Superconducting properties of Ba(Fe_1–xNi_x)₂As₂ thin films in high magnetic fields

The Fe-based superconductors are intriguing materials for both basic research and potential applications. In particular, the electronic phase diagrams show competing ground states, which lead to unique normal state properties and unconventional superconductivity.¹ These materials also have the potential to supersede low-temperature superconductors in high-field applications since they combine the advantage of high upper critical fields with a small anisotropy at low temperatures.² Also, a higher tolerance to low angle grain boundaries compared to cuprates has been found for Co-doped BaFe₂As₂ (Ba122).³ Ba122 is among the most studied systems of the Fe-based superconductors since single crystals and thin films are relatively easy to grow and several kinds of doping (hole, electron, isovalent, direct/indirect) lead to superconductivity.⁴ We used Ni as dopant,⁵ which has two electrons more in the d shell than Fe and will therefore dope electrons in the system similar to the extensively studied Co substitution. Ni-doped Ba122 was found to be an interesting candidate for applications due to inherently strong pinning effects,⁶ leading to a high critical current density J_c.

Here, we report on the thin films of Ba(Fe_1–xNi_x)₂As₂ with a thickness of 100 nm which have been prepared by pulsed laser deposition (PLD) using a KrF excimer laser (λ = 248 nm, pulse duration 25 ns, energy density 3 J/cm², repetition rate 7 Hz). The deposition was performed under ultra high vacuum conditions (base pressure 10⁻⁹ mbar) at a deposition temperature of 750 °C. A polycrystalline pellet was prepared from a nominal Ba(Fe_0.95Ni_0.05)₂As₂ powder and served as PLD target. The Ni-content of the final target was determined to be in the overdoped regime (x = 0.065 ± 0.015) using energy dispersive X-ray spectroscopy (EDX) analysis in a JEOL scanning electron microscope. CaF₂ (001) was used as substrate that has been proven as a suitable template for the growth of Ba122 thin films.⁷ 

X-ray diffraction (XRD) using a Bruker D8 Advance diffractometer with Co-K_α radiation shows only (00l) reflections of the Ba122 and the substrate (Figure 1(a)), indicating a c-axis oriented film, together with peaks corresponding to a BaF₂ impurity phase. The distribution of this BaF₂ phase was investigated by transmission electron microscopy (TEM) on a cross sectional lamella along the [100] direction (prepared with a focused ion beam technique) using an FEI Tecnai T20 microscope (accelerator voltage = 200 kV). Precipitates with a lateral size of about 150 nm were found primarily on the film surface (Figure 1(b)), i.e., not incorporated in the superconducting layer. Selected area diffraction confirmed them as BaF₂. The BaF₂ is formed presumably due to a reaction of excess Ba with fluorine diffusing out of the substrate. Besides these precipitates, the film shows a clean microstructure. Planar defects, which were reported occasionally for Co-doped Ba122 PLD films,^8–10 are almost absent in our film. A partly amorphous reaction layer at the film-substrate interface of about 5–10 nm thickness was observed (Figure 1(c)) similar to the Co-doped Ba122 films on CaF₂.⁷ It is likely caused by beam damage during the lamella preparation. The XRD texture measurements (data not shown) reveal the epitaxial relation (001)[110]Ba122||(001)[100]CaF₂. The full widths at half maximum (FWHM) of the (103) $ϕ$ scan (⁠$Δϕ=0.93°$⁠) and of the (004) rocking curve (Δω = 0.71°) (both values not corrected for instrument broadening and geometrical effects) indicate a good crystalline quality of the superconducting layer and are comparable to the results for the Co-doped Ba122 thin films on CaF₂.⁷ For the determination of the c-axis length, the peak positions of the 2θ scan and the Nelson Riley extrapolation¹¹ were used, while the a-axis was extracted from reciprocal space maps measured in a high resolution X-ray diffractometer. With the lattice parameters c = 13.031 ± 0.002 Å and a = 3.949 ± 0.001 Å, the Ba122 unit cell is elongated along the c-direction in the thin film in comparison to the single crystals with similar doping (c = 12.986 Å a = 3.963 Å for x = 0.065).^12,13 This originates from compressive strain in the film due to the smaller a-axis parameter and larger thermal expansion coefficient of the CaF₂ substrate.^14,15

Transport properties have been measured using a four-point technique on a bridge of 2 mm length and 90 μm width prepared by laser cutting. Measurements were performed in static magnetic fields up to 35 T in maximum Lorentz force configuration at the National High Magnetic Field Laboratory. The critical temperature T_c evaluated at 90% of the normal resistance is 17.3 K (Fig. 2). The superconducting transition is sharp with ΔT_c = T_c90 − T_c10 < 1 K. The broadening of the transition with an increasing external field is relatively small, which is commonly observed in other Ba122 systems due to a small Ginzburg number. The observed T_c value is lower than the results on optimally doped single crystals¹⁶ but fits well to data for slightly overdoped material in agreement with the measured Ni-content of the target. However, the direct comparison of T_c values between single crystals and thin films might be problematic due to the complex effects of strain on the phase diagram. It has been shown for Co-doped Ba122 that compressive strain can even lead to higher transition temperatures in slightly overdoped thin films compared to optimally doped single crystals.¹⁵ 

A 90% criterion at 17.3 K was used for the evaluation of the upper critical field $Hc2$⁠, and the irreversibility field H_irr was evaluated at ρ = 10⁻⁴ mΩ cm (which is roughly 0.5% of the normal state resistivity at 30 K). The data shown in Figure 3 are in good agreement with the recent pulsed field measurements for overdoped single crystals.¹⁶ The $Hc2$ data were fitted using a two-band model for a clean superconductor including the paramagnetic effects.¹⁸ The fit suggests an upper critical field of 45 T and a smaller anisotropy than in overdoped single crystals with a similar critical temperature.¹⁶ The slope of the upper critical field –dH_c2/dT = 8.5 T/K (⁠$H∥ab$⁠) near T_c is higher for the film than for single crystals with similar doping level and more comparable to optimally doped crystals.¹⁶ This might be explained with the presence of epitaxial strain in the film leading to a change in the band structure, which results in smaller Fermi velocities.^15,19 Interestingly, at low temperatures, the irreversibility field almost seems to reach the H_c2 line as it is the natural limitation for both field directions. This would mean that Ba(Fe_1–xNi_x)₂As₂ thin films show a small vortex liquid phase at low temperatures in contrast to results for Co-doped films.⁸ However, one should take into account that H_c2 values at low temperatures could be additionally enhanced due to the formation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state.¹⁸ This possibility was not taken into account in the H_c2 analysis in the present work due to the lack of experimental data at low temperatures. Future investigations in high fields will clarify this question.

The linear dependence of Arrhenius plots of the resistivity (not shown here) indicates thermally activated motion of the flux lines above H_irr. The pinning potential U₀ extracted from the Arrhenius slopes is shown in the inset of Figure 3(b). The solid lines represent fits with the phenomenological function^8,17

We achieved the best fits with parameters a = 0.4, b = 1.0, μ₀H_irr = 45 T for $H∥ab$ and a = 0.7, b = 1.0, μ₀H_irr = 42 T for $H∥c$⁠.

The critical current density J_c is shown in Figure 4. The J_c at 4.2 K in self field exceeds 5.7 × 10⁵A/cm². This is lower than J_c values for differently doped Ba122 films,^21,22 presumably due to the lower T_c. Also, magnetisation measurements on optimally doped single crystals⁶ showed a higher J_c, while it was highest for $H∥c$⁠, i.e., an inversion of the J_c-anisotropy occurred. This inversion was not observed for our thin films.

Figure 4(a) shows the angular dependence of J_c at T = 4.2 K. Only one maximum for $H∥ab$ is observed. The data can be scaled over an effective field²⁰ 

An anisotropy value of γ = 1.8 was found for the critical current density at 4.2 K.

The field dependence of J_c is shown in Figure 4(b). The inset shows the normalized pinning force density F_p, which was fitted with the Dew Hughes model²³ 

The respective fit parameters for $H∥ab$ and $H∥c$ are p = 0.56, q = 1.32 and p = 0.48, q = 1.67. The corresponding H_irr values are shown in Figure 3. The p-values of the pinning force fits for both field directions suggest that the pinning is influenced by the elastic effects of the vortex lattice and vortex interactions. This contribution to the pinning is significant if the size of the pinning centers r is smaller than or comparable to the coherence length ξ.²⁴ For $H∥c$⁠, the fit is close to (p = 0.5, q = 2), which can be attributed to pinning at two-dimensional nonmagnetic defects.²³ In our film, these defects could be growth domain boundaries or small-angle grain boundaries, although they have not been directly confirmed in the TEM investigations. For $H∥ab$⁠, the exponent q is smaller, which has been observed before in Co-doped⁸ and P-doped²² Ba122 films at low temperatures. This might be related to the small film thickness, which restricts the bending of vortices. For $H∥ab$⁠, the smaller q value is in qualitative agreement with the results of the activation energy, since the exponents of the activation energy (1) and the pinning force density (3) should fulfill the relations a ≈ 1 – p, b ≈ q.¹⁷ For $H∥c$⁠, these equations are not fulfilled, which has also been observed for Co-doped films.⁸ 

The anisotropy γ of the critical fields and critical current density is shown in Figure 5. For H_c2 and H_irr, it is calculated by $γ=HabHc$⁠, where H^ab and H^c represent the critical field for the respective field orientation. The data points and the two-band fit for H_c2 suggest a small anisotropy close to 1 at low temperatures. This agrees well with the anisotropy extracted from the activation energy fits. Such a small anisotropy despite the highly anisotropic crystal structure is a key feature of the iron-based superconductors.²⁵ The J_c anisotropy follows the H_irr anisotropy and both are noticeably increased compared to the H_c2 anisotropy. This indicates that the incorporated defects in the film affect the H_irr anisotropy, differentiating it from the intrinsic H_c2 anisotropy.

The enhancement of the H_irr anisotropy is typically observed in the Fe-based superconductors by introducing the pinning centers,^8,26 which is in contrast to cuprate high-T_c superconductors, where the addition of nanoparticles often leads to a reduction in the H_irr and J_c-scaling anisotropy.²⁷ 

In summary, we reported the epitaxial growth of Ba(Fe_1–xNi_x)₂As₂ thin films, investigated the structural and superconducting properties and evaluated their performance in high magnetic fields. The films show a T_c value of about 17 K and an enhanced slope of the upper critical field at T_c in comparison to single crystals with similar doping level. The enhanced slope –dH_c2/dT might be explained by the presence of compressive strain in the film. The critical current density reaches 5.7 × 10⁵A/cm² at 4.2 K in self field, which is smaller than the best results achieved for Co-doped Ba122 thin films.²¹ The pinning is dominated by elastic pinning at grain boundaries or growth domain boundaries, and the anisotropy at low temperatures is small similar to the results for other Fe based superconductors. Furthermore, we found the vortex liquid region of the vortex-matter phase diagram for Ni-doped films to be rather small, which is surprisingly different to the Co-doped Ba122 films.

This work was supported by the German Research Foundation (DFG) within the research training group GRK 1621. A portion of this work was performed at the National High Magnetic Field Laboratory, which is supported by the National Science Foundation Cooperative Agreement No. DMR-1157490 and the State of Florida. This work was also partially supported by the JSPS Grant-in-Aid for Scientific Research (B) Grant No. 16H04646 and the DFG Grant No. GR4667/1-1.