Study of the second magnetization peak and the pinning behaviour in Ba(Fe 0.935 Co 0.065 ) 2 As$_2
Shyam Sundar, J. Mosqueira, A. D. Alvarenga, D. Sóñora, A. S. Sefat, S. Salem-Sugui Jr
aa r X i v : . [ c ond - m a t . s up r- c on ] J a n Study of the second magnetization peak and thepinning behaviour in Ba(Fe . Co . ) As pnictidesuperconductor Shyam Sundar , J. Mosqueira , A. D. Alvarenga , D. S´o˜nora ,A. S. Sefat and S. Salem-Sugui Jr. Instituto de Fisica, Universidade Federal do Rio de Janeiro, 21941-972 Rio deJaneiro, RJ, Brazil LBTS, Dept. Fisica de Particulas, Universidade de Santiago de Compostela,E-15782, Spain Instituto Nacional de Metrologia Normalizac˜ao e Qualidade Industrial, 25250-020Duque de Caxias, RJ, Brazil Oak Ridge National Laboratory, Oak Ridge, TN 37831, USAE-mail: [email protected]
August 2017
Abstract.
Isothermal magnetic field dependence of magnetization and the magneticrelaxation measurements were performed for H k c axis on single crystal ofBa(Fe . Co . ) As pnictide superconductor having T c = 21.7 K. The secondmagnetization peak (SMP) for each isothermal M ( H ) was observed in a widetemperature range from T c to the lowest temperature of measurement (2 K). Magneticfield dependence of relaxation rate R ( H ), shows a peak (H spt ) between H on (onset ofSMP in M ( H )) and H p (peak field of SMP in M ( H )), which is likely to be relatedwith a vortex-lattice structural phase transition, as suggested in literature for similarsample. In addition, the magnetic relaxation measured for magnetic fields near H spt show some noise which might be the signature of the structural phase transition of thevortex lattice. Analysis of the magnetic relaxation data using Maley’s criterion andthe collective pinning theory suggests that the second magnetization peak (SMP) inthe sample is due to the collective (elastic) to plastic creep crossover, which is alsoaccompanied with a rhombic to square vortex lattice phase transition. Analysis of thepinning force density suggests single dominating pinning mechanism in the sample andis not showing the usual δ l and δT c nature of pinning. The critical current density ( J c )estimated using the Bean’s critical state model is found to be 5 × A/cm at 2 K inthe zero magnetic field limit. Surprisingly, the maximum in the pinning force densityis not responsible for the maximum value of the critical current density in the sample. Keywords : Iron-based superconductors, Single crystal, Second magnetization peak,Magnetic relaxation, critical current density, unconventional pinning. tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor
1. Introduction
Superconductivity in iron-based superconductors (IBS) was discovered in 2008 and soonafter it has been realized that the vortex dynamics in this class of superconductors is ofgreat importance due to their moderately high superconducting transition temperature( T c ) [1], high upper critical field ( H c ) [2, 3], smaller anisotropy than cuprates [4, 5],high intergrain connectivity [6, 7] and low Ginzburg number ( G i ) [8]. These salientfeatures of IBS make them suitable for technological applications [9, 10, 11, 12, 13]and hence intensive research is still going on to study the vortex dynamics in thesesystems [8]. In past years, a few pnictide superconductors have been recognized aspotential materials for high field applications such as Co and K-doped BaFe As (Ba-122) pnictide superconductors [7, 14, 15, 16]. Beside the technological interest, thevortex dynamics in the pnictide superconductors is also very interesting because of thedifferent phases that exist in the vortex phase diagram. Among these different phases,the second magnetization peak (SMP), also known as the fish-tail effect, has been widelystudied in different systems and is still a topic of intense research [10, 17]. The SMP insuperconductors is observed in the isothermal M ( H ) below T c , and is associated witha peak in the magnetic field ( H ) dependence of the critical current density ( J c ). In theliterature, the SMP behaviour in different superconductors is explained in terms of anorder-disorder transition [18, 19], elastic to plastic creep crossover [10, 20], vortex latticephase transition [21, 22] and is still under investigation for a few compounds [23, 24].The superconductivity in Co-doped Ba-122 was observed by Sefat et. al [25]just after the discovery of iron based superconductors [26]. Later, Prozorov et.al. [27] constructed the vortex-phase diagram and observed the SMP behaviourin Ba(Fe . Co . ) As , which is described in terms of crossover from collective toplastic creep [27, 28]. Further, Kopeliansky et. al. [21] suggested that the SMP inBa(Fe . Co . ) As is associated with a vortex lattice structural phase transition.However, they also argued that a crossover in the pinning mechanism (collective toplastic) may also be accompanied with the vortex lattice structural phase transition asit has also been observed in LaSCO superconductor [29]. In the literature, a varietyof superconductors such as LiFeAs [22], ErNi B C [30], YNi B C, LuNi B C [31],YBa Cu O [32], CeCoIn [33] and Sr RuO [34] show a structural phase transitionin the vortex lattice. These studies motivated us to choose a Ba(Fe, Co) As samplewith a Co-content similar to those used by Prozorov et. al. [27] and Kopelianskyet. al. [21] to investigate whether a clear signature of pinning crossover (collective toplastic) exists within the vortex lattice structural phase transition picture. Hence, weperformed a detailed study of isothermal M ( H ) and magnetic relaxations M ( t ) for H k caxis in Ba(Fe . Co . ) As pnictide superconductor (similar composition as used byProzorov et. al. [27] and Kopeliansky et. al. [21]) below T c and analyzed the data usingMaley’s analysis [35] and collective pinning theory [36]. Our results clearly suggest thatthe SMP in this compound is associated with the crossover in the creep mechanism(collective to plastic) which is likely to occur above a rhombic to tetragonal vortex tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor J c using Bean’scritical state model [37] and compared it with other studies. The pinning force densityis also analyzed using models developed by Dew-Hughes [38] and Griessen et. al. [39].
2. Experimental Details
In the present work, we performed a detailed study on Ba(Fe . Co . ) As singlecrystal to understand the nature of SMP and pinning behaviour in the sample. Thesingle crystal was synthesized using a flux method described in previous reports[25, 40, 41]. The chemical doping of the single crystal was checked by energy-dispersiveX-ray spectroscopy, and confirmed through the refinement of lattice parameters withX-ray diffraction. The sample used in the study is a 3.168 mg platelet with a surfaceof 6.84 mm . These parameters (together with the density resulting from the latticeparameter [42]) were used to estimate the average thickness of the sample as ∼ µ m.Through microscopic inspection, it is found that the crystal surface is somewhat irregularand uniformity of the thickness may be estimated within ∼
10% accuracy. Themeasurements were performed with a Quantum Design’s squid-based magnetometer(model MPMS-XL). The sample was installed in a quartz sample holder with the Fe-Aslayers perpendicular to the applied magnetic field. The hysteresis cycles were performedafter zero-field cooling (ZFC) the sample to the target temperature, and then chargingthe magnetic field with the so-called hysteresis (non persistent) mode. The magneticrelaxation measurements were also performed after ZFC to the desired temperature,and then charging the successive magnetic fields with the hysteresis mode. For eachmagnetic field the data were collected during ∼
80 min while the field was held stablein the non-persistent mode.
3. Results and Discussion
Figure 1a shows the isothermal magnetic field dependence of the magnetization, M ( H ),for selected temperatures well below T c . The measured isothermal M ( H ) show the welldefined second magnetization peak (SMP) at all temperatures from near T c to the lowesttemperature of our measurement (2K). However, in few superconductors, the SMP existsonly in a limited temperature range below T c [17, 43, 44]. Fig. 1b shows the temperaturedependence of zfc magnetization, M ( T ), measured with a 3 Oe magnetic field showingthe onset of superconducting transition at 21.7 K. The characteristic fields H on , H p and H irr are well defined in Fig.1c. Magnetic relaxation measurement is a widely usedtechnique to examine the characteristics of SMP [10, 17, 20, 23]. Similarly, we performedmagnetic relaxation, M ( t ), measurements on selected isothermal M ( H ), for about 80minutes to study the SMP in present sample. The observed magnetic relaxation showsthe usual logarithmic time dependence, ln | M | ∼ ln t and the relaxation rate ( R =dln | M | /dln t ), was obtained using the plot of ln | M | vs. ln t .Figure 2a shows the H dependence of relaxation rate ( R ) at different temperatures. tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor
15 18 21 24-0.6-0.30.0 0 10 20 30 40-14-70714
Ba(Fe Co ) As M ( e m u / g ) H (k Oe) 2 K 5 K 7 K 11 K 13 K 16 K 19 K (a) M ( e m u / g ) T (K)zfc dataH = 3 Oe T c = 21.7 K (b) M ( e m u / g ) H (k Oe) T = 19 KH irr H p H on (c) Figure 1. (a) Isothermal magnetic field dependence of the magnetization, M ( H ),at selected temperatures well below T c . (b) Temperature dependence of zfcmagnetization, M ( T ), at H = 3 Oe, showing the onset of superconducting transitionat 21.7 K. (c) The characteristic fields H on , H p and H irr are well defined for M ( H )measured at T = 19 K. -5 -5 -5 R = d l n M / d l n t H (kOe) 15 K 16 K 19 K (a) p = - . p - . . U * = T / R ( K ) A -1 ) 22 kOe 32 kOe
13 K11 K . (b) Figure 2. (a) Magnetic field dependence of relaxation rate, R = dlnM/dlnt , atconstant temperatures. Each curve shows a peak behaviour in R ( H ). (b) Inversecurrent density (1 /J ) dependence of activation energy ( U ∗ ) measured for differentisothermals. In each isothermal R ( H ) curve, the absolute value of R decreases initially then increasesfor higher fields and shows a peak at intermediate fields. This peak in each isothermal tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor R ( H ) suggests some correspondence with the respective M ( H ) and is lying in the peakeffect region ( H on < H < H p ), which is discussed further. we have also obtained thetemperature dependence of the relaxation rate and plot the corresponding activationenergy, U ∗ = T /R , as a function of the inverse current density 1 /J ( J is obtained usingBean’s model). These methods has already been exploited previously to examine thevortex dynamics in different pnictide superconductors [10, 17, 20, 45]. The relationbetween J and the activation energy U ∗ is defined as U ∗ = U ( J c /J ) µ , where µ and J c (critical current density) depend on the dimensionality and size of the vortex bundlesunder consideration [36]. The exponent µ may be extracted using the double logarithmicplot of U ∗ vs. 1 /J , which is shown in Fig. 2b. In the present case, the µ values are foundto be about 2.3 and 4.4 for 22 kOe and 32 kOe respectively. However, for 3D systems, µ values were predicted to be 1/7, 3/2, 7/9 for single-vortex, small-bundle, and large-bundle regimes, respectively [36, 46]. Further, the exponent for higher temperaturesside is estimated to be about -2, which is also different from the predicted value ( p =-1/2) for plastic creep mechanism [47]. In-spite of the difference between the obtainedand the predicted exponents, the U ∗ vs. 1 /J curves for both fields suggest a crossoverin the pinning mechanism. However, in our recent study [17], it has been suggestedthat the above method must be used with caution to study the SMP behaviour insuperconductors. Co ) As H ( k O e ) T (K) H on H p H irr H spt Figure 3. H - T phase diagram for the sample used in the present study. In Fig. 3, the H - T phase diagram shows the different characteristic fields, H on , H p , H irr and H spt , associated with the SMP, the irreversibility line, and the peak in R vs. H .It is shown that both H on and H p exist well below the H irr line in the whole temperaturerange below T c . It should be noted that the H spt line falls between H on and H p as hasbeen previously observed by Kopeliansky et al. [21] for Ba(Fe . Co . ) As . Similar tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor − x Sr x CuO system [29], Kopeliansky et al. [21] explained the observed H spt line in terms of a vortex-lattice structural phase transition, from a rhombic to squarelattice, caused by the softening of the vortex lattice. Recently, similar vortex latticestructural phase transition (rhombic to square) was also suggested in BaFe2(As . P . ) superconductor by Salem-Sugui et. al. [48]. It suggests that the H spt line in the presentcase might also be associated with a similar vortex-lattice structural phase transitionand such phase transition may be accompanied with a crossover from elastic to plasticcreep. However, no direct evidence has been observed to support the claim made byKopeliansky et al. [21] and Salem-Sugui et. al. [48]. In addition, vortex imaging studiesrevealed highly disordered (no long range order) vortex-lattice configuration in differentCo-doped BaFe As [49, 50] and other pnictide superconductors [51], which makes itdifficult to observe a clear signature of structural phase transition. M ( e m u / g ) ln(t) T = 16 K(a) R = d l n M / d l n t H (kOe) (b)T = 16 KH on H p Figure 4. (a) Magnetic relaxation at T = 16 K measured under different magneticfields. The circle shows the noise observed for magnetic fields near the peak in R ( H )for the same temperature. (b) Magnetic field dependence of the relaxation rate for T= 16K. Figure 4a shows the isothermal magnetic relaxation data at T = 16 K measured fordifferent magnetic fields, and Fig.4b shows R ( H ) for T = 16 K. It is interesting to observethat the magnetic relaxation data is quite smooth for low magnetic fields but show anoisy behavior as the field approaches the peak in R ( H ) for the same temperature. Asimilar behaviour has also been observed in the magnetic relaxation data measured atother temperatures as well (not shown). Since the peak in R ( H ) (between H on and H p )suggests a vortex lattice structural phase-transition, the noise in the experimental data(Fig. 4) may have the same origin. However, such explanation must be taken withcaution, since the vortex lattice does not show long range order in such compounds[49, 50, 51]. Another interesting observation (shown in Fig. 5) is that the onset of tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor on ) in measured isothermal M ( H ) is quite sharp, which has not beenobserved before. It has also been noticed that R ( H ) changes its slope in the vicinity ofH on . This may be explained in terms of the pinning crossover which renders a peak in M ( H ), as has been also discussed in our recent study [17]. M ( e m u / g ) H (kOe) -6-4-2 10 -2 RT = 13 K (a) H on -2 R M ( e m u / g ) H (kOe)T = 15 K (b) H on -6-4-20 Figure 5.
Isothermal magnetic field dependence of magnetization and relaxation ratefor T = 13 K and 15 K. In both panels, vertical arrows show a sharp peak in H on andthe associated change of slope in the magnetic relaxation rate ( R ). To study such a possible pinning crossover, we obtained the activation energy ( U )as a function of magnetic moment ( M ) from the M ( t ) data, by using the approachdeveloped by Maley’s et. al. [35] and later exploited in many recent studies [17, 10, 20]. U = − T ln [ dM ( t ) /dt ] + CT, (1)where C is a constant depending on the hoping distance of the vortex, the attemptfrequency and the sample size. The inset of Fig. 6, shows U ( M ) for H = 6 kOe in thetemperature range from 9 K to 17 K (in the SMP region, see the H - T phase diagram).For each temperature, the activation energy was obtained by using C = 15, which iscommensurate with the values presented in the literature [52]. As it is observed that theinset of Fig. 6 do not shows the smooth behaviour of U vs. M curve. Hence, to obtainthe smooth curve of U ( M ), we scaled U with the function g ( T /T c ) = (1 − T /T c ) . ,as suggested by McHenry et. al. [52]. The main panel of Fig. 6, shows the smoothcurve of U ( M ) after scaling and follow the power law behaviour. In this analysis, bestsmooth curve of U ( M ) was used for C = 15, which is further exploited to estimate theactivation energy from the different M ( t ) curves measured in different magnetic fieldregimes ( H < H on , H on < H < H p and H > H p ) at T = 15 K.To study the creep mechanism above, below, and in the intermediate field regimeof SMP, we plotted the U ( M ) curves in the inset of each panel of Fig. 7 for magnetic tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor
15 20 25 30 35 40 451234
20 30 40200300400 U / ( - T / T c ) . M (emu/g)
C = 15
U M -2.2
16 K17 K 15 K 13 K 11 K 9 K U = U * + C T M (emu/g)H = 6 kOe Ba(Fe Co ) As Figure 6.
Activation energy U ( M ) after scaling with the function g ( T /T c ) =(1 − T /T c ) . for H = 6 kOe. Inset: U ( M ) before scaling. fields H < H on , H > H p and H on < H < H p at T = 15 K. The activation energyshown in each inset of Fig. 7 is analysed using the collective creep theory [36, 47],in which, U ( B, J ) = B ν J − µ ≈ H ν M − µ , where the critical exponents ν and µ dependon the specific pinning regime. It has been shown that the activation energy increases(decreases) with magnetic field for collective (plastic) creep [47]. Hence, the expressionfor U ( B, J ), mentioned above, suggests a positive (negative) value of exponent ν forcollective (plastic) creep. Each panel of Fig. 7 shows the smooth behaviour of U ( M )after scaling with different values of ν . It is interesting to observe that each smoothcurve of U ( M ) follows a power law. The scaling of the U ( M ) curves with H , clearlysuggests the collective creep nature in the regime H on < H < H p (Fig 7c), which changesto plastic creep above H p (Fig 7b). This result unambiguously demonstrate that theSMP in the present case is due to a crossover in the creep mechanism from collectiveto plastic. The scaling of U ( M ) in Fig. 7a, suggests the plastic nature of creep for H < H on . However, similar behaviour of scaling below H on has also been observed inmany studies which explained this behaviour in terms of single vortex pinning (SVP)[17]. The change of SVP to collective creep above H > H on also shows a peak at H on in M ( H ) which is quite different than the SMP observed at H p .A similar, elastic (collective) to plastic creep crossover has been also reportedto explain the SMP in other pnictide superconductors of the 122 family, such as K-doped BaFe As [17, 20], Na-doped BaFe As [53]. However, such pinning crossoveris also observed through magnetic relaxation measurements in Ca . Na . Fe As x Fe x )OHFeSe, thatdo not show the SMP [55]. Also, some superconductors of the 122 family, such as tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor − x Co x ) As (x= 0.056) does not show the SMP [56]and its vortex dynamics isdescribed in terms of plastic creep theory. The reason for SMP in Ni-doped BaFe As
122 superconductor is still under investigation [23, 24].
24 28 32 36253035404516 18 20 22 24
18 21 24280320
20 24 28 320.10.20.30.4
20 24 28 32280320360 24 27 30 33280320 U * H . ( K O e . ) M (emu/g)
H > HpT = 15 K
35 kOe32 kOe 29 kOe 26 kOe M -1.3 (b) U * H . ( K O e . ) M (emu/g)
H < HonT = 15 K (a) U ( K ) M (emu/g) . k O e . k O e U * H - . ( K O e - . ) M (emu/g)
Hon < H < HpT = 15 KM -2.2
10 kOe13 kOe16 kOe19 kOe (c) U ( K ) M (emu/g) . k O e k O e M (emu/g) k O e k O e U ( K ) Figure 7.
Insets of each panel shows the U ( M ) obtained through M ( t ) measured at T = 15 K, in presence of different magnetic fields. The main panels show the U ( M )curve scaled according to the collective creep theory. Figure 8a shows the H dependence of the critical current density ( J c ( H )) atdifferent temperatures as estimated using the Bean’s critical state model [37] through J c ( A/cm ) = 20∆ M/a (1 − a/ b ), where ∆ M (emu/cm ) is the difference in the field-increasing and field-decreasing branches of isothermal M ( H ), and a , b are the dimensions(cm) of the sample perpendicular to the magnetic field. The J c value at T = 2 K in thezero magnetic field limit is about 5 × A/cm . A similar value of J c has also beenobserved for the Ba(Fe . Co . ) As and Ba(Fe . Co . ) As single crystals at T = 5K in the zero magnetic field limit [27, 57]. This J c value is of same order of magnitudeas for K-doped BaFe As superconductors [17, 58] and may be exploited for futuretechnological purpose. However, in thin films of Co-doped BaFe As superconductors,the observed J c value is more than 10 A/cm at T = 4.2 K [6, 15, 59]. Recently,high J c was reported in P-doped BaFe As thin film [60]. In the literature, pnictidesuperconductors of the 122 family are considered as the most promising for practicalusage [61]. Fig. 8b shows J c ( T ) /J c (0) in zero magnetic field as a function of the reducedtemperature ( T /T c ) to explore the pinning mechanism using the model proposed byGriessen et. al [39]. It clearly shows that at low temperatures the pinning does not followthe δl ( J c ( t ) /J c (0) = (1 − t ) / (1 + t ) − / ) and δT c ( J c ( t ) /J c (0) = (1 − t ) / (1 + t ) / )models. A similar pinning behaviour has already been observed in our previous studyon Ba . K . Fe As single crystal [17] and in many other pnictide superconductors of122 family, which is argued in terms of unconventional intrinsic pinning [62]. However, tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor J c ( T ) /J c (0) curve shows its resemblance with the δ l pinningbehaviour, which suggests that at high temperature (below T c ) the pinning is related tothe spatial variations of the charge carrier mean free path. A detailed description aboutthe δ l and δT c pinning in high T c superconductors is provided in Ref. [63]. J c ( A / c m ) H (kOe) (a) J c ( T ) / J c ( ) T/T c T c lH = 0 (b) Figure 8. (a) H dependence of J c for different temperatures, as follows from Bean’scritical state model. (b) Reduced temperature ( T /T c ) dependence of J c ( T ) /J c (0) inzero applied magnetic field. The lines correspond to the indicated pinning models. To further explore the pinning mechanism in the sample, J c and the normalizedpinning force density F p /F p − max are plotted as a function of the reduced magnetic field( h = H/H irr ) in Fig. 9 a,b respectively. It is commonly considered and has also beenseen by Fang et. al. [64] that the maximum in F p is responsible for the maximum in J c (or SMP). However, in the present case, it is interesting that the maximum in J c (Fig.9a) lies at about h = 0.35, whereas, the maximum in F p (Fig. 9b) is found at h = 0.5. Itsuggests that the maximum in J c or the SMP in the sample is not directly related withthe maximum in the pinning force density. This important issue needs to be sort out infuture investigations. The normalized pinning force curves ( F p /F p − max ) vs. h shown inFig. 9 b has been analysed using the pinning model suggested by Dew-Hughes [38], inwhich, the normalized pinning force density may follow a general mathematical form, F p /F p − max = Ah p (1 − h ) q , where, A is multiplicative factor, F p − max , is the maximumpinning force density at constant temperature and the parameters p and q provide thedetails about the pinning mechanism [65]. The above expression leads to a single peakbehaviour in the case of single dominating pinning mechanism. In the present case,the functional form of the fitted function is found as F p /F p − max = 12 . h . (1 − h ) . ,which is shown in Fig. 9b. It should be noted that the data show a good scaling with h and a single peak behaviour at h = 0.5, which suggests a single dominating pinningmechanism in the sample. As suggested by Dew-Hughes [38] the peak at h = 0.5 of the tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor κ -type pinning, however, for such pinning toexist, p and q parameters should be equal to 1. J c ( A / c m ) h = H/H irr
15 K 16 K 17 K 18 K 19 K h = 0.35(a) F p / F p m a x h = H/H irr
15 K 16 K 17 K 18 K 19 K 20 K p/(p+q) 0.5 (b)
Figure 9. (a) Critical current density ( J c ) as a function of the reduced field ( h ) atdifferent temperatures (15 K ≤ T < T c ). The maximum in each curve is shown at h = 0.35. (b) Normalized pinning force density ( F p /F p − max ) as a function of reducedmagnetic field ( h ) at different constant temperatures. The data for all temperaturescollapse in one single curve and showing a maximum at h = 0.5. The solid red line isthe best fit of the Dew-Hughes model (see main text for details).
4. Conclusion
A detailed study of isothermal magnetic field dependence of the magnetization, M ( H ), and the magnetic relaxation, M ( t ), on a Ba(Fe . Co . ) As single crystalis presented. Below T c (= 21.7 K), the isothermal M ( H ) shows the clear signatureof the second magnetization peak (SMP) with a sharp H on . The field dependence ofthe relaxation rate R measured for different isothermals shows a peak (H spt ) betweenH on and H p . In the literature, the peak in R ( H ) is related to a rhombic to sqaurevortex-lattice structural phase transition. The magnetic relaxation data measured formagnetic fields near H spt shows a noisy behavior, which might be related to suchphase transition. However, literature suggests that the vortex lattice in Co-dopedBaFe As superconductors is highly disordered in nature and masks the observationof the structural phase transition. More direct evidences are required in future studiesto observe such phase transition in Ba(Fe, Co) As superconductors. The magneticrelaxation data is used to obtain the activation energy ( U ) and is analysed using theMaley’s method and collective pinning theory. The analysis convincingly shows that theSMP is due to the collective (elastic) to plastic creep crossover which accompanies the tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor H p . The pinning properties in the sample areexplored using the models developed by Dew-Hughes and Griessen et. al. It suggestsa single dominating pinning mechanism which is different than the conventional δ l and δT c pinning behaviours. The critical current density ( J c ) is estimated using the Bean’scritical state model and found to be about 5 × A/cm at T = 2 K in the zeromagnetic field limit, which is comparable to other Co-doped pnictide superconductors.Interestingly, the maximum critical current density in the sample is not directly relatedto the maximum in the pinning force density ( F p ). Acknowledgements
SS acknowledges a fellowship from FAPERJ (Rio de Janeiro, Brazil), processo: E-26/202.848/2016, and also would like to thank Prof. Luis Ghivelder for his constantsupport & encouragement during the work. JM and DS acknowledge financial supportfrom project FIS2016-79109-P (AEI/FEDER, UE), and from the Xunta de Galicia(project AGRUP 2015/11). SSS and ADA acknowledges support from CNPq. Thework at Oak Ridge National Laboratory was supported by the U.S. Department ofEnergy (DOE), Office of Science, Basic Energy Sciences (BES), Materials Science andEngineering Division.
References [1] Ren Z A, Lu W, Yang J, Yi W, Shen X L, Li Z C, Che G C, Dong X L, Sun L L, Zhou F andZhao Z X 2008
Chin. Phys. Lett. Phys. Rev. B Phys. Rev. B Nature(London, United Kingdom)
Phys. Rev. B Nat. Commun. Nature Mater. Nature Materials Supercond. Sci. Technol. Sci. Rep. Physics Procedia Supercond. Sci. Technol. Sci. Rep. Appl. Phys. Expr. Appl. Phys. Lett. tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor [16] Togano K, Matsumoto A and Kumakura H 2012 Solid State Commun.
Phys. Rev. B Supercond. Sci. Technol. Supercond. Sci. Technol. Phys. Rev. B Phys. Rev. B Phys. Rev. B Supercond. Sci.Technol. Phys. Rev. B Phys. Rev. Lett.
J. Am. Chem. Soc.
Phys. Rev. B Phys. Rev. B Phys. Rev.B Phys.Rev. Lett. Phys. Rev. Lett. Phys. Rev. Lett. Phys. Rev.Lett. Phys. Rev. B Phys. Rev. B Phys. Rev. Lett. Rev. Mod. Phys. Philos. Mag. Phys. Rev. Lett. PhysicaC: Superconductivity
Current Opinion in Solid State & Materials Science Phys. Rev. B Physica C
Phys. Rev. B Phys. Rev. B Physica C
Phys. Rev. Lett. tudy of the second magnetization peak and the pinning behaviour in Ba(Fe . Co . ) As pnictide superconductor [48] Salem-Sugui Jr S, Mosqueira J, Alvarenga A D, Sora D, Herculano E P, Hu D, Chen G and LuoH 2015 Supercond. Sci. Technol. Physica C
Phys. Rev.Lett.
JETP Letters Phys.Rev. B J. Phys.:Condens. Matter Phys. Rev. B Supercond. Sci. Technol. Phs. Rev. B J. Phys. Soc. Jpn. Sci. Rep. Appl. Phys. Express ApplPhys. Lett.
Supercond. Sci. Technol. Physics Procedia Supercond. Sci. Technol. Phys. Rev. B Int. J. of Mod. Phys. B30