Critical current density and flux pinning in Zr0.96V0.04B2 superconductor with AlB2 structure

We have investigated the critical current density ( J c ) and the ﬂux pinning behavior in Zr 0.96 V 0.04 B 2 superconductor with an AlB 2 structure. V substitutions in Zr sites of non-superconducting ZrB 2 system lead to superconductivity, and the 4% V-substituted Zr 0.96 V 0.04 B 2 compounds show the highest superconducting transition temperature ( T c ) of (cid:2) 8.7 K. The magnetic hysteresis ( M (cid:3) H ) loops for the Zr 0.96 V 0.04 B 2 demonstrate type-II superconducting behavior in a broad temperature range, and the J c is estimated from the M (cid:3) H loops using the Bean model. The analysis of the double-logarithmic J c ( H ) plots indicates the dominance of collective pinning in Zr 0.96 V 0.04 B 2 , and that J c ( H ) and magnetic ﬁeld dependences of the ﬂux pinning force density ( F p ) are well ﬁtted by the double exponential model which takes into account the existence of two superconducting gaps.


I. INTRODUCTION
The discovery of the superconducting transition at $40 K in MgB 2 has brought about great interest to materials with an AlB 2 structure (space group P6/mmm) because of their potential for having a high superconducting transition temperature (T c ). 1,2 AlB 2 -type metal diborides, such as NbB 2 , ZrB 2 , TaB 2 , and so on, have been extensively studied, and a superconducting transition is observed in nonstoichiometric boride compounds such as MoB 2þx and NbB 2þx . [3][4][5][6][7] In addition, AgB 2 and AuB 2 were predicted to have T c higher than 50 K from the theoretical estimates, 8,9 but recently much lower T c $ 7 K than theoretically predicted was found experimentally in AgB 2 thin films. 10 It should also be noted that, despite a favorable prediction of their high T c , [11][12][13][14] it is difficult to synthesize these materials with an AlB 2 structure.
The presence of superconductivity in stoichiometric diboride compounds of TMB 2 (TM: Nb, Mo, Ta, Zr) is a controversial issue. [15][16][17] On the other hand, boron rich MoB 2þx and NbB 2þx compounds and the Mo or the Nb substituted diboride compounds by other metals, such as (Mo 0.96 Zr 0.04 ) 0.88 B 2 , Mo 1Àx M x B 2.5 and Nb 1Àx M x B 2.5 (M: Sc, Zr, Y, V, Hf, etc.), and so on, clearly show the superconducting behavior with a stable AlB 2 structure. [3][4][5]18 Among them, ZrB 2 is a very interesting material due to similar lattice parameters with MgB 2 and the possibility of the multiband superconductivity. 19,20 However, a well defined superconducting transition was not yet observed in ZrB 2 , and the reported occurrence of superconductivity at 5.5 K in ZrB 2 polycrystals could be attributed to the presence of the dodecaboride ZrB 12 phases as impurities in the samples. 20,21 The ZrB 12 shows a superconductivity below $6 K and has an UB 12 structure. 22 Very recently, we have studied the effect of the V substitution for the Zr site in ZrB 2 compounds and found its favorable effect on T c . Interestingly, a small percent of V substitution on the Zr sites induces superconductivity in a non-superconducting ZrB 2 , and 4% V-substituted Zr 0.96 V 0.04 B 2 compounds show a maximum T c of $8.7 K. 23 Moreover, basic properties of these compounds suggest a multiband behavior, and they have a high upper critical field (H c2 (0)) of $16 T in spite of a low T c , which make these material more interesting for further studies. The critical current density (J c ) is one of the important parameters of superconductor, but the research concerning J c of the ZrB 2 with Zr substituted by V has not yet been carried out. In addition, the study on the J c and flux pinning force for metal diboride superconductor with multigap except for MgB 2 is rarely reported, although they are very important factors for basic properties and real applications in superconductor.
In this paper, we report on the critical current density (J c ) and the flux pinning behavior of a new superconducting compound Zr 0.96 V 0.04 B 2 at various temperatures. The J c is estimated from the magnetic hysteresis (MÀH) loops using Bean's critical state model. We have found that collective pinning is dominant at most temperatures, and the field dependences of the J c and the flux pinning force density are well fitted by the double exponential model consistent with the presence of two superconducting gaps.

II. EXPERIMENTS
The Zr 0.96 V 0.04 B 2 polycrystals with a typical size of 2 Â 3 Â 0.5 mm 3 were synthesized from high purity elements by using a Ti gettered arc furnace under Ar atmosphere. The sample was re-melted five times to improve its homogeneity a) Author to whom correspondence should be addressed. Electronic mail: albino@df.ufpe.br.
of the sample. The details of the fabrication and the basic properties for the Zr 1Àx V x B 2 compounds are described in Ref. 23. X-ray diffraction (XRD) and scanning electron microscopy (SEM) were used for the structural analysis for the Zr 0.96 V 0.04 B 2 samples after polishing to make a flat surface. The superconducting transition was measured resistively by the standard four-probe method and magnetically by a magnetic property measurement system (MPMS, Quantum Design). In order to investigate the critical current density (J c ) and the flux pinning force, the magnetization hysteresis (MÀH) loops were measured by a vibrating sample magnetometer (VSM, Oxford Instruments). Figure 1 presents the Zr 0.96 V 0.04 B 2 XRD pattern, and in the inset SEM image for the polished sample. The XRD data present no diffraction peaks ascribable to impurities, and it is obtained that the lattice constants a-axis and c-axis are a ¼ 3.164 Å and c ¼ 3.524 Å , respectively. The a-axis lattice constant of the Zr 0.96 V 0.04 B 2 is rarely changed compared to ZrB 2 , while the c-axis lattice constant is reduced by $1.7%, 23 which affects the electronic properties and eventually induce superconductivity. The SEM image of the polished Zr 0.96 V 0.04 B 2 sample, shown in the inset in Fig. 1, shows irregular grain sizes with clear grain boundaries. This microstructure could have an influence on flux pinning and critical current density. 24 Figure 2(a) presents a well defined superconducting transition of a new superconducting Zr 0.96 V 0.04 B 2 compound. The temperature dependences of its magnetization (M) were measured in a field of 0.5 Oe. The splitting of zerofield cooling (ZFC) and field cooling (FC) curves was occurred at $8.7 K and the ZFC shows a sharp transition, indicating the presence of bulk superconductivity. The inset of Fig. 2(a) gives the resistance as a function of temperature, which shows the T c at $8.6 K with the transition width (DT c ¼ T c,90% -T c,10% ) of about 0.4 K. The reason of a slightly lower T c compared to T c observed from the M-T curve is probably due to the high applied current of 10 mA for the four-probe method which was needed due to very low resistance of the Zr 0.96 V 0.04 B 2 . Magnetic hysteresis (MÀH) loops were measured by a VSM with applied magnetic fields varying from À5 to 5 T with a sweep rate of 0.2 T/min over broad temperature range, which show obvious type-II superconducting MÀH curves, presented in Fig. 2(b).

III. RESULTS AND DISCUSSION
The critical current density (J c ) for the Zr 0.96 V 0.04 B 2 was estimated from the MÀH loops using the Bean's critical state model with J c ¼ 20DM/[w(1 À w/3b)], where DM is the width of the MÀH loops as indicated in Fig. 2  and b are the dimensions of the sample with w < b. 25,26 The obtained magnetic field dependence of the J c are presented in Fig. 3. The J c (H,T) is much lower than that of MgB 2 , for instance, J c (0) at 1.9 K is $4,000 A/cm 2 for Zr 0.96 V 0.04 B 2 and is $10 6 A/cm 2 for MgB 2 polycrystals. 1,27 The low J c (0) of the Zr 0.96 V 0.04 B 2 is considered to be due to the poor electrically connectivity between the grains. 28 Furthermore, the irreversible regions lie at much lower fields than the upper critical fields, H c2 (T), determined from the electrical transport measurement, 23 which is usually observed in high-T c superconductors or in superconducting samples with weak pinning. [29][30][31] The double-logarithmic plots for the J c (H) shown in the inset of Fig. 3 suggest that the pinning mechanism for the Zr 0.96 V 0.04 B 2 is probably associated with collective pinning, if one takes into account the power law J c (H) / H Àb in the slope regions indicated in Fig. 3 by the solid line. 32 The values of the exponent b in the sloped regions are 0.85 6 0.04.
The exponential decrease in J c (H) has been reported for other superconducting materials, 33,34 and the J c (H) for the new superconducting Zr 0.96 V 0.04 B 2 compound also shows the exponential decrease. The J c (H) curves over wide temperature regions for the Zr 0.96 V 0.04 B 2 can be well explained by using double exponential model associated with the two superconducting gaps, as shown in Fig. 4. This double exponential model is the stretched exponential function from a single exponential model in order to describe the J c (H) behavior of two-gap superconductor of MgB 2 . 35 The solid lines correspond to double exponential formula J c (h) ¼ J 1 exp(ÀA 1 h) þ J 2 exp(ÀA 2 h), where h ( ¼ H/H*) is the reduced field, A 1 and A 2 are constants, and J 1 and J 2 are partial critical current densities corresponding to the large and the small gap, respectively. 33 Temperature dependences of all fitting parameters used in double exponential model are shown in Figs. 5(a) and 5(b). The temperature dependence of A 1 is roughly fitted by (1 À t), indicated by the solid line. On the other hand, as shown in Fig. 5(a), A 2 is temperature independent having a constant value of 4.6 6 0.1 for all temperatures studied. Figure 5(b) shows that J 1 and the J 2 are almost equal and present the same behavior with increasing temperature. Temperature dependence of the J 1 is similar with that of MgB 2 . 35 The inset of Fig. 5(b) presents the curves of each part of double exponential model, J c (h) ¼ J 1 exp(-A 1 h) þ J 2 exp(ÀA 2 h). The decreasing rate of the first parts is largely adjusted by the fitting parameter A 1 and these are merged at the point of h ¼ 0.195 6 0.002, indicates that the small gap is probably to be almost suppressed at h % 0.195. On the other hand, the second parts are slightly separated at h % 1, due to broad non-linear regions at high fields in the Kramer plots. Figure 6 shows the dependence of the normalized flux pinning force density, f p (¼ F p /F p,max ), on the reduced field, h (¼ H/H*), where F p is the flux pinning force density and fitting is quite good for scaling the f p (h) of the Zr 0.96 V 0.04 B 2 , suggesting that two different superconducting gaps are indeed present in the Zr 0.96 V 0.04 B 2 system.

IV. CONCLUSIONS
In conclusion, we have investigated critical current density (J c ) and the flux pinning behavior in the new boride Zr 0.96 V 0.04 B 2 superconductor with an AlB 2 structure. The J c (H) is derived from the magnetic hysteresis (MÀH) loops using Bean model in a broad temperature range, and it shows the dominance of collective pinning leading to the power law of J c (H) / H -b . The J c 's in magnetic field show the exponential decrease, and the J c (H)'s are well fitted by the double exponential model based on the presence of two superconducting gaps. In addition, reduced field dependences of the normalized flux pinning force density (f p ) are also well scaled by the double exponential model in comparison with a generally used model for flux pinning force scaling, such as Kramer model.