Enhanced upper critical field in Co-doped Ba122 superconductors by lattice defect tuning

Iron-based superconductors (IBSCs)^1,2 discovered by Kamihara and Hosono et al. have attracted significant attention, owing to their unconventional pairing mechanism and unique physical properties. From a chemical perspective, IBSCs have many parent materials, e.g., 1111, 122, and 11, and variations of constituent element choice. For example, in BaFe₂As₂ (Ba122), superconductivity can be induced by hole doping via K substitution on the Ba site, electron doping via Co substitution on the Fe site, or chemical pressure by P substitution on the As site. IBSCs are an excellent candidate for strong superconducting magnets, owing to their high critical temperature (T_c) and upper critical field (H_c2).² 122-phase IBSCs demonstrate small electromagnetic anisotropy,^3–10 a high irreversibility field that is close to H_c2,⁴ and a critical grain boundary angle that is twice as large as that of yttrium barium copper oxide (YBCO),^11,12 wherein application in the polycrystalline form is expected. In fact, a 1-cm diameter compact bulk magnet that traps 1 T¹³ and tapes exhibiting transport J_c exceeding 1 × 10⁵ A/cm² at 4.2 K and 10 T^14,15 have been developed recently using K-doped Ba122.

Tuning the magnetic phase diagram of a superconducting material is important in both basic and application aspects. Upon comparing 122 to other materials, it is interesting to note that there are very few reports of enhanced H_c2 via defects such as those caused by particle irradiation.¹⁶ Furthermore, there is no substantial difference in H_c2 among single crystals, polycrystalline bulks and wires, and thin films. Specifically, in the case of an 8% Co-doped Ba122, H_c2(0 K) is ≈60 T.^4,5,8,17 In conventional superconductors, H_c2 can be improved by introducing defects caused by particle irradiation or by adding nonmagnetic impurities. For example, in Nb₃Sn, H_c2(0 K) is improved by fast neutron irradiation,^18,19 proton irradiation,²⁰ or ball-milling the elements.²¹ In MgB₂, H_c2(0 K) is improved approximately twofold by thermal neutron irradiation²² and C doping.^23,24 Moreover, in MgB₂, H_c2(0 K) is multiplied several times up to 15–70 T^25,26 from clean single crystals to moderate bulks/wires and dirty thin films. In the case of IBSCs, magnetic scattering by excess Fe in Fe_1+y(Te_1−xSe_x) increases the slope of H_c2(T).²⁷ Herein, for Ba122 polycrystalline bulks, high-energy ball-milling conditions of a precursor powder were changed systematically and the effects of introducing defects to H_c2 were evaluated. To facilitate comparison with previous studies, experiments were conducted on Co-doped Ba122 for which single crystal and thin film data are available.

Ba(Fe, Co)₂As₂ polycrystalline bulk samples were prepared by sintering mechanically alloyed powders. To prevent oxidization, all powder processing was performed in a high purity Ar glove box. Elemental metals, such as Ba, Fe, Co, and As (molar ratio, 1:1.84:0.16:2), were ball-milled using a planetary ball-mill apparatus (Premium line P-7, Fritsch). Herein, the ball-milling condition was varied systematically by changing the ball-milling time and evaluated quantitatively by ball-milling energy (E_BM), which is an applied energy to powder per mass. E_BM is expressed as follows:

where c is the dimensionless constant of the order of 0.1, β is the mass ratio of balls to the powder, ω_p is the angular frequency, r_p is the revolution radius, r_v is the rotation radius, and t is the ball-milling time.²⁸ The milled powders were pressed into disk-shaped pellets with a diameter and thickness of 7 and 1.2 mm, respectively. The pellets were vacuum sealed in quartz tubes and sintered at 600 °C for 48 h. The obtained polycrystalline bulk Ba(Fe, Co)₂As₂ samples had relative densities of 65%–75%. For reference, a sample synthesized from hand-milled powder mixed in a mortar is denoted as 0 MJ/kg. The phase and structural properties were analyzed by powder X-ray powder diffraction (XRD) (D2 PHASER, Bruker) for the milled powders prior to sintering and ground powders of sintered samples using CuK_α (λ = 1.5418 Å) radiation. Lattice parameters a and c were calculated by Rietveld refinement (DIFFRAC.TOPAS). Co-doping levels were estimated by energy-dispersive X-ray spectroscopy (EDS) (QUANTAX, XFlash, Bruker) for the polished surface of the samples. The electrical resistivity measurements were performed under 0–9 T using the conventional four probe method with a physical property measurement system (Quantum Design) for samples cut into 1 × 2 × 6 mm³. T_c and H_c2 values were determined by 90% of superconducting transitions. In this determination, H_c2 is considered as the highest upper critical field in the samples, i.e., H_c2^//ab, because these samples are untextured polycrystalline bulks. Note that H_c2(T) was nonlinear; thus, the slopes of H_c2(T) were determined according to three definitions: between 0 and 1 T (near T_c), 0 and 9 T (field range measured in this study), and 2 and 9 T (linear part).

Figure 1 shows the powder XRD patterns of the milled powders prior to sintering and the ground powders of sintered bulk samples with E_BM values of 0, 50, and 590 MJ/kg. As shown in Fig. 1(a), the unsintered powders demonstrated elemental metal peaks of Fe and As at 0 MJ/kg, while Ba122 peaks were observed at 50 and 590 MJ/kg. This indicates that mechanical alloying of Ba122 occurred due to high-energy milling.²⁹ In the sintered bulk samples [Fig. 1(b)], multiphase peaks of Ba122 and Fe₂As were observed at 0 MJ/kg, while nearly single-phase Ba122 peaks were confirmed at 50 and 590 MJ/kg. These results suggest that sintering mechanically alloyed powder is effective to obtain high purity Ba122 polycrystalline samples.

Figure 2 shows the E_BM dependencies of the (a) Co-doping level, [(b) and (c)] full-width at half maximum (FWHM) of the XRD main peak of Ba122 (103) [(b) before sintering and (c) after sintering], (d) relative peak intensity of (200) and (004) to (103), (e) a-axis length, and (f) c-axis length. The Co-doping level in Fig. 2(a) shows the average value and standard deviation of the elemental analysis results for approximately 20 points on the polished surface of the sintered bulk samples. The standard deviation decreases with an increase in E_BM, which suggests that high-energy milling enhances the compositional homogeneity. There was almost no average change against E_BM, and the actual composition was x ≈ 0.084. Microstructural observation by a scanning electron microscope (not shown) demonstrated that the E_BM < 40 MJ/kg samples contained impurities such as Fe, FeAs, and Fe₂As, which are not detected by XRD. Since our sintering temperature is rather low (600 °C), sufficient mechanical alloying is required to obtain single-phase Ba122 samples. In the following, the E_BM > 40 MJ/kg samples are treated as single-phase Ba122 and discussed.

With an increase in E_BM, systematic broadening of FWHM was observed for the powder prior to sintering [Fig. 2(b)]. A similar but less pronounced systematic broadening was also observed for the sintered samples [Fig. 2(c)]. STEM observation³⁰ for the sintered samples showed that the grain size of Ba122 was refined with an increase in E_BM. This is considered as one of the reasons for the increased FWHM, i.e., degradation of crystallinity. The relative peak intensity of (200) increased systematically with an increase in E_BM, while that of (004) was almost constant [Fig. 2(d)]. This indicates that the reflection from the ab plane was disturbed with an increase in E_BM since (200), (004), and (103) are influenced by the reflection from the ac plane, ab plane, and both crystallographic parameters, respectively. These suggest the introduction of lattice defects parallel to the ab plane, such as stacking faults,³¹ by high-energy milling. In fact, STEM observation³⁰ revealed linear contrasts which were parallel to each other with a spacing of several nanometers, comparable to the coherence length near T_c. The lattice constants of the sintered sample with E_BM of 40 MJ/kg were a = 3.9604(2) Å and c = 12.9963(7) Å [Figs. 2(e) and 2(f)]. The reported lattice constants of 8% Co-doped Ba122 single crystals are a = 3.9600,³² 3.9604(1),³³ and 3.962 Å,³⁴ and c = 12.9779,³² 12.9793(3),³³ and 12.991 Å.³⁴ a and c of the 40 MJ/kg sample are longer than those of a single crystal³² by 0.01% and 0.14%, respectively. With an increase in E_BM, a decreased monotonically and c increased to reach saturation. At 590 MJ/kg, the lattice constants were a = 3.9588(3) Å and c = 13.0133(15) Å, which means that a decreased by 0.04% and c increased by 0.13% from 40 MJ/kg. The observed evolution of lattice constants a and c cannot be explained by the change in the Co-doping level because the literature states that both a and c decrease with Co doping,^32,34 and EDS analysis showed no change in the Co-doping level [Fig. 2(a)]. This opposite trend in a and c is frequently observed in thin films. For Ba122 thin films, it has been reported that the lattice constants and cell volume vary due to in-plane lattice strain (epitaxial strain) caused by lattice mismatch with the substrate.^35,36 Epitaxial strain can be regarded as equivalent to uniaxial pressure or tension along the c-axis. Figure 3 shows Δc/c₀ vs Δa/a₀ and ΔV/V₀ vs Δa/a₀ for thin films with epitaxial strain^35,36 and the polycrystalline bulks examined herein, where V is the cell volume, and a₀, c₀, and V₀ are the values of the thin film deposited on the YAO substrate or values of the 40 MJ/kg sample. As can be seen, the slope (Δc/c₀)/(Δa/a₀) for the polycrystalline bulks is at least three times greater in comparison with the epitaxial strain. Therefore, the defects introduced into the polycrystalline bulks by high-energy milling cannot be explained only by a lattice strain. In addition, while ΔV/V₀ decreased with decreasing Δa/a₀ in the thin films, it increased in the polycrystalline bulks. In the thin films, the decrease in ΔV/V₀ is due to Poisson’s ratio different from 0.5.³⁷ In the polycrystalline bulks, the increase in ΔV/V₀ suggests introduction of lattice defects with vacancy, which is consistent with the results of Figs. 2(d)–2(f) and should be responsible for the broadening of FWHM.

Figure 4 shows the temperature dependencies of the normalized electrical resistivity for the samples with E_BM values of 50, 80, 170, and 590 MJ/kg. The data of a single crystal (Co 10%)³⁸ are shown for comparison. With an increase in E_BM, the resistivity at 30 K (ρ_{30 K}) increased fourfold (0.76, 2.00, 3.19, and 2.82 mΩ cm, respectively), and RRR (ρ_{300 K}/ρ_{30 K}) decreased by 35% (1.72, 1.64, 1.37, and 1.11, respectively). In comparison with those of Co-doped Ba122 single crystals, ρ_{30 K} is an order of magnitude higher and RRR is about a half [ρ_{30 K} = 0.09 (Co 6.3%),³⁹ 0.09 (Co 8%),⁹ 0.11 (Co 10%),⁴⁰ and 0.16 (Co 10%)³⁸ mΩ cm, RRR = 2.69 (Co 6.3%),³⁹ 1.82 (Co 8%),⁹ 2.85 (Co 10%),⁴⁰ and 2.53 (Co 10%)³⁸]. The temperature dependencies of the electrical resistivity demonstrated metallic behavior at 30–300 K for samples with low E_BM (<170 MJ/kg), whereas semiconductorlike upturn at T < 100 K was observed for samples with high E_BM (>230 MJ/kg). The inset of Fig. 4 shows the temperature dependencies of the electrical resistivity under magnetic fields of 0–9 T for the samples with E_BM values of 50 and 590 MJ/kg. Although all the samples exhibited superconducting transition and reached zero resistance even under a magnetic field, they showed a broadening of resistive transition under a magnetic field. Since the samples are randomly oriented polycrystalline bulks, an increase in anisotropy, refinement of grain size, and change in intergranular structure are possible causes of the broadening. Moreover, the samples with >120 MJ/kg showed double transition. Transitions at higher and lower temperatures are considered to correspond to those of grains and grain boundaries, respectively, analogous to cuprates.⁴¹ Such broadening or double transition is also observed in K-doped Ba122 samples.^42–44 Figures 5(a)–5(c) show the magnetic phase diagram (a) and the E_BM dependencies of (b) T_c and (c) the slope of H_c2(T). T_c showed a maximum value of 26.6 K at 50 MJ/kg, which decreased slightly to 25.1 K with an increase in E_BM. Note that the T_c value was greater than optimal T_c values of typical single crystals (22.0–24.8 K^{4,5,9,32,38,40,45}) at all E_BM values despite the low crystallinity of our samples. With an increase in E_BM, H_c2(T) near T_c changed from an upward to downward curvature. Due to the curvature change near T_c, the slope value changed with its definition. The slope of H_c2(T) increased with E_BM, i.e., an enhancement of approximately 50% from 4.1 (20 MJ/kg) to 6.2 T/K (430 MJ/kg) was observed with the most conservative definition (approximation in the linear part). Moreover, higher slope values than those of single crystals (5.0 T/K,⁴⁶ 5.2 T/K³⁸) and thin films (5.1 T/K⁴⁷) were obtained at >80 MJ/kg. Anticorrelation between T_c and the slope of H_c2(T) suggests an existence of optimum intermediate E_BM for H_c2(0 K).

The reduction in T_c and increased slope of H_c2(T) can be explained roughly by the enhanced electron scattering model induced by high-energy milling. It is considered that the introduction of lattice defects makes the samples dirtier, leading to reduction in the electron mean free path and increase in the electron scattering rate. The low temperature upturn in resistivity and change in H_c2(T) curvature near T_c suggest that the introduced lattice defects modified the electronic structure, especially the multiband structure, which strongly affects H_c2.⁴⁸ Moreover, since c/a increased with an increase in E_BM, the effective electron mass anisotropy is likely increasing. Given the relationship between the anisotropy and the effective mass, this would also increase the H_c2 anisotropy, with possible enhancement of H_c2^//ab. Furthermore, the noticeable increase of H_c2(T) near T_c is similar to the well-established theory of H_c2 in weakly coupled S-I-S multilayers.⁴⁹ As expected in this scenario, the stacking faults introduced by high-energy milling may behave as weakly coupled planer Josephson junctions.

Attempts have been made to introduce various types of lattice defects/strains into 122 single crystals, thin films, and polycrystalline bulks and wires. In the case of Co-doped Ba122, nonmagnetic impurities introduced by fast neutron irradiation and proton irradiation were reported to decrease T_c at a ratio of 10⁻²² Km² and 0.5–5.8 × 10^–20 Km², respectively.^{16,45,47,50–55} When epitaxial strain is introduced into thin films, T_c changes continuously with c/a from 16 to 28 K.^35,36 In these cases, lattice defect/strain changed T_c but did not alter H_c2; therefore, the high-energy milling developed herein is a unique way to introduce lattice defects that differ from other methods and to tune the 122 system’s H_c2. At the present stage, we have not been able to specifically identify the defects that correspond to the enhanced H_c2. A study into the intragranular structure and the physical properties under higher magnetic fields should clarify the defects introduced by high-energy milling and the mechanism by which H_c2 is enhanced.

Here, we briefly discuss the applicability of this defect engineering by high energy milling to the ongoing development of 122 bulks and wires. The broadening of resistive transition would cause a decrease in intergranular J_c, which in turn reduces the applicable range in the magnetic field. For all kinds of anisotropic, polycrystalline superconducting materials, the alignment of grain orientations and/or increasing packing factor of superconducting phase are known as effective approaches to improve intergranular J_c.⁵⁶ Since our samples are 65%–75% in the packing factor with randomly oriented grains, texturing and/or densification would be required to maximize the effectiveness of the defect engineering to J_c of the bulks and wires. The introduction of anisotropic intragranular defects and modulation of elemental pinning force in which H_c2 is a prefactor would bring new developments in flux pinning engineering of 122 polycrystalline materials.

In summary, to improve H_c2 of 122 phase IBSCs, Co-doped Ba122 polycrystalline bulk samples were synthesized as E_BM was changed systematically, and the effects of high-energy milling on the structural and transport properties were evaluated. High-energy milling improved phase purity and introduced lattice defects into the Ba122 grains. These lattice defects deteriorated crystallinity, decreased a-axis length, increased c-axis length, and changed the shapes of ρ(T) and H_c2(T). Moreover, this resulted in continuous improvement of the slope of H_c2(T) by 50% without changing the doping level, while T_c was suppressed slightly by 5.5%. In principle, it can be expected that this method can also be applied to K-doped Ba122, P-doped Ba122, and other iron-based superconductors.

The authors would like to thank Dr. Soshi Iimura and Dr. Kota Hanzawa (Tokyo Institute of Technology) for their help with the high-field measurements. The authors also thank Dr. Kazumasa Iida (Nagoya University) and Dr. Yusuke Shimada (Tohoku University) for their fruitful discussions. This work was supported by JST CREST, Grant No. JPMJCR18J4, and by JSPS KAKENHI, Grant Nos. JP15H05519 and JP18H01699. A.Y. was supported by MEXT Elements Strategy Initiative to Form Core Research Center.