Jia-Ming Zhao(趙佳銘) and Zhi-He Wang(王智河)

1School of Physics,Nanjing University,Nanjing 210093,China

2Center for Superconducting Physics and Materials,Collaborative Innovation Center of Advanced Microstructures and National Laboratory of Solid State Microstructures,Nanjing University,Nanjing 210093,China

Keywords: FeSe1-xTex single crystal,anisotropy,resistivity,magnetization

1. Introduction

The discovery of superconductivity at 8 K in FeSe with a PbO-type structure[1]has attracted great interest because of its simple crystal structure. The superconducting transition temperatureTcof FeSe has been enhanced to 14 K through the partial substitution of Te for Se,[2]to 38 K under high hydrostatic pressure[3]and to above 100 K in monolayer thin film.[4]In bulk Fe1+yTe1-xSexcrystals the optimal Te content to achieve the highestTcis considered to bex ≈0.5, and phase separation occurs in the region of 0.1≤x ≤0.4.[5]Although Fe1+yTe1-xSexcrystals have a layered structure, they have an anisotropy smaller than that of cuprate superconductors.[6,7]Maoet al.reported an anisotropy of 2.8 nearTcfor FeSe0.5Te0.5,[8]close to the 2.6 reported by Yadavet al.[9]and 3.17 reported by Daset al.[10]For the applications of superconducting wires/tapes,the anisotropy ofJc, which also reflects its intrinsic crystallographic anisotropy,is an important parameter. The small superconducting anisotropy may facilitate fabrication of a dense superconducting wire/tape with a high critical current density.Therefore,detailed knowledge of the anisotropic properties of iron-based superconductors is important for potential applications.

2. Experimental method

The single crystals of FeSe0.5Te0.5used in this experiment were grown by the self-flux method. Starting materials were powders of Fe (purity 3N), Se (purity 3N) and Te(purity 4N). The powders in the nominal composition were thoroughly mixed in an argon-filled glove box. The mixed powders were sealed in an evacuated quartz tube. The sealed quartz ampoule was placed in a furnace so that single crystals were grown from the bottom of an alumina crucible. The ampoule was heated at 650°C for 24 h and then at 1110°C for 72 h, then cooled down to 420°C at a rate of 6°C/h and kept there for 70 h, followed by quenching in water.The as-grown single crystal with a shiny flat surface is easily cleaved. Recently, Uhriget al.[11]reported the effect of annealing FeSe0.35Te0.65single crystals in different atmospheres on the surface chemistry, the superconducting transition temperatureTcand the critical current densityJc. Their experimental results indicate that the improvement in the superconducting properties is strongly correlated with the formation of a thin iron oxide surface layer. To avoid possible oxidation of the surface layer and uncertain consequences for the intrinsic superconducting properties,we chose unannealed FeSe0.5Te0.5single crystal to study its anisotropy.

The x-ray diffraction (XRD) pattern of FeSe0.5Te0.5single crystal was detected by a standard Cu-anode powder diffractometer (Siemens D5000) at room temperature. The electric transport measurements were performed on a commercial physical properties measurement system (PPMS-9 T,Quantum Design) using a standard four-probe configuration.Gold wires of diameter 0.05 mm were pasted on the sample surface with silver paste. To obtain the resistivity along thec-axis, we used symmetrical current and voltage electrodes on the top and bottom surfaces using indium metal to decrease the contact resistance. The area of the current electrode was larger than that of the voltage electrode to keep the current along thec-axis. The magnetization measurements were also carried out on the PPMS with a vibrating sample magnetometer (VSM). The magnetic field was applied along thec-axis and/or theab-plane. The sample sizes used in transport measurements forI//ab-plane andI//c-axis and magnetization measurements forH//c-axis andH//ab-plane were about 2.8 mm×2 mm×0.4 mm and 2 mm×1.4 mm×0.4 mm,respectively. The smaller sample was cut from the larger size single crystal.

3. Results and discussion

Figure 1 shows the XRD pattern of FeSe0.5Te0.5single crystal tested at room temperature. Compared with the standard card,we see tetragonal symmetryP4/nmmfor the main FeSe0.5Te0.5phase and hexagonal symmetryP63/mmcfor the impurity phase Fe7Se8. This impurity also appears in other papers.[12,13]What is more, the appearance of the(104)peak may come from the twin boundaries.[14,15]The strong (00l)peaks indicate that thec-axis of the crystal is perpendicular to the cleaved surface. The lattice parameters obtained from different peaks were averaged by the Bragg formula, for example,c=0.60165 nm,which agrees with the data from previous papers.[16-18]

Fig.1. XRD pattern for FeSe0.5Te0.5 single crystals.

Fig.2. (a)Temperature dependence of reduced resistance near Tc for I//abplane and I//c-axis. The inset is for temperature from 300 K to 10 K. (b)Temperature dependence of magnetic susceptibility from 15 K to 4 K at 0.01 T for H//c-axis and H//ab-plane. The inset shows enlarged plots in the vicinity of Tc.

The angular dependences of in-plane resistanceRaband out-of-plane resistanceRcmeasured at 13.5 K for several fixed fieldsH0up to 9 T are shown in the inset of Figs.3(a)and 3(b),respectively. AllR(θ)curves show a periodic change. The resistance is maximum at 0°and/or 180°(H//c-axis)and minimum at 90°(H//ab-plane),indicating there is a field-induced anisotropy of resistance. In additionRcis smaller than 1 mΩ and the signal of thermal fluctuation,especially at large angles,is not negligible and results in an unsmooth curve, as seen in inset of Fig. 3(b). Based on the anisotropic G-L theory, an anisotropic material can be transformed into an isotropic material by means of a scaling approach[23]in the following form:

whereγis the anisotropy parameter of the single crystal andθis the angle between the applied magnetic field and thecaxis of the crystal. However,the scaling approach is based on a simple rescaling of the coordinate axes (i.e.,x=x＇,y=y＇,γz=z＇),which is incomplete for a complex system.Therefore,in order to have a reference curve for scaling,we measured the field dependence of resistance at 13.5 K forH//c-axis(empty squares in Fig. 3(a) forI//ab-plane and Fig. 3(b) forI//caxis). For the best value of the anisotropic parameter,R(θ)curves (orR(Heff)) were fitted to the experimentalR(H) to ensure the best possible agreement in a range of angles starting from zero. The best fitting results are plotted in Fig.3(a)for in-plane resistance and in Fig.3(b)for out-of-plane resistance. From Figs.3(a)and 3(b),it is no surprise to see that the best fit lies near 0°and/or 180°(H//c-axis)and meanwhile the biggest deviation fromR(H)is at angles approaching theabplane.The deviant angle appears with increasing applied field,meanwhile the anisotropy parameterγHdecreases with it. The field dependence of the anisotropy parameterγHis shown in Fig.3(c). As seen in the inset of Fig.3(c),the twoγHcurves agree reasonably well with each other and both show a power law behavior,

whereα=0.76 forI//ab-plane andα=0.64 forI//c-axis.This result shows that the anisotropy parameterγin G-L theory is not a constant and depends on the applied magnetic field and the temperature.

Fig.3. (a)Field dependence of resistance at 13.5 K(a)for I//ab-plane and(b)I//c-axis,and the scaled result of R(θ)in the inset. (c)Field dependence of anisotropic parameter for both I//ab-plane and I//c-axis with a double logarithmic plot.

Fig. 4. Temperature dependence of resistance in the vicinity of Tc at several fixed fields: (a) I//ab, H//ab; (b) I//ab, H//c; (c) I//c, H//ab;(d)I//c,H//c.

Figure 4 gives the temperature dependence of in-plane and out-of-plane resistivity measured at several fixed applied magnetic fields up to 9 T forH//ab-plane andH//c-axis,respectively. With increasing field,the low-resistance part of theR(T)curve gets broader towards low temperatures. The fieldinduced broadening forH//cis larger than that forH//ab,indicating that the single crystal has an anisotropic upper critical field. If we define the temperature where the resistance is 10%of the normal state resistanceRnas the critical temperatureTc,the temperature dependence of the upper critical fieldHc2(T)can be obtained as shown in Fig.5(a). AllHc2(T)curves are upward,indicating that they should follow the expression

The relationship betweenHc2and 1-(Tc/Tc0) is plotted in the inset of Fig.5(a)and it is linear with differentn. For current parallel to theabplane,nis 1.23 forH//c-axis and 1.30 forH//ab-plane; while for current parallel to thec-axis,nis 1.36 and 1.25, respectively. From theHc2(T) expression we can get the temperature dependence of the anisotropic upper critical field parameterγHc2=Habc2/Hcc2as shown in Fig.5(b).γHc2increases slightly with decreased temperature, and the anisotropyγHc2forI//ab-plane is bigger than that forI//caxis. This result implies that the anisotropyγHc2relates to the direction of the applied current and the effective flux pinning energy. The electric field along thec-axis may promote the coupling of electrons between superconducting layers and weaken the anisotropy of the sample.

It is well known that theR(T)curve in applied fields nearTccontains the dynamics of magnetic flux motion. In thermally activated flux flow models,the resistivity below 1%ρncan be described by the Arrhenius relation[24]

whereUis the thermally activated energy or effective pinning energy. From Fig. 4, the effective pinning energy can be extracted from the in-planeR(T)data.We transfer theR-Tcurve into a lnρ-1/Tplot. The slope of the lnρ-1/Tcurve is the effective pinning energyU. The field dependence of the effective pinning energyU(H) is depicted in Fig. 5(c). TheUvalues forH//abare much higher than those forH//c, indicating that an intrinsic-like flux pinning originating from the layered structure plays an important role in the single crystal.This result is often reported for high-Tcsuperconductors[25,26]and iron-based superconductors.[27,28]The field dependence of the effective pinning energyU(H)follows with a crossover at about 2 T.In low-field region,theβvalue is 0.17 forH//c-axis and 0.09 forH//ab-plane. In the higherfield region, theβvalue is 0.28 forH//c-axis and 0.29 forH//ab-plane. For the low-field region flux pinning is considered to be dominated by a single magnetic flux line,while for the higher field region collective flux pinning plays an important role.[27]β ≈0.3 implies that the flux lines are collectively pinned by the planar dislocations and columnar defects.[8]In addition,we take the ratioγUofUabtoUcas the anisotropy parameter of effective pinning energy,as shown in the inset of Fig. 5(c).γUincreases quickly forH ＜2 T and then becomes constant forH ＞2 T. This result may support the crossover from single flux pinning to collective flux pinning in the crystal.

Fig.5. (a)Field dependence of the upper critical field Hc2(T)determined by certain criteria of R=10%Rn. The inset is a log-log logarithmic plot. (b)Temperature dependence of Habc2/Hcc2 for I//ab-plane and I//c-axis.(c)Field dependence of the effective pinning energy with I//ab-plane for H//ab-plane and H//c-axis. The inset is the field dependence of the anisotropic effective pinning energy.

Fig. 6. Isothermal magnetization loops at several temperatures from 4 K to 13 K at intervals of 1 K and a sweep rate of 100 Oe·s-1: (a)H//c-axis,(b)H//ab-plane.

Figure 6 shows the isothermal magnetization loops measured at several temperatures from 4 K to 13 K in intervals of 1 K forH//c-axis andH//ab-plane. In order to avoid the influence of the residual magnetic moment,the isothermal magnetization loop from-9 T to 9 T at 14 K is measured as a background magnetization and deducted from the other loops.The isothermal magnetization loops forH//c-axis is different from that forH//ab-plane. TheM(H) curve forH//c-axis has a significant peak,and the peak moves towards a low field as the temperature increases. The peak disappears nearTc. A similar peak effect also exists in FeSe0.5Te0.5single crystal,[10]YBa2Cu3O7-δsingle crystal[29]and Ba0.6K0.4Fe2As2.[30]The peak effect is considered to be related to the transition from an elastic to a plastic deformation regime in the vortex lattice,in which the strong pinning centers exist from correlated disorder such as twin boundaries, planar dislocations and/or columnar defects.[14]However,forH//ab-plane,none of the isothermal

Fig.7. [(a),(b)]The field dependence of critical current density Jca band Jcc,respectively, at several temperatures from 4 K to 13 K.(c)Temperature dependence of critical current density at 0 T for Jca band Jcc. The inset shows the temperature dependence of anisotropic critical current density.

According to the Bean critical state model,[31]the field dependence of critical current densityJc(H) can be obtained from the following equations:

wheremis 1.23 forH//c-axis and 1.11 forH//ab-plane.

Fig. 8. (a) Field dependence of magnetic moments at a sweep rate of 10 Oe·s-1. (b) Temperature dependence of the dip field for H//c-axis and H//ab-plane.The inset shows the temperature dependence of the anisotropic dip field. (c)The magnetic penetration depth and coherence length resulting from (b) and Fig. 5(a). The inset shows the temperature dependence of the anisotropic parameter of penetration depth and coherence length.

The magnetic penetration depthλand coherence lengthξare important parameters for superconductors. They are estimated from the following basic relations:[33]

For the FeSe0.5Te0.5single crystal, the temperature dependences of the magnetic penetration depth (λabandλc) and the coherence length (ξabandξc) are obtained from theHabc2,Hcc2,Habc1, andHcc1shown in Figs.5(a)and 8(b), and given in Fig. 8(c). From Fig. 8(c),λabis larger thanλc. This result shows that the flux lines forH//c-axis enter more easily into the sample than those forH//ab-plane.This is consistent with our above result originating from the layered structure. Meanwhile,ξabis larger thanξc,indicating that the coupling of superconducting electrons in theab-plane is stronger than along thec-axis. This is consistent with the anisotropic critical current density. Extrapolating toT=0 K,we haveλab=74 nm,ξab(0)=1.9 nm,λc=78 nm andξc(0)=0.64 nm. The extrapolated coherence lengthξab(0)is close to that reported in the literature,[34]but the penetration depth is an order of magnitude smaller than previously reported,[6]which is ascribed to our larger dip fieldHdipthanHc1that deviates from the linearM(H). Furthermore, the anisotropy of penetration depth and coherence length,γλandγξ,is shown in the inset of Fig.8(c).They decrease monotonously with decreasing temperature.

4. Conclusion

By combining measurements of electric transport forI//ab-plane andI//c-axis and magnetization forH//c-axis andH//ab-plane we obtain detailed anisotropic superconducting properties of FeSe0.5Te0.5single crystal. The in-plane resistivity shows a metallic-like temperature dependence,while the out-of-plane resistivity shows a broad hump with a maximum at around 64 K.The scaling ofR(θ)gives a field-induced anisotropic parameter. The electric transport measurements imply that the anisotropy of the upper critical fieldγHc2may relate to the direction of the applied current and the effective flux pinning energy. The magnetization measurement shows an anisotropic critical current density. Decreasing temperature can enhance the critical current density and suppress the coupling between the superconducting FeSe(Te) layers. The coherence length and penetration depth estimated by the GL theory are consistent with the electric transport and magnetization data. The anisotropic superconducting properties are related to its layered structure.

Acknowledgments

The authors acknowledge National Laboratory for Solid State Microstructures and Center for Superconductivity Physics and Materials, Nanjing University for sample preparation and physical property measurements.

Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300401)and the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB25000000).