The Fe-based superconductors (FBS), the second class of high-temperature superconductors beside the cuprates, are considered as possible candidates for high-field magnet applications1,2,3,4,5. Among them, LnFeAs(O,F) (Ln: Nd and Sm) has the highest depairing current density Jd of ~ 170 MA/cm2 at zero kelvin6. Additionally, LnFeAs(O,F) shows the highest superconducting transition temperature Tc. These two features together with their high upper critical fields make LnFeAs(O,F) attractive, although the electromagnetic anisotropy is slightly higher than that of other FBS.

Very similar to the partial substitution of fluorine for oxygen in LnFeAsO, hydrogen also leads to electron doping (O2− → H− + e−)7, resulting in a Tc of up to ~ 55 K. The distinct difference between H- and F-doping is the substitution limit: x ≤ 0.8 for LnFeAsO1−xHx8 in contrast to x ≤ 0.2 for LnFeAsO1−xFx9. Furthermore, a high Tc of ~ 50 K is maintained in the range 0.13 < x < 0.43 for LnFeAsO1−xHx7. The growth of LnFeAs(O,H) opens new opportunities to explore how heavily electron doping influences the superconducting properties. However, most of the studies have been carried out on polycrystals7,8 or tiny single crystals10, on which measurements of the transport critical current density are rather complicated. The successful growth of LnFeAs(O,H) epitaxial thin films gives a great opportunity to explore the intrinsic physical properties by electrical transport measurements especially for critical current characteristics, since thin films are the ideal platform for such investigations.

SmFeAs(O,H) epitaxial thin films have recently been grown on single-crystal MgO(001) by a combination of pulsed laser deposition and topotactic chemical reaction through post-annealing with AeH2 (Ae = Ca, Sr, Ba, and Mg) powders that serve as hydrogen source11,12. By referring to this hydrogen doping method, we have fabricated H-doped NdFeAsO epitaxial thin films13. In this article, we present the electrical transport properties of a NdFeAs(O,H) epitaxial thin film with a thickness of ~ 24 nm. The film was characterised over a wide temperature range and in magnetic fields up to 14 T.

Results

Microstructure

Microstructural analysis by transmission electron microscopy (TEM) confirmed that our NdFeAs(O,H) film is almost free of defects in the matrix as well as at the interface (Fig. 1a). The atomic-resolution annular dark-field (ADF) image agrees well with the crystal structure of NdFeAs(O,H) projected along the b-axis, as shown in the inset of Fig. 1a (top left). This ADF image also revealed the atomic arrangement at the NdFeAs(O,H)/MgO interface. The first atomic layer in the NdFeAs(O,H) film exhibits brighter contrast than surroundings, indicating that a Nd layer is firstly formed on the MgO substrate at the beginning of film growth. In this interfacial Nd layer, a large density of dislocations is introduced, as shown in the inset of Fig. 1a (bottom left). Those misfit dislocations compensate the large lattice parameter difference, i.e., a (NdFeAsO) = 3.99 Å while a (MgO) = 4.23 Å, resulting in the defect-free matrix inside the NdFeAs(O,H) film.

Figure 1
figure 1

Microstructural analysis by TEM. (a) TEM cross-sectional view of the NdFeAs(O,H) epitaxial thin film revealed almost no apparent defects. Additionally, no reaction layer between the film and the MgO substrate was observed. (b) The magnified ADF images of NdFeAsO and (c) NdFeAs(O,H). (d) Image intensity profiles along the c-axis direction extracted from (b) and (c), averaged in the a-axis direction. The c-axis lattice parameters averaged over 10 layers are 8.64 Å and 8.50 Å, respectively. The distances from the 1st to the 11th layer and from the 18th to the 28th layer are the same in the NdFeAs(O,H) film.

Full size image

Figure 1b,c shows magnified ADF images of NdFeAsO and NdFeAs(O,H), respectively, clearly indicating a shrinkage of the lattice in the c-axis direction by H substitution for oxygen. The c-axis lattice parameter decreased from 8.64 to 8.50 Å, as shown in the extracted intensity profiles (Fig. 1d). It is reported that the c-axis lattice parameter decreases with increasing hydrogen content x in LnFeAsO1−xHx7,10,11 with a rate of Δc/Δx ~ −2–3 × 10–3 Å/at%. The lattice parameter c of our NdFeAs(O,H) film determined by X-ray diffraction (XRD) was 8.437 ± 0.003 Å, which also supports the lattice shrinkage due to hydrogen doping although the value was slightly shorter than the average value evaluated from TEM. In order to check the homogeneity of hydrogen doping, the c-axis lattice parameters in the vicinity of the MgO substrate and near the film surface were compared, resulting in the same value (Fig. 1d). This result implies a homogeneous H substitution for oxygen, which guarantees that the transport properties shown below are not affected by local inhomogeneity.

Resistivity measurements for determining the magnetic phase diagram

Figure 2a,b summarises the field dependence of resistivity for both major field directions, H parallel to the ab-plane and to the c-axis. Tc is recorded at 44 K, which is 2 K lower than the as-processed NdFeAs(O,H) film (Supplementary information fig. S1). The reason for the reduced Tc may be that the sample was slightly damaged during bridge fabrication.

Figure 2
figure 2

Temperature dependence of the resistivity at various magnetic fields for the NdFeAs(O,H) epitaxial thin film. Direction of the applied fields H parallel to (a) the ab-plane and (b) the c-axis. (c) Magnetic phase diagram. Irreversibility fields determined from the field dependence of Jc and the corresponding Fp for H || c follow well the irreversibility field line down to 20 K, which is expressed by Eq. (1).

Full size image

A clear shift of Tc to lower temperatures with magnetic fields is observed for both directions. This shift together with a broadening of the transition is more obvious for H || c than || ab. The temperature dependencies of Hc2, Fig. 2c, show slopes of − 11.8 T/K for H || ab and − 2.7 T/K for H || c in the range 0 ≤ µ0H ≤ 4 T. Hence, the anisotropy of Hc2 near Tc is around γHc2 = 4.4, which is lower than for NdFeAs(O,F) film (γHc2 = 5.1) of similar thickness (22 nm)14. For cuprate superconductors, it has been shown that the anisotropy decreased with doping because of the increase in the interlayer coupling15. The decreased γHc2 for NdFeAs(O,H) may be explained similarly.

The temperature dependence of the irreversibility field Hirr, Fig. 2c, for H || ab shows a kink around 4 T, which is due to a matching field effect. This effect has the same origin as reported for the 22-nm thick NdFeAs(O,F) film in ref.14. The matching field corresponds to the film thickness and is related to the Bean–Livingston barrier16. Hence, the origin of this matching field effect differs distinctly from the one commonly observed for H || c in REBa2Cu3O7 (REBCO, RE: rare earth elements) films containing highly correlated columnar defects with diameter of a few nano meters17,18. The results of Hirr for H || c are discussed later.

Pinning potential

The field dependence of the activation energy, U0(H), for vortex motion can be estimated from linear fits to the Arrhenius plots of ρ(T), Fig. 3a,b, under the assumption of U(T,H) = U0(H)(1 − T/Tc) leading to lnρ(T,H) = lnρ0(H) − U0(H)/T and lnρ0(H) = lnρ0f. + U0(H)/Tc19. Here, ρ0f. is a pre-factor. For both main orientations and all fields, U0(H) is systematically larger than for the 22 nm-thick NdFeAs(O,F) film reported earlier14, e.g., for H || c at 1 T, 4.2 × 103 K for NdFeAs(O,H) and 3.5 × 103 K for NdFeAs(O,F). U0(H) shows a power law relation H−α for both main orientations, Fig. 3c, except for H || c in high fields, where U0(H) is better expressed by U0(H) ~ H−0.5(1 − H/H*)2 (µ0H* ~ 48 T). This fitting formula has been used for polycrystalline MgB2 samples by Thompson et al.20 who argued that the exponents should be the same as the ones in the pinning force density analysis. These exponents (i.e., 0.5 and 2) suggest that Kramer’s scaling for the pinning force density holds, which will be discussed later. For both directions, the exponent α is 0.07 at low fields, which can be explained by single vortex pinning21. The distinct feature for H || ab is that α changes from 0.07 to  ~ 1 in the range 2–4 T, followed by 0.34 above 4 T, although the value of α ~ 1 may contain somewhat large uncertainty as we have only three data points in this field regime. Nevertheless, the exponent α = 1 indicates that collective pinning is dominating in this field regime21. The transition field at which the exponent α changes from 1 to 0.34 corresponds to the matching field shown in Fig. 2c. It is intriguing that the pinning mechanism for H || ab changes from single vortex pinning to collective pinning, followed by plastic pinning (i.e., α ~ 0.522).

Figure 3
figure 3

Arrhenius plot of the field dependence of the resistivity traces shown in Fig. 2. Applied field parallel to (a) the ab-plane and (b) c-axis. (c) Field dependence of the activation energy U0 of thermally assisted flux motion for both main crystallographic directions. The exponent α for H || ab changes from 0.07 to 1 between 2 and 4 T, as indicated by a red arrow, before again changing to 0.34.

Full size image

Field dependence of J c and the pinning force density

Field dependence of Jc for both H || ab and || c, and the corresponding pinning force density Fp are summarised in Fig. 4a–d. Self-field Jc of NdFeAs(O,H) at 5 K exceeds 10 MA/cm2. Another film with a Tc of 45 K prepared by the same condition showed even a self-field Jc of over 17 MA/cm2 at 4 K13. These values are higher than our best-performing NdFeAs(O,F) film of similar thickness (22 nm)14 (purple line in Fig. 4a–d), albeit the reduced temperature (t = T/Tc ~ 0.114) of NdFeAs(O,H) was higher than that of NdFeAs(O,F) (t ~ 0.093). Below 20 K, Jc is rather insensitive against the applied field for H || ab (Fig. 4a) and Fp shows a linear increase above 4 T, indicative of strong single-vortex pinning. The reason for that is intrinsic pinning and will be discussed later. The elemental pinning force density per length for intrinsic pinning can be calculated by \(f_{\rm p}^{^{\prime}} = \frac{1}{{\mu_{0} }}\frac{{dF_{\rm p} }}{dH}\phi_{0}\). The respective fp’ are \(8.0 \times 10^{ - 5}\) N/m at 5 K, \(4.2 \times 10^{ - 5}\) N/m at 10 K, \(1.5 \times 10^{ - 5}\) N/m at 15 K, and \(1.7 \times 10^{ - 6}\) N/m at 20 K. On the other hand, for H || c, Jc monotonously decreases with increasing applied field, which reflects the absence of macroscopic defects in our film (i.e., a clean microstructure as can be seen in Fig. 1).

Figure 4
figure 4

In-field electrical transport Jc characteristics and pinning force density Fp. Field dependence of Jc at various temperatures for (a) H || ab and (b) H ||c. Corresponding pinning force density Fp for (c) H || ab and (d) H ||c. For comparison, the data of NdFeAs(O,F) measured at 4.2 K are superimposed14. (e) Temperature dependence of exponents p and q in fp ~ hp(1 − h)q for H || c.

Full size image

In order to understand the pinning mechanism for H || c, the normalised pinning force densities fp = Fp/Fp,max were plotted as a function of the reduced field h = H/Hirr. Hirr was evaluated from Jc-H characteristics with a criterion of 1.4 kA/cm2 in the temperature range 20 ≤ T ≤ 35 K. The fit of fp ~ hp(1 − h)q to each fp at given temperatures is shown in Supplementary information fig. S2, and the resulting fitting parameters p and q are plotted as a function of temperature (Fig. 4e). Although both p and q show a slight temperature dependence, the respective values of p and q are almost close to 0.5 and 2, suggesting that the Kramer model for shear breaking of the flux line lattice is mainly responsible for depinning23.

For T ≤ 15 K Hirr cannot be evaluated from Jc-H characteristics due to the experimental limitation. Hence, Hirr was determined from fits to the pinning force density, on the assumption that the Kramer model prevails in the whole T range [i.e., (p, q) = (0.5, 2)].

The temperature dependence of Hirr for H || c evaluated by three different methods (i.e., ρ(H, T), Jc-H, and Fp-H) is summarised in Fig. 2c. Hirr in the temperature range 20 ≤ T ≤ 35 K from Jc-H follow well the Hirr-line expressed by Eq. (1) with an exponent k = 1.2, which is close to the theoretically predicted value of 4/3 for a glass-liquid transition24,25.

$$\mu_{0} H_{{{\text{irr}}}} = 36.6\left( {1 - \frac{T}{{T_{{{\text{irr}}}} }}} \right)^{k}$$
(1)

Here, Tirr is the irreversibility temperature for self-field, which is 37.4 K. This result indicates that the criterion for determining Hirr is quite reasonable and consistent. However, Hirr starts to deviate from Eq. (1) at around 15 K. A steep increase of Hirr at low temperatures was also observed in LaFeAs(O,F)26, where it was related to a similar increase of Hc2 at the same temperature. This is due to the 2-dimensional multiband character of the superconductivity of these compounds in contrast to the 3-dimensional multiband superconductor Co-doped BaFe2As227, where such an increase of Hirr and Hc2 was not observed.

Angle dependence of J c

To further understand the pinning mechanism, the angular dependence of Jc was measured at three different temperatures, T = 10, 20, and 30 K (Fig. 5). Simultaneously, the corresponding n values in E ~ Jn is also plotted. As expected from the microstructural observation, the minimum Jc is always observed at θ = 0° (i.e., H || c), whereas the maximum Jc is located at θ =  ± 90° (i.e., H || ab). Additionally, the Jc peak at H || ab becomes sharper with increasing the applied field. Because the exponent n is proportional to the pinning potential U, Jc(T, H, θ) should show a behaviour similar to n(T, H, θ)28. Indeed, this relation holds at 30 K. However, n(θ) at 20 K shows a dip at θ close to ± 90° for applied magnetic fields exceeding 3 T. At an even lower temperature of 10 K, a peak located at the local minimum around H || ab is observed (see, Fig. 5e: for clarity n(θ) at 14 T was plotted), which evolves with decreasing the field. Such behaviour can be explained by intrinsic pinning, as observed in REBCO28,29,30 and FBS31,32,33, arising from the modulation of the superconducting order parameter along the crystallographic c-axis. Vortices depin from intrinsic pinning through the double-kink mechanism34, which easily creep along the ab-plane, resulting in small n. Here, the flux creep rate is proportional to the inverse of n − 135. The cross-over temperature Tcr from 3-dimensional Abrikosov to 2-dimensional Josephson vortices is, accordingly, located between 20 and 30 K. To determine Tcr precisely, n(θ) around H || ab at 10 T with a step size of 1 K and n(T) for H || ab under magnetic fields 5 ≤ µ0H ≤ 14 T were measured (Supplementary information, Figs. S3 and S4). As a result, Tcr is determined as 24.5 ± 0.5 K. Given that the FeAs layer spacing d is 0.8437 nm determined by XRD, the out-of-plane coherence length at zero kelvin, ξc(0), can be estimated by \(\xi_{{\text{c}}} \left( 0 \right) = d\sqrt {\left( {1 - \frac{{T_{{{\text{cr}}}} }}{{T_{{\text{c}}} }}} \right)/2}\)21. The resultant ξc(0) is 0.39 ± 0.01 nm, which is comparable to NdFeAs(O,F)14,33.

Figure 5
figure 5

Angular dependence of Jc and the corresponding exponent n. Measurement temperatures were (a) 10 K, (b) 20 K, and (c) 30 K. Enlarged view of n(θ) in the vicinity of − 90° is shown at the bottom of each panel. (d) n(θ) at 10 and 20 K under a fixed field of µ0H = 14 T. (e) n(θ) at 10, 20 and 30 K under a fixed field of µ0H = 5 T.

Full size image

To decouple the pinning contributions arising from uncorrelated and correlated defects, the anisotropic Ginzburg–Landau (AGL) scaling36 for the angle dependence of Jc can be applied. This approach has been widely used for REBCO37 and FBS26,32,33,38. In the absence of correlated pinning centres (i.e., mainly randomly distributed and sufficiently small, isotropic pinning centres determine the pinning behaviour), all Jc(θ) curves at a given temperature collapse onto a single curve if plotted as a function of effective field Heff:

$$H_{{{\text{eff}}}} = H\sqrt {{\text{cos}}^{2} \theta + \frac{{{\text{sin}}^{2} \theta }}{{\gamma_{J}^{2} }}}$$

where γJ is the anisotropy parameter. The AGL scaling, Fig. 6, shows that some portion of Jc(θ) curves at given temperatures indeed scale with Heff when γJ is appropriately chosen. γJ decreases from 1.6 to 1.25 with decreasing temperature in contrast to NdFeAs(O,F)14,33, where it increased. Clear deviations from the master curves due to the ab correlated pinning (here mostly intrinsic pinning because of the layered crystal structure) become obvious with decreasing temperature and also increasing field.

Figure 6
figure 6

Scaling behaviour of Jc(θ) as a function of effective field. All Jc(θ) data except for those where the contribution of the ab-correlated pinning is dominant fall onto the measured curves of Jc (i.e., field dependence of Jc for H || c (lines), shown in Fig. 4a) with γJ values of 1.25–1.6.

Full size image

Discussion

Our NdFeAs(O,H) film shows a high self-field Jc exceeding 10 MA/cm2 at 5 K, which is a record level value for pnictides without artificial pinning centres. According to Talantsev and Tallon39, self-field Jc for type-II superconductors can be expressed by Hc1/λ, if the sample thickness is less than λ. Here, Hc1 is the lower critical field and λ the relevant London penetration depth. Hence, the high self-field Jc of NdFeAs(O,H) may be due to a short London penetration depth at heavily electron doping.

Another effect of heavily electron doping is the reduction of anisotropy. The Hc2 anisotropy near Tc for NdFeAs(O,H) is γHc2 = 4.4, which is smaller than that of NdFeAs(O,F) (γHc2 = 5.1). Additionally, compared with NdFeAs(O,F), the temperature dependence of the anisotropy γJ evaluated from the AGL scaling for NdFeAs(O,H)14,33 shows an opposite behaviour. It is also worth mentioning that γJ of NdFeAs(O,H) is comparable to that of Co-doped BaFe2As238.

Heavily electron doping by means of hydrogen substitution for oxygen in LnFeAsO is a novel method to tune superconducting properties, whilst Tc is maintained around 45 K, comparable to NdFeAs(O,F). For most FBS in contrast, a high carrier concentration reduces Tc. Additionally, this method is rather simple, once the parent LnFeAsO films are fabricated. Now the parent compound can be fabricated by both pulsed laser deposition40,41 and molecular beam epitaxy (MBE)42,43. Hence, our study motivates coated conductor preparation, for which films with thicknesses in the micrometer range are needed. However, a homogeneous H substitution for oxygen seems to be difficult in such thick films. Indeed, the H concentration showed to be inhomogeneous for 90-nm thick SmFeAs(O,H) films11. To realise LnFeAs(O,H) coated conductors and eventually applications of hydrogen-doped LnFeAsO, new approaches to a homogeneous H substitution should be explored.

To conclude, we have grown hydrogen-doped NdFeAsO epitaxial thin films. TEM investigations supported that hydrogen is homogenously distributed. Detailed electric transport measurements revealed the benefits of heavily electron doping to LnFeAsO in terms of high self-field Jc and low anisotropy without compromising Tc.

Methods

Thin film fabrication

Parent NdFeAsO was grown on MgO(001) at 800 °C by MBE40. The structural characterisation by X-ray diffraction (XRD) confirmed that the 24-nm thick film was phase pure and epitaxially grown with (001)[100]NdFeAsO || (001)[100]MgO. After structural characterisation by XRD, the NdFeAsO films were cut into pieces of approximately 5 × 5 mm2 and subsequently sealed in an evacuated silica-glass tube filled with ~ 0.5 g of CaH2 powder that serves as a hydrogen source. Here, it is important that the film surface is in direct contact with the CaH2 powders to promote a topotactic chemical reaction. The sealed silica-glass tube was heated to 490 °C at a rate of 100 °C/h, held at this temperature for 36 h, and then cooled to room temperature at a rate of 100 °C/h. The NdFeAs(O,H) film was also phase pure after processing, indicating that the crystalline quality is not compromised.

Microstructural analysis by TEM

The cross-sectional samples for TEM observation were fabricated by focused ion beam. Atomic-resolution observations were performed using a transmission electron microscope (Titan Cubed 60–300 G2, Thermo Fisher Scientific) which is equipped with a spherical aberration corrector (DCOR, CEOS GmbH) for the probe-forming lens system. The microscope was operated in the scanning TEM (STEM) mode at an accelerating voltage of 300 kV. The convergence semi-angle of the electron probe was set to 18 mrad. The typical probe diameter was less than 0.1 nm. An annular dark field (ADF) detector was positioned to detect scattered electrons of an angular range from 38 to 184 mrad. In order to measure the lattice parameters as accurately as possible, we employed a drift corrected frame integration available in Velox software (Thermo Fisher Scientific) to avoid image distortion due to sample drifting. The magnification of each image was calibrated by the lattice parameters of the MgO substrates.

Electrical transport properties

For temperature (T)-, field (H)-, and direction (θ)-dependence measurements of resistivity, ρ(T, H, θ), and critical current density, Jc(T, H, θ), the NdFeAs(O,H) film was photolithographically patterned and Ar-ion beam etched to fabricate a small bridge of 30 µm width and 1 mm length. The sample was mounted on a rotator with maximum Lorentz force configuration, where the direction of the bias current is always perpendicular to that of the applied field. The angle θ is measured from the crystallographic c-axis. The critical temperature Tc was determined as the intersection between the fit to the normal state resistivity and the steepest slope of resistivity. By measuring Tc at various fields, the upper critical field Hc2 versus T diagram was obtained. The bias current for resistivity measurements was 10 µA, corresponding to a current density of Jb ~ 1.4 kA/cm2. The irreversibility field Hirr was evaluated from ρ(T, H) and Jc(T, H) data. For the former Hirr is determined by the intersection between the ρ(T, H) curves and the resistivity criterion ρc = Ec/Jb ~ 7.2 × 10−7 mΩ cm, where Ec (1 µV/cm) is the electric field criterion for determining Jc (Supplementary information fig. S5). For the latter Hirr was determined by the intersection between Jc(T, H) curves and Jb. At Hirr, the electric field—current density J characteristics showed a relation that can be expressed as E ~ Jn, where n was close to 1.