Comparison of the pinning energy in Fe(Se1−xTex) compound between single crystals and thin films

Among the families of iron-based superconductors, we investigate flux pinning mechanisms in the Fe(Se1−xTex) compound. We perform magneto-resistance and current-voltage measurements on single-crystals, as well as on several epitaxial thin films grown on different substrates (CaF2, LaAlO3). The activation energy is derived as a function of magnetic field, U(H). The influence of magnetic field orientation on the pinning energy activation mechanism is also studied, leading to the anisotropy analysis which reveals low anisotropy in thin films grown on CaF2 substrate with respect to single crystals and films grown on LaAlO3. Concerning the dominant pinning regime, the exponents of the power law dependence U0(H) ∝ H−α have been evaluated, confirm that weak pinning is a general characteristic of this compound. The single exponent feature, generally noticed on thin films grown on SrTiO3 substrate and associated to a strong single vortex regime, has been observed in thin films grown on LaAlO3, only in the parallel configuration. At the end, this overall comparison can be useful to develop a technological material able to compete with high temperature superconductors.


Introduction
About seven years have gone by the discovery of superconductivity in iron-based compounds [1] and this new class of high-T c superconductors is already looking promising for the applications. Indeed, iron-based superconductors show very high upper critical fields (H c2 ) even close to the critical temperature (T c ), similarly to MgB 2 . Likewise MgB 2 , they are also characterized by small anisotropy factors (γ). Moreover, they do not present the technical hurdles (such as the metal-insulator transition or the d-wave symmetry of the order parameter) presented by copper oxide superconductors and show an high robustness to impurities. Up to now, the main technical limit of iron-based superconductors is the low critical temperature (the highest T c for this class has been reported to be 56 K [2]), while the critical current density (J c ) values are comparable to those of the other high-T c superconductors (J c at 4.2 K and 30 T up to 10 5 A cm −2 have been reported [3]).
Almost all known iron-based superconductors belong to one of the following four families: a) the 1111 ReOFeAs (Re = Rare earth), b) the 122 AFe 2 As 2 (A = alkaline earth), c) the 111 XFeAs (X = Li, Na), and d) the 11 Fe(Se, Ch) (Ch = S, Te). As it is well known [4,5], the highest T c 's are shown by the 1111 compounds, while the 122 family presents the highest upper critical fields. Nonetheless, the interest in 11 compounds is increasing [3,6], mainly due to their low magnetic field anisotropy, the high H c2 (T ) slope near T c , the absence of poisonous elements and the possibility to increase the relative low T c by growing thin films on proper substrate inducing the Volmer-Weber growth mode, which mimic the application of an external pressure (see Ref. [7] and references therein).
In this paper we study the pinning properties of the Fe(Se 1−x Te x ) (FST) compound grown as single crystals and thin films on different substrates to show that such thin films can be promising for high-field applications.

Experimental details
Single crystals of Fe 1+y (Se 1−x Te x ) (y < 0.1, 0 < x < 0.45) were grown in self-flux by using a modified Bridgman method from high purity precursors (Fe, Se and Te granules, all with purity ≥ 4N) melted inside a vacuum-sealed quartz tube vertically placed in a gradient furnace, and slowly cooled down (more details in Ref. [8]). Single crystals are easily cleaved in the ab-plane and characterized by X-Ray Diffraction (XRD) and Energy Dispersive X-Ray Spectroscopy (EDX) in order to check the crystal quality, composition and homogeneity. The actual composition of the crystals used in this work was found to be Fe 1.02 Te 0.68 Se 0.32 (nominal x = 0.3). Thin films were prepared in an ultra-high vacuum Plasma Laser Deposition (PLD) system from a starting target prepared by a two steps procedure from high purity materials (Fe 99.9 + %, Se 99.9% and Te 99.999%), with a nominal composition FeSe 0.5 Te 0.5 , on single crystals substrates with different cell parameters and different chemical composition (more details in Ref. [9]).
Magneto-resistance and current-voltage measurements have been carried out in a Cryogen Free Magnet (CFM) system by Cryogenic Ltd. equipped with a cryogen-free variable temperature insert and a 9 T superconducting magnet. Magneto-resistance measurements have been performed by a standard 4-probe technique. Fig. 1 shows two typical field versus temperature (HT ) phase diagrams realized acquiring more than 35 resistance-temperature (R(T )) curves, with the applied field direction parallel to the c-axis of the samples (H // c). Current-voltage measurements have been performed in a pulsed current 4-probe technique [7] biasing the sample with rectangular current pulses 2.5 ms wide and a delay of 200 ms.

Results and discussion
In the following, we will present results on three different FST samples: a single crystal, which we will identify as sample CRY, and two thin films grown on a LaAlO 3 and on a CaF 2 substrate, namely sample FL and sample FC respectively.  In Fig. 1 the HT phase diagrams of sample CRY and FC, with H //c, are shown. In both phase diagrams the irreversibility line (H irr (T )) and the H c2 (T ) curve are reported. The H irr (T ) line is determined by the 10% criterion of the normal state resistance (R N ) in the R(T ) curve, while the H c2 (T ) line is defined by 90% of R N . In Fig. 2 we show H irr (T ) and H c2 (T ) data of all three samples both in the case of applied field parallel to sample c-axis and to ab-plane (H // ab). It results that the H c2 (T ) slope values evaluated near T c are equal to 3 for sample CRY, to 14 for sample FL and to 6 for sample FC, in good agreement with the literature [5]. Moreover, it is evident the larger field anisotropy of sample CRY with respect to sample FL, while sample FC shows a substantial isotropy. Indeed, the anisotropy factors γ = H / / c2 /H ⊥ c2 evaluated at 0.98 T c (0) are 1.9 for sample CRY, 1.7 for sample FL and 1.3 for sample FC. We found the same anisotropic behavior in the activation energy for vortex motion as a function of the applied field U 0 (H) displayed in Fig. 3. Here, U 0 has been evaluated via the relation U (H, T ) = U 0 (H) g(t) [10], with g(t) = (1 − t) (1 − t 4 ) 1/2 and t = T /T c , where U (H, T ) values have been deduced from the Arrhenius plots of the R(T ) at different applied magnetic fields. The U 0 (H) curve for sample FL shows a crossover from a weak field dependence to a power law dependence in the case H//c, which can be associated to the crossover from a single vortex pinning regime [11] to a collective-pinning one [12], according to the literature [13]. On the contrary, in the case H //ab no crossover is present thus pointing out the higher anisotropic behavior of the pinning properties in the films grown on LaAlO 3 substrates. For sample CRY, the U 0 (H) curves for H //c and H //ab exhibit anisotropy, although in both cases a field dependence crossover is observed. Instead, for sample FC no evident anisotropy can be observed in the U 0 (H) curves, in the full field range. This feature is confirmed by the pinning force f p = F P /F P,max curve as a function of the reduced field h = H/H irr shown in Fig. 4. Here, the H irr values have been evaluated as the extrapolated zero value in the Kramer plots, where J 1/2 c H 1/4 is plotted as a function of H [14], with the critical current density J c defined by the standard 1 µV/cm criterion. In Fig. 4 the f p (h) curves are shown at three different temperatures (8.0, 8.6, 9.3 K) in the case H //c and also at 9.3 K for the case H //ab. All three curves can be fitted by a single  function C h p (1 − h) q with p = 1 and q = 1.3. According to the Dew-Hughes model [15], this behavior can be ascribed to the presence of δT c volume pins, regardless of the temperature.

Conclusions
We have carried out a comparison of the pinning properties of the 11 iron-based compound Fe(Se 1−x Te x ) realized in the form of single crystal and thin films on different substrates. We have shown that the thin films deposited on CaF 2 substrate are characterized by an high isotropy, whereas films deposited on LaAlO 3 and single crystals have a similar anisotropy. Moreover, the pinning sites in the CaF 2 samples have been basically identified having 3D δT c nature.
Considering that for high field applications high H c2 (T ) slope near T c , good in-field isotropy and strong pinning are required, we conclude that Fe(Se 1−x Te x ) films grown on proper substrates are good candidates for further developments in coated conductors.