 41,42. Despite a high Tc of over 45 K for both SmFeAs(O,F) wires, self-field Jc shows only a few thousand A/cm2 at 4.2 K, which is presumably due to grain boundaries (GBs), poor grain connectivity and low density. Obviously these PIT processed wires contain a high density of large angle GBs. In the case of Co-doped Ba-122 GBs with misorientation angles above 9° seriously reduce the critical current43. However, PIT processed K-doped Ba-122 and Sr-122 wires showed a relatively high inter-grain Jc15,16. Clean GBs (i.e., no segregation of secondary phases around GBs), good grain connectivity and a low anisotropy may be responsible for these high performance wires. An approach similar to the one employed in K-doped Ba-122 and Sr-122 wires fabrication may be useful for improving inter-grain Jc in SmFeAs(O,F) wires as well. Nevertheless bicrystal experiments on SmFeAs(O,F) will give a valuable information on these issues.

To conclude, we have explored intrinsic electro-magnetic properties of epitaxial SmFeAs(O,F) thin films prepared by MBE on CaF2 (001) substrate by measuring field-angular dependence of transport properties up to 45 T. Our findings strongly support the presence of a competition behaviour between extrinsic pinning below 28 T and intrinsic pinning above 28 T. We also determined that the intrinsic pinning starts being effective below T = 30 ~ 40 K, at which the crossover between the out-of-plane coherence length and the interlayer distance occurs. This knowledge of SmFeAs(O,F) electro-magnetic properties could stimulate future development of superconducting applications of this class of material.

Methods

Epitaxial SmFeAs(O,F) film preparation by MBE

SmFeAs(O,F) films of 80 nm thickness have been grown in the customer-designed MBE chamber. A parent compound of SmFeAsO film was prepared on CaF2 (001) single crystalline substrate at 650°C, followed by the deposition of a SmF3 cap layer. Empirically, Fe-rich pnictide films fabricated by MBE showed high Jc values44. Hence a slight Fe excess was supplied during the growth of SmFeAsO layers. After the overlayer deposition, the sample was kept at the same temperature in the MBE chamber for 0.5 h for the purpose of F diffusion into the SmFeAsO layer. The detailed fabrication process can be found in ref. 17. SmFeAs(O,F) films are grown epitaxially with high crystalline quality confirmed by x-ray diffraction, which is summarised in Supplementary Fig. S1.

Microstructural analyses by TEM

A TEM lamella was prepared by means of focused ion beam. Microstructural analyses have been performed by using a JEOL TEM-2100F transmission electron microscope equipped with an energy-dispersive x-ray spectrometer.

In-plane transport properties measurement

A small bridge of 70 μm width and 0.7 mm length was fabricated by laser cutting. I-V characteristics on this sample were measured with four-probe configuration by a commercial physical property measurement system [(PPMS) Quantum Design] up to 12 T. Transport measurements up to 45 T were carried out in the high field dc facility at the National High Magnetic Field Laboratory (NHMFL) in Tallahassee, FL. A voltage criterion of 1 μV/cm was employed for evaluating Jc. The magnetic field H was applied in maximum Lorentz force configuration during all measurements (H ⊥ J, where J is current density).