Upper critical field, lower critical field and critical current density of FeTe0.60Se0.40 single crystal

The transport and magnetic studies are performed on high quality FeTe0.60Se0.40 single crystals to determine the upper critical fields (Hc2), lower critical field (Hc1) and the Critical current density (Jc). The value of upper critical field Hc2 are very large, whereas the activation energy as determined from the slope of the Arrhenius plots are was found to be lower than that in the FeAs122 superconductor. The lower critical field was determined in ab direction and c direction of the crystal, and was found to have a anisotropy of 'gamma'{=(Hc1//c) / (Hc1//b)} ~ 4. The magnetic isotherms measured up to 12 Tesla shows the presence of fishtail behavior. The critical current densities at 1.8K of the single crystal was found to almost same in both ab and c direction as 1X105 Amp/cm2 in low field regime.


Introduction
The discovery of superconductivity in the Fe based oxypnictide compounds has enriched and opened up newer horizons in the field of superconductivity [1]. The tetragonal compounds FeSe and FeTe 1-x Se x have relatively simpler structure than the FeAs based superconductors, where the Fe(Te/Se) layers stack along the c axis, and has transition temperature (T c ) as high as 15K [2,3,4,5,6,7,8,9]. Pressure studies on the FeSe compounds show an increase in the T c up to 36K at 38GPa pressure [2,10,11]. Though the T c in these compounds is much less compared to the FeAs based superconductors, the simplicity of structure and similarity in the Fermi surface make them a potential material to understand the superconducting mechanism in the Fe based oxypnictides. The Fermi surface of the FeS, FeSe and FeTe is very similar to that of FeAs based superconductors, with the cylindrical hole and electron sections at the center and the corner of the brillouin zone respectively [12]. The end member FeTe in the FeTe 1-x Se x series is antiferromagnetic below 65K and shows a simultaneous structural transition [4,5,8,9]. Among the Fe mono-chalcogenide compounds, only FeSe shows superconductivity (T c = 8K), but it is difficult to prepare FeSe in pure form as 1-2% impurity of Fe 7 Se 8 hexagonal phase forms along with the superconducting tetragonal FeSe phase [2,4,6,7,8]. The substitution of Te at the Se site in FeSe increases the T c , showing a maximum close to 40% Se concentration [4,5,9].
In this paper we have estimated the upper critical field (H c2 ), activation energy (U 0 ), lower critical field (H c1 ), and the critical current density (J c ) of a high quality single crystal of FeTe 0.60 Se 0.40 with more than 95% superconducting volume fraction. We have also observed the fishtail behavior in the high field magnetization loop at temperatures below T c for both directions.

Experimental Methods
The single crystal of FeTe 0.60 Se 0.40 compound were prepared by the chemical reaction of the elements (Fe chunk of 99.999% purity, Te powder of 99.99% purity and Se powder of 99.98% purity) in the stochiometric proportion, inside a sealed quartz tube under vacuum. The charge was slowly heated to 950 0 C at the rate 50 0 C/hrs and kept for 12 hours before cooling down to 400 0 C at the rate of 6 0 C/hrs, and then furnace cooled to room temperature for growing the crystals.
The magneto-transport measurements were done using a Quantum Design PPMS (Physical Properties Measurement System). The Specific heat of crystal was measured using relaxation technique in the PPMS. AC susceptibility measurements, and low field DC magnetization was carried out using a SQUID magnetometer and high magnetic field measurements were done using a 12 Tesla Vibrating Sample Magnetometer (Oxford Instruments).

Results and Discussions
The crystals were found to be very shiny, grown along the 'ab' plane, and were very easy to cleave along this plane. The X-Ray Diffraction (XRD) analysis done on the powdered sample, confirmed the compound to be in their single tetragonal phase (space group P4/nmm), with the lattice parameters 'a' = 3.798Ǻ and 'c'= 6.058Å. The compositional analysis by EDAX (Energy Dispersive Absorption X ray Spectroscopy), showed the crystals to be formed in the stochiometric ratio. XRD pattern of the crystal flake shows peaks only at the angles corresponding to the {00l} planes, confirming the orientation of the flakes along the ab plane. To further check the quality of crystal, the TEM (Transmission Electron Microscope) diffraction pattern (shown in the figure 1) was taken, which again confirmed the tetragonal phase and, growth of crystal along the ab-plane. In the Figure 2, we have shown the resistivity data of FeTe 0.60 Se 0.40 single crystals for magnetic field parallel to 'c' and the electrical current in the 'ab' plane. The room temperature resistivity is about 0.9m -cm. It is metallic below about 150K and superconducts with a T c onset of 15.3K (inset of figure  2). At zero magnetic field, the transition width is 0.5K, which is considerably broadened to 2.3K at 14T field. However the T c onset is not affected very much by the magnetic field as reported in the case of cuprate superconductors. Like the two dimensional cuprate superconductors, the FeAs based layered systems are also reported to have very high critical field [13]. In the figure 3, we have plotted the H-T phase diagram for the crystal corresponding to the temperatures where the resistivity drops to the 90% of the normal state resistivity n , (where n is taken at temperature T = 16K), 50% of n and 10 % of n. Since the transition temperature does not shift much towards the low temperatures, it indicates to a very high value of H c2 (0) at zero temperature. The linear extrapolation of the lines on field axis at T = 0K, gave the values of high critical field H c2 (0) as 184T, 88T and 69T corresponding to the transition temperature taken at the point of 90% of n , 50% of n and 10 % of n respectively. Using the Werthamer -Helfand -Hohenberg (WHH) formula

T(K)
T onset T mid T offfset Figure 3. Upper critical field versus temperature phase diagram is shown for the points where electrical resistivity drops to 90% of n , 50% of n and 10% of n , shown by T onset and T mid and T offset . n is the value of resistivity taken in the normal state at 16K. to the H-T phase diagram shown in figure 3, the H c2 (0) were found to be 126T, 65T and 51T corresponding to the points 90% of n , 50% of n and 10 % of n respectively. Using these zero temperature value of H c2 , the corresponding value of 0 H c2 /k B T c comes out to be 8.21T/K, 4.26T/K and 3.30T/K, which are much higher than the Pauli limit for 0 H c2 /k B T c = 1.84T/K in case of singlet pairing and weak spin orbit coupling [13,14]. This indicates toward the unconventional nature of the superconductivity. In order to get a rough idea about the superconducting parameters, we have used the Ginzburg-Landau (GL) formula for the coherence length ( ) , = ( 0 / 2 µ 0 H c2 ) 1/2 , where 0 = 2.07×10 -7 Oe cm 2 , the coherence length at the zero temperature was calculated as 16.2Ǻ, 22Ǻ and 25.5Ǻ for the H c2 at 90% of n , 50% of n and 10% of n respectively.
The Arrhenius plot for the FeTe 0.60 Se 0.40 in the figure 4, shows that the electrical resistivity is thermally activated in the region of resistivity between 2×10 -4 Ω-cm and 2×10 -6 Ω-cm. The activation energy U 0 is determined from the slope of the curve in this linear region using the formula ρ(T, H) = ρ 0 exp( -U 0 /k B T).
The magnetic field versus the activation energy U 0 plot shown in the inset of the figure 4 suggests the different power law dependence on magnetic field U 0 H -, with = 0.10 for 0 < H < 6T and = 0.57 for 6T < H < 14T. Similar kind of power law dependence has also been observed for other superconducting compounds viz. Bi 2 Sr 2 CaCu 2 O 8+ , MgB 2 , SmFeAsO 0.9 F 0.1, and NdFeAsO 0.82 F 0.18 [15,16,17,18]. The activation energy varies linearly from 710K to 1490K for the magnetic field of H = 14T and H = 0T, respectively.   [22]. Using this formula we estimated effective demagnetizing factor N eff ~ 0.79 for our sample of dimension 'a' = 2.2mm and 'b' = 0.25mm. As shown in the figure 5(d), the H c1 values for H //c and H //ab are highly temperature dependent and show upward trend with negative curvature. Similar trend is reported for FeAs based superconductors viz. Ba 0.60 K 0.40 Fe 2 As 2 and SmFeAsO 0.9 F 0.1 also. This has been pointed as not conforming with the single band gap description of the mean field theory, and hence as evidences of two energygaps like the MgB 2 superconductor [23,24,25]. The density functional study of the FeSe and FeTe done by Subedi et.al. showed that the band structure of these copounds consists cyndirical electron fermi surface at the zone corner and two concentric cynderical hole surface a the zone center, indicating that the superconductivity in this system results from two bands [12], and the upward curvature of H c1 is dictated by both electrons and the heavy holes. The H c1 values for our FeTe 0.60 Se 0.40 crystal were found to have an anisotpy ratio ( = (H c1 //c)/(H c1 //ab)) of 2 -4 for temperature range 1.8K < T < 14K. This anisotropy is large compared to that in PrFeAsO 1-y and Sm 0.95 La 0.05 FeAs 0.85 F 0.15 [26,27].  Figure 6(a, b) shows the M-H loop in positive field direction at several temperatures in the magnetic field parallel to ab-plane (H//ab) and parallel to c axis (H//c), which was measured up to 12 Tesla. The magnetization '-M' goes through a first maximum on increasing the magnetic field and shows a second peak before it finally collapses to zero near the upper critical field H c2 . This second maximum is known as fishtail effect in the literature and has also been observed for crystals of LaSrCuO, YBCO, BSCCO and more recenlty in the Ba(Fe 0.93 Co 0.07 ) 2 As 2 single crystals [28,29,30,31]. Though the origin of this behavior is not fully explained yet, one model correlates it to the presence of some weakly superconducting or non superconducting regions which can act as the efficient pinning centers [29,30]. It is also propounded that the crossover from the single to collective flux creep induces a slower magnetic relaxation at the intermediate field and give rise to the second peak [29,30,31]. However the fishtail is strongly dependent on the sample orientation of the externally applied field, and for H parallel to the ab plane this feature get diminished. Using the Bean's model for the field independent critical current density (J c ), it can be calculated by the relation [32,33] where M is M up -M dn and M up and M dn are the magentization while decreasing and increasing magnetic field respectively; a, b are the sample width (a < b). We took sample dimensions as a = 2.2mm , b = 3mm and a = 0.25mm, b =2.2mm for the J c calcualtion for H // ab and H // c respectively. It should be mentioned that though the Bean's model is strictly applicable only in the case of field independent critical current density, since the variation of J c is moderate upto 6T for H//ab (upto 1T for H//c), it serves as a good approximation to the actual value. The critical current density J c obtained for the FeTe 0.60 Se 0.40 single crystal sample for H // ab and H // c are shown in the figure 6(c, d). The value of J c at low field and 1.8K temperature are almost same as 1×10 5 Amp/cm 2 , for both directions. The fishtail feature is also more clearly evident. Our value of J c agrees with the one recent report by Taen et.al. for the crystal of FeTe 0.61 Se 0.39 . [33] However in earlier report for Fe 1+y Te 1-x Se x ; x = 0.133, Rongwei Hu et.al. have reported an anisotropy in critical current density (J c //ab /J c //c ) ~5, in their single crystal with 10% superconducting volume fraction [34]. The current density J c values also compare well with for the Co doped BaFe 2 As 2 supercondcutor [35].

Conlcusions
We have determined the upper critical field (H c2 ), activation energy (U 0 ), lower critical fields (H c1 ) and the critical current density (J c ) of the FeTe 0.60 Se 0.40 single crystal. The H c2 value at T = 0K measured along the ab plane, from the extrapolation of H-T phase diagram and also using WHH formula are found to be very high. The activation energy shows linear dependence with the magnetic field. The H-T phase diagram for H c1 shows a positive curvature and does not saturate till 1.8K. The lower critical field was found to be anisotropic with the anisotropy parameter ( = (H c1 //c )/(H c1 //ab )) ~ 4 at 1.8K. The high field M-H behavior shows the fishtail behavior and is more pronounced for H // c direction. The critical current density J c of the compound is found to be 1×10 5 Amp/cm 2 at low field and 1.8K temperature, and appears to be isotropic in nature.