Substantial reduction of the anisotropy in the critical current densities J_c of Ni-doped CaKFe₄As₄ single crystals by chemical and irradiation-induced disorder

The reasonably high values of the superconducting transition temperature (T_c), very high upper critical magnetic fields (H_c2), and small upper critical field anisotropy (γ) of iron-based superconductors make them promising for applications such as superconducting magnets [1–4]. Among the candidates for these technologies is CaKFe₄As₄, which is a member of the so-called 1144 family AeAFe₄As₄ (Ae = Ca, Sr, and A = K, Rb, Cs) [5]. CaKFe₄As₄ is a multiband superconductor with T_c ≈ 35 K and with no other identified phase transition (magnetic or structural) [6]. Gradual suppression of the T_c and the emergence of antiferromagnetic magnetic order occur via Co or Ni substitution into the Fe site [7, 8]. The undoped compound displays an extrapolated upper critical field at zero temperature H_c2(0) ≈ 70 T and an anisotropy parameter $\gamma = {{{H_{{\text{c}}2}^{ \bot c}}}/ {{H_{{\text{c}}2}^{//c}}}}{ }$ that increases with the temperature being 1.5 at 25 K and 2.5 near T_c [6]. An interesting feature in CaKFe₄As₄ is that the superconducting anisotropy related penetration depth (λ) reduces with both chemical and irradiation-induced disorder [9]. These variations in the superconductor parameters, combined with controlled inclusion of pinning centers, may be relevant for applications that require close to isotropic critical current densities (J_c).

The vortex dynamics in the CaK(Fe_1−x Ni_x )₄As₄ system depend on the chemical composition, and, as in any superconductor, J_c increases with additional pinning centers [10–12]. The undoped single crystals display two outstanding features. The first refers to an anomalous peak in the temperature dependence of J_c with the magnetic field parallel to the c-axis (H || c) [13–16]. The second is related to a significant increase of J_c for H || ab, associated with stacking faults and planar CaFe₂As₂ intergrowths [15, 16]. For H || c, the vortex pinning in undoped single crystals is well described by a low density of strong pinning centers and random point disorder [10, 17, 18]. The J_c values increase for small Ni additions and then decrease as Ni substitution increases further [10]. Moreover, a substantial increase of J_c has been shown for undoped crystals by introducing point-like defects [11]. Considering the high anisotropy in J_c displayed by undoped crystals [13, 15] and the strong influence of random disorder and Ni substitution in the superconducting parameters [9], it may be stimulating to test their combination on the vortex pinning of CaK(Fe_1−x Ni_x )₄As₄ single crystals under different magnetic field configurations.

Here, we analyze the anisotropy in J_c for CaK(Fe_1−x Ni_x )₄As₄ (x = 0, 0.015, 0.025 and 0.030) single crystals by performing magnetization measurements. The results for crystals with x = 0 and x = 0.030 are compared before and after irradiation with 3 MeV proton (p) with a fluence of 3 × 10¹⁶ p cm⁻². The anisotropy and the absolute values of J_c are analyzed for H || c and H || ab configurations.

Single crystals of Ni-doped CaKFe₄As₄ were grown out of a high-temperature solution rich in transition-metals and arsenic similar to the procedure used for the pure compound [6, 19]. The single crystals exhibit a plate-like morphology with the c-axis perpendicular to the plane of the plate. The samples used were roughly rectangular plates with length l, width w, and thickness d. The dimensions (l, w, d) of the samples in (cm) are (0.11, 0.055, 0.0031) for x = 0; (0.159, 0.046, 0.0017) for x = 0.015; (0.135, 0.05, 0.0027) for x = 0.025; and (0.156, 0.056, 0.0036) for x= 0.030 (pristine and irradiated). The dimensions for the irradiated undoped crystal were (0.119, 0.038, 0.0016). The magnetization (M) measurements were performed using a superconducting quantum interference device magnetometer. The volume and the mass of all the single studied crystals agree with the density (5.22 g cm⁻³) determined from lattice parameters [5]. The J_c values were calculated from the magnetization data using the appropriate geometrical factor in the Bean Model [20]. For H || c, ${J_{\text{c}}} = {{{20\Delta M}}/ {{w\left[ {1 - w/3l} \right]}}}$, where ΔM is the difference in magnetization M (emu cm⁻³) between the top and bottom branches of the hysteresis loop. For H || ab, we evaluate $J_{\text{c}}^{{\mathbf{H}}\parallel ab}$ considering two J_c components, i.e. $J_{\text{c}}^{ab}$ and $J_{\text{c}}^c$. Detailed information of the extended Bean's critical state model for anisotropic J_c is provided in [15, 16, 20] (see supplementary information (available online at stacks.iop.org/SUST/34/035013/mmedia)). In the following, J_c2 and J_c3 refer to $J_{\text{c}}^{ab}$ and $J_{\text{c}}^c$ with H || ab. A schematic picture of the critical current densities with H applied parallel and perpendicular to the c-axis is presented in figure 1. It is important to note that a good correlation between J_c values obtained by magnetization and electrical transport is expected [21].

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The single crystals were irradiated with 3 MeV protons using a fluence of 3 ×10¹⁶ p cm⁻² along the normal of the crystal plane (parallel to the c-axis) using a tandem accelerator. This fluence was selected considering that it is close to the optimal for J_c enhancement in CaKFe₄As₄ [11]. For the irradiation, the crystals were fixed to the holder with silver paint. Typical beam currents of ≈30 nA were used. The irradiations were performed on samples with typical area 0.05 cm × 0.15 cm with the ion beam positioned at the center of the sample (spot diameter ≈ 0.16 cm). Proton irradiation produces mainly vacancies and a large number of small defects (2–5 nm) [21]. Simulations using the SRIM-TRIM software package [22] indicate that irradiation with 3 MeV protons produces a damage profile in which most of the ion's cross the samples (damage is close to uniform).

Figure 2 shows typical curves of magnetization versus magnetic field for H || c and H || ab at 5 K. For H || c, the loops are almost symmetric with respect to both H- and M-axes, indicating that bulk pinning dominates. For H || ab, the loops at high fields are mostly symmetric. However at low fields, a broad dip appears for x = 0 and x = 0.015. This feature has been previously observed in proton irradiated Ba_0.6K_0.4Fe₂As₂ [23] and Ba.(Fe_0.93Co_0.07)₂As₂ irradiated by 800 MeV Xe [24], and has been related to Meissner hole and matching field effects produced by correlated disorder, respectively. In our case, as we show below, the dip around zero-field could be related to the high pinning produced by planar defects in x = 0 and x = 0.015. Figure 3 shows the magnetic field dependence at different temperatures of the critical current density J_c of CaK(Fe_1−xNi_x )₄As₄ single crystals for different magnetic field configurations (H || ab and H || c) and the resulting anisotropy in J_c, defined as ${\gamma _{{J_{\text{c}}}}} = {{{{J_{{\text{c2}}}}}}/ {{{J_{\text{c}}}}}}$. The values of J_c3 are not included, being usually up ten times smaller than J_c2 [15, 16]. The J_c(H) dependences for the H || c configuration were previously discussed in [10]. The vortex pinning is well described by a mixed pinning landscape, including random disorder and a small number of strong pinning centers [17]. The crystals display several vortex pinning regimes that depend on temperature and magnetic field. The main features at low and middle temperatures are related to a power-law dependence with J_c∝ H^−α (related to strong pinning centers) followed by a region with J_c≈ constant that progressively, as temperature increases converts in a second peak in the magnetization (related to collective pinning) [10, 17]. The latter, as evidence in the J_c(H) curves at high temperatures, is followed by a fast drop in J_c due to a crossover between elastic and plastic vortex creep regimes [25]. The undoped crystal also has a peak in J_c(T), as shown in figure 3(a). This unusual feature has been associated with planar CaFe₂As₂ inclusions [16]. Small substitution of Fe by Ni improves the pinning masking the unusual peak displayed by undoped crystals, which evidences in the absolute values of J_c as in the α values. Figure 3(b) shows the J_c2(H) dependence with H || ab for the undoped crystal, which is characterized by much larger values with respect to those observed for H || c and give rise to high ${\gamma _{{J_{\text{c}}}}}$ values (see figure 3(c)) [13, 15, 16]. The ${\gamma _{{J_{\text{c}}}}}$ values show a marked dependence with temperature and magnetic field, being close to 30 at low temperatures, and decreasing systematically to close to 5 at 30 K and moderate fields. Moreover, the results show that with the exception of high temperatures where the crossover to fast creep appears first for H || c, usually ${\gamma _{{J_{\text{c}}}}}$ decreases as the magnetic field increases. The high ${\gamma _{{J_{\text{c}}}}}$ for undoped crystals has been associated with stacking faults and planar CaFe₂As₂ intergrowth [15, 16]. Figure 3, in panels (e), (h), and (k), displays J_c2 (H) for Ni-doped CaKFe₄As₄. The panels (f), (i), and (l) show ${\gamma _{{J_{\text{c}}}}}\left( H \right)$. Assuming that the Ni-doped crystals display a microstructure with stacking faults as the undoped ones [15], several differences appear, and a clear evolution in ${\gamma _{{J_{\text{c}}}}}$ is observed as doping increases. Unlike the undoped crystal, Ni-doped crystals display a substantial reduction in ${\gamma _{{J_c}}}\,$ with weak changes in temperature. Indeed, the ${\gamma _{{J_c}}}$ values for x = 0.015 reduce to ≈ 8 remaining approximately constant in temperature (see figure 3(f)). The decrease in ${\gamma _{{J_c}}}$ with doping becomes more significant for x = 0.025 and x = 0.030, with values that range from ≈ 2.5 and ≈ 2 towards 1 as the magnetic field increases, respectively.

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There are two points to consider in anisotropy of the vortex pinning for Ni-doped CaKFe₄As₄ single crystals, which are mainly summarized in figure 4. First, for H || c and at low and intermediate temperatures, the J_c values increase for small Ni additions and then decrease as Ni substitution increases further. For H || ab, the J_c values at low and intermediate temperature decrease as Ni doping increases (see left axis in figure 4(a) for μ₀ H = 1 T and T = 5 K). Moreover, the Ni addition modifies the in-field dependences of J_c, as evidence in the α exponent (see right axis in figure 4(a)). The value of α usually relates to the pinning centers' geometry, varying from ≈ 0.5–0.6 for nanoparticles [26] to 0.2 for correlated disorder [27]. Mixed pinning landscapes typically display intermediate values, which depend on the combination of defects. For H || c, α decreases systematically from ≈ 0.68 to ≈ 0.46 as x increases to 0.030. For H || ab, α starts at 0.32 for x = 0, displays a minimum of ≈ 0.22 for x = 0.015 and tends to reach similar values than for H || c as x increases. This evolution indicates that correlated pinning produced by planar defects are more efficient in x= 0 and x = 0.015, and decreases for x = 0.025 and x = 0.030. This dependence may be understood as a balance between the vortex pinning produced by a combination of correlated disorder and random point defects [28] and its influence in superconducting parameters such as the penetration depth λ and the coherence length ξ [9]. Indeed, an increment in the penetration depth, λ and an increment in the vortex fluctuations may be expected from chemical disorder [29]. Moreover, the upper critical field is usually reduced as T_c decreases. The second point to mention relates to both absolute values and temperature dependence of $\,{\gamma _{{J_c}}}$. Figure 4(b) shows ${\gamma _{{J_c}}}$(T) at μ₀ H = 1 T and μ₀ H = 2 T for the different samples. The data show a marked temperature dependence of the anisotropy for x = 0. Both absolute value and temperature variations decrease as Ni doping increases. Indeed, $\,{\gamma _{{J_c}}}$ evolves from ≈ 8 for x = 0.015 to ≈ 2.5 for x = 0.025 and remains in ≈ 2 for x = 0.030. The jump between x = 0.015 and x = 0.025 agrees with the magnetic order's appearance in the crystals [7]. The reduction in ${\gamma _{{J_c}}}$ with x also agrees with the decline in the anisotropy of λ reported in [9]. Moreover, the substantial decrease in ${\gamma _{{J_c}}}$(T) for the undoped sample suggests that the ξ size plays a role in the pinning produced by planar defects, which also may explain the reduction observed in Ni-doped samples.

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To understand the role of the disorder on the ${\gamma _{{J_c}}}$ values, we added random point disorder to the x = 0 and x = 0.030 samples via proton irradiation. The T_c values for these crystals decreased from 35 K to 33.5 K and from 20.6 K to 18 K for x = 0 and x = 0.030, respectively. Figure 5 shows the magnetic field dependence of J_c at different temperatures for the irradiated samples in the different magnetic field configurations (H || ab and H || c) and γ J_c (H). The results for the undoped crystals with H || c were previously shown in [11]. The absolute values of J_c as well its magnetic field dependence increase significantly after irradiation, reaching values up 9 MA cm⁻² for low temperatures with α = 0.39. For H || ab, the J_c (H) dependence and their absolute values are weakly affected (see figure 5(b)). Consequently, ${\gamma _{{J_c}}}$ reduces substantially, taking values close to 0.85 at 5 K and decreases to around 0.7 at intermediate temperatures in the entire magnetic field range. Because the analysis does not match the cases in which the extended Bean model can be applied (see supplementary information), the $J_{\text{c}}^{{\mathbf{H}}\parallel ab}$ values at 5 K for the irradiated undoped crystal were evaluated using the simplified formula taking by taking $J_{\text{c}}^{ab}$ = $J_{\text{c}}^c$. As is discussed in [16], $J_{\text{c}}^{{\mathbf{H}}\parallel ab}$ taking the average of the two components is smaller than J_c2. Therefore, values at 5 K using J_c2 should be slightly higher than those presented in figure 5(c). The reduction of ${\gamma _{{J_c}}}\,$ and the close to isotropic pinning after irradiation is also observed for x = 0.030. Indeed, ${\gamma _{{J_c}}}$ remains close to 1 at low temperature and increase slightly with field as temperature increases. The latter is related to a fast drop of J_c in high magnetic fields for H || c. Regarding the irradiation's influence on the J_c values with H || c for x = 0.030, the most significant effects occur at low temperatures. For example, J_c increases from ≈ 1 to ≈ 1.4 MA cm⁻² at 5 K and self-field. Moreover, the α value decreases from 0.46 to 0.34. On the other hand, and as in the undoped crystal, the addition has a weak influence on the vortex pinning J_c values with H || ab. It is important to note that in both cases, pinning centers' addition increases J_c for H || c, and its values tend to the observed in pristine samples for H || ab. The latter suggests that vortex pinning for H || ab is close to being optimal in pristine crystals, and their absolute J_c values relate to superconducting parameters such as T_c, ξ and λ. Moreover, it is notorious that after irradiation, the α exponent in the undoped crystal for H || ab increase slightly, indicating that as in Ni-doped samples (x = 0.025 and 0.030), the disorder modifies the pinning produced by planar defects.

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The results indicate that the inclusion of random disorder through chemical substitution and irradiation reduces the ${\gamma _{{J_c}}}$ in CaKFe₄As₄ single crystals. Usually, J_c can be increased significantly by introducing artificial pinning centers. The strategies include from irradiation damage to precipitation of secondary phases [30, 31] CaKFe₄As₄ displays a short coherence length ξ [6], which enhances the vortex pinning produced by point disorder [18]. According to our study, the random disorder in the undoped compound enhances the vortex pinning mainly for H || c configuration and has a weak contribution for H || ab. The crystalline defects generated by proton irradiation, with no significant reduction on T_c, produce more substantial changes on ${\gamma _{{J_c}}}$ than that provided by Ni-doping. The reduction of ${\gamma _{{J_c}}}$ in Ni-doped crystals is mainly a consequence of a decrease in J_c for H || ab. The latter is opposite to the addition of disorder by proton irradiation, where the reduction in ${\gamma _{{J_c}}}$ is a consequence of a substantial enhancement in J_c for H || c. These results suggest that the vortex pinning for H || ab in all the samples is close to optimal. The possible reason for the decrease in the J_c values with Ni-doping for this magnetic field configuration is by changes in superconducting parameters such as ξ and λ, and related depairing current density J₀. To better understand the crystals' pinning mechanisms, a detailed analysis of the microstructure is also necessary. Future studies by transmission electron microscopy should help to clarify possible differences in the microstructure of the crystals as Ni doping increases.

In summary, we evaluate the anisotropy of the J_c values by magnetization measurements in CaK(Fe_1−x Ni_x )₄As₄ single crystals. The results show a substantial reduction in the anisotropy of the J_c by Ni-doping and by adding random point disorder using irradiation. These types of defects are expected to produce isotropic pinning. The possibility to enhance J_c significantly by adding disorder together with attractive values of T_c and upper critical fields make the CaKFe₄As₄ system promising for applications that require close to isotropic J_c values.

We thank C Olivares for technical assistance during irradiations. This work was supported by the U.S. Department of Energy, Office of Basic Energy Science, Division of Materials Sciences and Engineering. The research was performed at the Ames Laboratory. Ames Laboratory is operated for the U.S. Department of Energy by Iowa State University under Contract No. DE-AC02-07CH11358. WRM was supported by the Gordon and Betty Moore Foundation's EPiQS Initiative through Grant GBMF4411. NH and SS were partially supported by ANCYP PICT2015-2171 (Argentina). NH is member of the Instituto de Nanociencia y Nanotecnología (INN), CNEA-CONICET.