Introduction

The reasonably high values of the superconducting transition temperature Tc, very high upper critical magnetic fields and generally low anisotropy of the recently discovered iron-based superconductors1,2,3 enable operation in economically interesting temperature-field ranges and, at the same time, minimize detrimental effects due to grain boundaries and thermal fluctuations4,5. However, the overriding application metric, the maximum loss-less electrical current density, is ultimately determined by the vortex pinning that can be engineered into the material. Significant advances towards high-performing superconducting materials based on the so-called 122-compounds, most notably Ba(Fe1−xCox)2As2 and Ba1−xKxFe2As2 (refs 6, 7, 8), and 11-compounds9 have been made. For instance, Ba0.6K0.4Fe2As2 has demonstrated a nearly field-independent critical current density of Jc=5 MA cm−2 at 5 K and H~7 T (ref. 10). These Jc(T,H) values are comparable to state-of-the-art YBa2Cu3O7-δ (YBCO)-coated conductors under similar conditions. However, the relatively low values of Tc, 23 and 38 K, respectively, pose serious limitations. FeAs-1111 compounds, such as SmFeAsO1−xFx, have Tc in excess of 50 K (ref. 11). In addition, high critical current densities approaching 1–2 MA cm−2 in as-grown SmFeAsO1−xFx crystals and films at 5 K and self-field have been reported12,13,14. However, the layered structure of SmFeAsO1−xFx, shown in Fig. 1a, leads to a rather high anisotropy, γ~8 (refs 15, 16), exceeding that of YBCO, which causes the suppression of the irreversibility field and limitation of applications at high fields and high temperature. To mitigate these drawbacks, nano-scale columnar defects in optimal-doped SmFeAsO0.8F0.15 crystals were produced. Columnar defects have been proven very effective in vortex pinning in high-Tc cuprates17 as they are capable of trapping vortices over extended sections of their length (see Fig. 1b). To date, the performance of SmFeAsO0.8F0.15 with columnar pinning landscape is unknown, and the ceiling of Jc of the iron-based superconductors remains an open question.

Figure 1: Heavy-ion-irradiated SmFeAsO0.8F0.15 and magnetization characterizations.
figure 1

a and b are schematic pictures of the layered structure of SmFeAsO1−xFx and of the correlated nano-scale defects produced by the high energy, heavy-ion irradiation. (c) Image of sample no. 1 placed on top of a micro-Hall array magnetometer. The black open squares represent the position of the individual Hall-probe sensing areas underneath the crystal. (d) and (e) Magnetization measurements of sample no. 1 and no. 2, pre- and post irradiation. Tc remains virtually unchanged following irradiation. (f) and (g) Magneto-optical imaging of magnetic flux in sample no. 1 in increasing and decreasing applied magnetic fields. The scale bars in (c) and (f) represent 100 μm.

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Here we incorporated a low density of columnar defects into pristine SmFeAsO0.8F0.15 crystals using high-energy, heavy-ion irradiation along the c-axis. The induced columnar defects produce record-high values of the critical current density without degradation of the transition temperature. The enhanced critical current to Jc (5 K, 0 T)≈20 MA cm−2 corresponds to ~20% of the depairing current. Furthermore, we found a pronounced reduction in the superconducting anisotropy from 8 to 4 following the irradiation. Such a phenomenon can be qualitatively understood in the framework of anisotropic electron scattering by columnar defects.

Results

Columnar-defect incorporation

SmFeAsO0.8F0.15 single crystals with an approximate size of 100 × 100 × 6 μm3 (shown in Fig. 1c) and submicrogram mass were grown at ETH Zurich in a high-pressure synthesis procedure using NaCl/KCl flux18,19. Two SmFeAsO0.8F0.15 crystals were irradiated at the ATLAS facility at Argonne National Laboratory with 1.4-GeV Pb –ions to doses of N=2 × 1011 (sample no. 1) and 5 × 1011 ions cm−2 (sample no. 2), corresponding to nominal dose-matching fields of BΦ=4 and 9.5 T along the crystal’s c-axis; BΦ=NΦ0, where Φ0=2.07 × 1015 Tm2. Heavy-ion irradiation leaves amorphous tracks (columnar defects) where the ions have traversed through the sample20. Compared with the structural density of 6 × 1014 unit cells cm−2 for SmFeAsO0.8F0.15, the concentration of tracks is rather dilute, ~2–5 tracks per 1,000 unit cells.

Transition temperatures

Figure 1d,e shows SQUID magnetic measurements in a field of 1 Oe (H//c) after zero-field cooling for the two SmFeAsO0.8F0.15 crystals before and after irradiation. We observe a temperature-independent magnetic moment at low temperatures and a sharp superconducting transition at Tc=50 K with ΔTc~1.5 K, underlining the high quality of the crystals. Our results show that the transition temperature and transition width do not change appreciably for irradiation doses up to 9.5 T. Similar robust transition temperatures against heavy-ion-induced defects were observed in Ba0.6K0.4Fe2As2 crystals with 1.4-GeV Pb-ion irradiation doses up to BΦ=21 T (ref. 10). These results suggest that in both, the FeAs-1111 and the FeAs-122-compounds, columnar defects induce non-magnetic small-angle intra-band scattering, which does not contribute to pair-breaking for s±-gap symmetry.

Critical current densities

The small size of the crystals used in our study precludes the use of a commercial SQUID magnetometer to obtain Jc through magnetic hysteresis measurements at temperatures above 20 K. We therefore placed the crystal onto a highly sensitive micro-Hall-array magnetometer (see Fig. 1c). The crystal was carefully aligned with a high precision manipulator to ensure that the same position within 5 μm was maintained for measurements before and after irradiation, corresponding to an uncertainty of <10%. The black squares in Fig. 1c denote the three active areas of the Hall-array, with the middle sensor located at the centre of the crystal. A magneto-optical (MO) indicator film technique21 was used to check for weak links such as grain boundaries in the samples. The images of field screening and trapped flux after switching off the external magnetic field are shown in Fig. 1f,g for sample no. 1. No weak-link areas for preferential entry/exit of vortices can be detected, confirming the single grain and homogeneous critical current density behaviour over the entire sample.

Figure 2a compares the magnetic hysteresis loops at the centre of sample no. 2 at T=10 K before and after irradiation to a dose of BΦ=9.5 T. A ten-fold enhancement can be observed for the irradiated sample. This large enhancement factor is observed over the entire temperature range from T=5 to 40 K. For comparison between local and global magnetization measurements, we measured the magnetization hysteresis curve of sample no. 2 with a SQUID magnetometer at T=5 K, where the signal was large enough to be detected from the small crystals. Using the Bean model22 Jc=20ΔM/a(1-a/3b), we obtained Jc values from the hysteresis loop width, ΔM. A calibration factor was obtained by comparing the Jc value determined by SQUID magnetometry at low temperature and the Jc values obtained from the micro-Hall-array magnetometer. This factor was used to convert the micro-Hall-array data to Jc values at high temperatures. The derived Jc(H,T)-values for the 9.5-T-irradiated sample no. 2 at various temperatures and fields are presented in Fig. 2b. At 5 K and self-field, the critical current density is remarkably high Jc=1.8~2 × 107 A cm−2, whereas Jc at 44 K and 0 T is 2 × 105 A cm−2. As for the 4 T-irradiated sample no. 1, the critical current derived using the same method yields Jc=9 × 106 A cm−2 at 5 and 0 T, ~4.5 times the Jc (5 K, 0 T) of the pristine sample. The depairing current of SmFeAsO0.85F0.15 can be estimated by , where Φ0 is the flux quantum, and using values of the penetration depth λ~200 nm and the coherence length ξab(0)~1.5 nm (refs 2, 16, 23). The calculated value of j0~1 × 108 A cm−2 indicates that we have achieved ~20% of the depairing current by simply incorporating a low density of columnar defects. To the best of our knowledge, such a high Jc value has not been reported on any of the iron-based superconductors. This is a remarkably high Jc for a single crystal, considering that even in state-of-the-art YBCO conductors, the self-field Jc has reached only 15–25% of the depairing current after a decade of pinning landscape engineering24,25,26. By increasing the density of defects and by combining different types of pinning centres into SmFeAsO0.8F0.15, further enhancement of Jc can be expected.

Figure 2: Critical current density and irreversibility field of irradiated SmFeAsO0.8F0.15.
figure 2

(a) Micro-Hall-bar voltage signal from the middle sensor for sample no. 2 before and after irradiation to a dose-matching field of BΦ=9.5 T. (b) Magnetic field dependence of Jc at various temperatures for sample no. 2. The magenta solid line is the Jc determined from SQUID measurements at T=5 K using the Bean model calculation. The open symbols are Jc obtained from the micro-Hall-array magnetometer. (c) Jc as a function of temperature for the pre-irradiated sample no. 1, postirradiated sample no. 1 (BΦ=4 T) and sample no. 2 (BΦ=9.5 T). 10% Jc uncertainty of postirradiated sample no. 1 arises from the different determinations between measurements of Hall array and magneto-optical imaging. (d) The irreversibility line for the investigated three samples. Jc=2,000 A cm−2 was used as a criterion to determine the irreversibility fields. Uncertainty comes from the noise in Jc measurement which is shown in b. The solid lines in c and d are guides to the eye.

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Figure 2c shows the temperature dependence of Jc before and after irradiation. The order-of-magnitude enhancement of Jc due to irradiation is apparent over the entire temperature range. The initial (almost) exponential decrease of Jc with temperature followed by a power-law variation has been observed for several 1111-materials27. It has been suggested that at low field (self-field) and low temperatures, strong single-vortex pinning is dominant27, whereas at higher temperature, effects due to collective pinning and creep become important. Using a criterion of Jc=2 × 103 A cm−2, we determined the irreversibility line Hirr. The slope of Hirr increases by a factor of 2–3 after irradiation, as shown in Fig. 2d. These results demonstrate that a low density of columnar defects can firmly pin the vortices and effectively extend the useful range in the H–T phase diagram into the vortex liquid region.

Thermodynamic superconducting anisotropy and model

Another remarkable aspect of columnar defects is the surprising reduction of the thermodynamic superconducting anisotropy. Here, we use a highly sensitive membrane-based steady-state ac micro-calorimeter to measure the specific heat of the submicrogram crystals28 and to determine the superconducting anisotropy. The specific heat anomaly near Tc~50 K of sample no. 1 in zero field is delineated in Fig. 3a. Subtraction of the normal state background as described in detail in Welp et al.16 yields the superconducting specific heat near the transition as shown in Fig. 3b for the pristine and BΦ=4 T irradiated sample no. 1, respectively. The height of the cusp-like anomaly of sample no. 1 before irradiation (pristine) is ~24 mJ per mol K2. After irradiation, the height of the C/T anomaly is slightly suppressed, which can be attributed to a fractional loss of the superconducting material due to the formation of amorphous damage tracks. The transition temperature as revealed by specific heat does not change appreciably with irradiation, in agreement with the magnetic characterization, shown in Fig. 1d,e.

Figure 3: Heat capacity and superconducting anisotropy of irradiated SmFeAsO0.8F0.15.
figure 3

(a) Temperature-dependent specific heat of sample no. 1 irradiated to a matching field of BΦ=4 T. The anomaly due to the superconducting transition near 49 K is clearly seen. The inset shows sample no. 1 with a size ~120 × 90 × 6 μm3 placed on top of the ac micro-calorimeter. (b) The electronic heat capacity anomaly near Tc for pristine sample no. 1 (before irradiation) and after irradiation (BΦ=4 T). The crosses mark the transition temperature as determined from the inflection point of . (c–e) Temperature-dependent specific heat at fixed fields for H||c and H||ab to determine the superconducting anisotropy γ. The ratio of the two orthogonal fields for which the C/T curves coincide is the anisotropy γ.

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The superconducting anisotropy can be directly obtained by comparing the resulting heat capacity anomaly at Tc when the magnetic field is applied along the c-axis and ab-plane of the crystal. As shown in Fig. 3c, the specific heat data for 0.5 T//c and 4.0 T//ab coincide, revealing a superconducting anisotropy of γ~8 in the pristine SmFeAsO0.8F0.15 crystal. Similarly, in the irradiated samples with doses of BΦ=4 T and BΦ=9.5 T, the temperature-dependent C/T curves at 0.5 T//c overlap with those at 2.0 T//ab, corresponding to an anisotropy of γ~4 (Fig. 3d,e). This result indicates that the incorporation of a low density of columnar defects reduces the superconducting anisotropy of SmFeAsO0.85F0.15 by one half without changing the transition temperature. This tailoring of the anisotropy reduces the Ginzburg number and thereby enhances the irreversibility line and vortex pinning in irradiated SmFeAsO0.8F0.15.

Our results can be qualitatively accounted for in a model based on anisotropic scattering by columnar defects. In the case of a dilute concentration of scattering centres, point defects mix all momentum states equally, whereas extended defects preserve the momentum along certain directions29. For columnar defects, the momentum along the column’s axis is preserved, which is the c-axis in our case. Therefore, after irradiation the electron mean free path l along the c-axis remains the same, whereas l in the ab-plane decreases due to additional scattering from the columns. This can be qualitatively described as and , where and lc represent the c-axis electron mean free path prior and post irradiation. Likewise, and lab denote the in-plane mean free paths. lirr is the average distance travelled by an electron between two consecutive scattering events from two columns. The anisotropy parameter γ is defined as,

where the upper critical fields and are determined in Ginzburg–Landau theory through the in-plane and out-of-plane coherence lengths ξab and ξc (ref. 30), and . For the qualitative description given here, we consider identical electron bands or the dominance of one major band in a two-band superconductor, which reduces to the one-band scenario for the upper critical field31,32. The change in anisotropy induced by the anisotropic scattering due to columnar defects can be expressed in terms of the change of the coherence lengths for both the clean and dirty limits. As presented in more detail in the Supplementary Notes 1 and 2, the anisotropy parameter γ for a single-band superconductor in the clean limit can be expressed as

here γ0 and denote the anisotropy and mean free path of the unirradiated sample, is the BCS (Bardeen-Cooper-Schrieffer) (or Pippard) coherence length, and is the inverse of the pre-irradiation coherence length. Correspondingly, the anisotropy parameter γ for a single-band superconductor in the dirty limit reads

Equations 2 and 3 reveal for both limiting cases that the additional electron scattering by columnar defects, represented by lirr, leads to a reduction of the superconducting anisotropy. As shown in Supplementary Fig. S1, γ decreases rapidly with increasing defect at low concentrations and levels off at higher concentrations. These results are qualitatively consistent with our experimental observation that at higher defect concentration the anisotropy does not decrease any further within the uncertainties. A quantitative description of the data will require precise knowledge of the relation between lirr and the number of columns and a microscopic modelling of the electron scattering induced by these defects, which are beyond the ambit of this paper. In any case, by incorporating columnar defects along the c-axis, the thermodynamic superconducting anisotropy can be reduced. The rate of reduction with increasing irradiation-induced columnar defects is determined by the number of pre-existing defects, carrier density and the scattering potential of the columnar defects. As the in-plane and out-of-plane upper critical fields are given by and , the reduction of ξab brought by anisotropic electron scattering causes a larger enhancement of than of as is directly shown in Fig. 3b for sample no. 1. The enhancement of dHc2/dT is 2 for fields along the c-axis and 1.2 for fields applied in the plane. The crosses in Fig. 3b mark the superconducting transition temperatures that correspond approximately to the inflection points of C/T according to pervious analysis of the specific heat data of SmFeAsO1−xFx (ref. 16).

Discussion

A reduction of the anisotropy after heavy-ion irradiation with virtually unchanged Tc was also observed in 122-compounds. For example, the anisotropy of Ba0.6K0.4Fe2As2 is reduced from 2.5 to 2.1 after 1.4 GeV Pb-ion irradiation to a dose of BΦ=21 T (ref. 10); heavy-ion-irradiated SrFe2(As1−xPx)2 shows an anisotropy change from 1.6–1.5 to 1.2–1.3 (ref. 33). The comparatively small reduction of anisotropy in the FeAs-122 materials can be attributed to the initial low anisotropy and the discontinuous morphology of the damage tracks10. Similar phenomena could be expected in high-Tc cuprates, MgB2 and other anisotropic superconductors. Very limited attention has been paid to the reduction of the superconducting anisotropy due to correlated defects in these materials. In the case of cuprates, any change of Hc2 is convoluted with a reduction of Tc, whereas the high conductivity of MgB2 and of most conventional superconductors has prevented the creation of columnar defects with heavy-ion irradiation34. For iron-based superconductors, their semimetal property and weak gap anisotropy2 enable us to tune the anisotropy via heavy-ion irradiation. We expect other poor-metallic and fully gapped type II superconductors to follow our predictions and demonstrate tailored anisotropy as well. This general phenomenon is important for the application of new superconducting materials.

The low anisotropy, high critical current and high Tc indicate that optimal-doped SmFeAsO1−xFx may be the best iron-based superconductor for application. Recent progress in SmFeAsO1−x Fx thin film synthesis has provided the premise for fabricating high-quality films using appropriate substrates13,14. Further improvement of the performance of these films can be expected when columnar-type defects are incorporated. Experiences accumulated over the past decades on creating self-assembled columnar defects in cuprates films35 via chemical synthesis could help promote similar critical current enhancement in iron-based superconducting films. In this respect, SmFeAsO1−xFx-based superconducting products with performance comparable to the state-of-the-art of cuprates can be expected.

Methods

Specific heat measurement

We applied a membrane-based steady-state ac micro-calorimeter to measure the calorimetric effect of submicrogram single crystals. It utilizes a thermocouple composed of Au-1.7% Co and Cu films deposited onto a 150-nm-thick Si3N4 membrane as a thermometer. SmFeAsO0.8F0.15 crystals with a size ~100 × 100 × 6 μm3 were mounted on the thermocouple using Apiezon N grease. An ac-heater current at low frequency (<200 Hz) is adjusted such as to induce oscillations of the sample temperature of 50–200 mK.

Critical current measurement

The Hall sensor is based on a two-dimensional electron gas GaAs/AlGaAs heterostructure. The Hall-bar array was fabricated by photolithography and chemical etching. The active area is 5 × 5 μm2 and the sensitivity is 0.27 Ω per Gauss. The low temperature magnetization was measured by a SQUID (Quantum Design) magnetometer with a resolution down to 2 × 10−8 emu. For both Hall sensor and SQUID measurements, the magnetic field was applied in a step mode and the magnetic responses were measured after a 10-s stabilization time.

Jc determination using the MO images

A high spatial-resolution (down to 1 μm) MO imaging technique was used to map the magnetic induction component, Bz, normal to the crystals’ ab-plane. It is based on the Faraday rotation of polarized light in a garnet indicator film placed on top of the sample. The field profile of the trapped flux, Bz(x) allows us to estimate the critical current density either by numerically integrating Biot–Savart’s law for the supercurrent flow pattern inside the sample or by using an approximate expression for the normal component of the magnetic induction in elongated rectangular thin samples.

here, t=6 μm is the thickness of the sample, a is width and z0 the gap between the MO indicator film and the sample surface. z0 is obtained from the ratio of the maximum Bz at the centre and minimum negative Bz near the sample edge , which for a known sample geometry is a unique function of z0 (ref. 36). In our case, k~10 gives the indicator position z0~10 μm and the critical current density ~105 A cm−2, in good agreement with estimates of Jc from the M(H) loops.

Additional information

How to cite this article: Fang, L. et al. Huge critical current density and tailored superconducting anisotropy in SmFeAsO0.8F0.15 by low-density columnar-defect incorporation. Nat. Commun. 4:2655 doi: 10.1038/ncomms3655 (2013).