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Anomalous local magnetic field distribution and strong pinning in CaFe1.94Co0.06As2 single crystals

Magneto-optical imaging of a single crystal of CaFe1.94Co0.06As2, shows anomalous remnant magnetization within Meissner like regions of the superconductor. The unconventional shape of the local magnetization hysteresis loop suggests admixture of superconducting and magnetic fractions governing the response. Near the superconducting transition temperature, local magnetic field exceeds the applied field resulting in a diamagnetic to positive magnetization transformation. The observed anomalies in the local magnetic field distribution are accompanied with enhanced bulk pinning in the CaFe1.94Co0.06As2 single crystals. We propose our results suggest a coexistence of superconductivity and magnetic correlations.

crystals, their quality, x-ray diffraction measurements confirming the tetragonal structure and bulk characterization of the sample via specific heat, transport and dc magnetization measurements of the single crystals have been presented elsewhere (Neeraj Kumar et al., ref. [9]). Spatial homogeneity of stoichiometry in the single crystals on local and macroscopic length scales has been verified via EPMA and spot EDX given in section II of supplementary information at ref. [14]. We use high-sensitivity MOI technique [13,14] for imaging the local magnetic field distribution across the sample surface, viz., B z (x,y) (z-component is perpendicular to the abplane (surface) of the single crystal), and the externalmagnetic field (H) is applied parallel to the crystallographic caxis. Prior to performing MOI, the sample was freshly cleaved to obtain a flat surface. Note that due to relatively long acquisition times (~ few tens of seconds) the present MOI technique is not sensitive to time-varying magnetization response. where the mean is computed by averaging B z (x,y) distribution over an area of just ~100 μm 2 region (10 μm × 10 μm) in the sample). The portions of the image with grayish contrast (e.g. just above the yellow dashed circle in fig. 1(a)) possess nonzero z B , due to vortex penetration in these regions of the sample. With increasing H the grayish regions turn brighter. In fig. 1 fig.1(a)) in the MO image suggests the persistence of Meissner like regions which shield the external H up to 90 Oe in the sample. Thus locally H = 90 Oe is less than the lower critical (or penetration) field of the superconductor. In the images of the lower panel (figs. 1(d)-1(f)), as H is reduced from 90 Oe, the Meissner like shielded regions (dark contrast) instead of maintaining their dark contrast down to 0 Oe, appear to progressively become brighter. Note in fig. 1(f) that at 0 Oe on the reverse run, there is a significant brightening indicative of remnant flux present within the Meissner like region when H is reversed from 90 Oe, a field value which is below the local lower critical field for the dark region. A Meissner phase being a perfectly diamagnetic state with zero flux cannot possess any remnant flux when H is cycled back to zero from below the lower critical field of that region. (The line-like light-gray features running diagonally across the image in fig. 1(f) are defects on the magneto-optical indicator placed on the sample for imaging).
The unusual observation in fig.1 is investigated and confirmed further by calculating the local field distribution (B z (x)) along the dashed line (drawn in fig. 1(c)) in figs. 2(a) and 2(b) at different H at 11 K. We define x-coordinate to be along the line (cf. fig. 1(c)). The dashed vertical lines in figs. 2(a) and 2(b) identify the sample edges encountered along the line. The enhanced B z (x) near the sample edges is associated with geometric barrier-related shielding of H from the sample interior [15]. With increasing H, fig. 2(a) shows a Bean-like [16] gradient in B z indicating penetration of vortices into the sample interior from the edges. Due to the large thickness to width ratio of the crystals ~ 0.13, the gradients appear straight [17] and from the slope of the linear portion of the B z (x) profile in fig.2(a), we estimate the critical current density (90 Oe, 11 )c J K dB z /dx ~ 7 x 10 3 A/cm 2 . The estimated J c is comparable to the typical value reported in literature on single crystals of other pnictides [18].
The periphery of the Meissner-like region identified in fig.1(a) (within the dashed circle) is identified in fig. 2(a) as the region AB located between the two arrows, where B z ~ constant inside AB with almost zero slope. From fig. 2(a) it appears that the region of the sample within AB maintains a Meissner like response with no gradient in B z up to fields of 90 Oe. Closer inspection, however, shows that within AB region there is an anomalous increase in z B from 0 G up to 20 G as H is increased, which we argue is intrinsic and not an experimental artifact. This observation is inconsistent with the region between AB being a perfectly shielded Meissner state. We have confirmed this anomalous behavior at other T's and in other samples of the same stoichiometry. In fig. 2(b), on decreasing H from 90 Oe to 0 Oe, conventional reversed Bean like gradients near the sample edges are observed. From the B z (x)-profile in fig. 2(b) note that B z within AB region does not decrease to zero but remains at a finite remnant value of ~ 3.5 G. It is this remnant B z ~ 3.5 G which is responsible for the bright contrast in the Meissner like region of the sample at H = 0 Oe as noted for fig. 1(f). Thus within the Meissner region of the sample it appears that the diamagnetic ((B z -H) < 0) gradientless B z (x) response within AB is not zero and it rides on a uniform background B z which increases with H and is hysteretic. Note that this behavior is observed only for the magnetooptical response over the sample and not outside the sample. It appears that within this Meissner like region there exists an unexpected response. To ascertain that the observations presented above is not unique to one sample, not related to any peculiar realization of inhomogeneity in the chemical composition of this sample, we have confirmed the presence of a similar features within a gradientless Meissner like region in another single crystal of CaFe 1.94 Co 0.06 As 2 obtained from the same batch (cf. section III in supplementary information in Ref. [14] and compare the behavior in the region between the arrows with that in figs.2(a) and 2(b)).  as T increases towards T c (cf. fig.3 and movie at section IV of supplementary information at ref. [14]). . We observe an increasing trend of peak pk χ + with H, which is opposite to the behavior seen for conventional and high T c superconductors associated with the paramagnetic Meissner effect (PME) [21] where a similar positive magnetization peak near T c is observed for superconductors field cooled in a small applied field. In conventional PME, ( ) pk H χ + decreases with increasing H [21]. As argued below, the unusual behavior of ( ) pk H χ + , we suggest, is associated with magnetic correlations in the system. The positive nature of ( z B -H) is uncovered only when the diamagnetic shielding response of the superconductor weakens close to T c . The increasing behavior of pk χ + with H suggests that the ( Oe for both the bulk and local behavior confirms the Meissner like shielding response (a response of the type seen within the dashed (yellow circled) region in fig.1(a)). While the bulk   fig. 3(a)-(e) and movie link at section IV of supplementary information at ref. [14]). We observe that the area with positive magnetization grows and spreads across the sample with increasing T thus suggesting suggests its origin is not associated with sample inhomogeneity. The behavior of A(T) fits to A(T) α 1/|T-T mgn | γ , where at 50 Oe the critical exponent γ = 1.12 ± 0.10 and the mean temperature scale T mgn =14.54 ± 0.06 K and at 100 Oe γ = 1.59 ± 0.12 and T mgn =16.06 ± 0.14 K. The above divergence in area suggests a diverging correlation length. The correlation length below T mgn is associated with the onset of magnetic correlations in the sample producing a positive magnetization response. The T mgn is a critical temperature associated with the onset of enhanced magnetic correlations found in close proximity to T c . The above inference is supported by the observation of a Curie-Weiss fit to ( z B -H) vs. T response (cf. solid black curve in fig. 3(f)). As one reduces T below T c , enhanced magnetic correlations lead to a positive feature in the local ( z B -H)-(T) response. However with further lowering of T the region over which the correlations exist shrinks at the expense of a growing superconducting fraction with a predominating diamagnetic response, leading to a positive peak like feature in ( z B -H)-(T). At low T the area over which magnetic correlations survive may fall below the resolution of our setup. Evidence for magnetic order coexisting with superconductivity at low T is suggested by the monotonic variation of ( ) pk H χ + (cf. fig. 3(h)) from the microscopic magnetically ordered regions which produce a uniform and hysteretic offset in B z (x) response within Meissner regions as discussed earlier for figs.2(a) and 2(b). The Curie Weiss fit χ = c/(T-T Curie ) to the positive decaying portion of ( z B -H)-(T) curve at 50 Oe (cf. solid black curve in fig. 3(f)) yields a mean T Curie ~ 12 K (the Curie T), and c = Nµ eff 2 = 1.207 cc K/mole, where N is the molar density of magnetic moments with effective magnetic moment μ eff . The low value of T Curie suggests that magnetic exchange interactions are weak. By using N = Avogadro number, we estimate the magnetic moment of ~ 1.5µ B /(Fe-atom) ), which is close to the theoretically proposed Fe moment value [23] in CaFe 2 As 2 parent pnictide compound. Alternatively, if we assume that not all Fe atoms in the material contribute to the moment, therefore using a reported value [24] of Fe μ eff = 0.75(4)µ B in c = Nµ eff 2 , we estimate N ~ 25% of Avogadro number, which implies a mean moments spacing of ~ 2(d Fe-Fe spacing = 2.7 Å). Note, Co concentration of 3% in CaFe 1.94 Co 0.06 As 2 corresponds to an average Co-Co spacing of ~ 9 Å. Recent STM study on the FeSe system [2] suggests it has superconducting state with s ± order parameter with nodes associated with strong nearest neighbour (NN) exchange interactions between Fe sites. Our study suggests that in CaFe 1.94 Co 0.06 As 2 , exchange interaction between next to nearest neighbor (NNN) Fe sites maybe playing an important role in mediating weak magnetic correlations to coexist along with superconductivity. Figure 4(c) shows the temperature dependence of the lower critical field H c1 (demagnetization corrected) which is estimated using deviation from Meissner linear behavior in the isothermal bulk magnetization, M vs. H measurements as shown by an upward arrow in the bulk M-H loop of 14K in fig. 4(b). Down to reduced temperatures t = (T/T c (0)) ~ 0.6, with T c (0) ~ 17.8 K (determined from extrapolation of the H c1 (T) data), the H c1 (t) behaves as (1-t) (cf. fig. 4(c)), which is unlike a BCS superconductor.

Local magnetic field distribution measured as
Bulk magnetization and strong pinning regime close to Tc. -Shown in fig. 4(a) is 4πM vs. T data measured on the Quantum design SQUID magnetometer (H || c). The sample was cooled from 30 K in H = 0 Oe down to 5 K and the isofield 4πM vs. T was recorded in an H = 50 Oe while warming up the sample. Note that at 5 K, the sample exhibits a strong diamagnetic shielding response indicating bulk superconductivity sets in the sample at low T. As T approaches 17 K (~T c (0)), the diamagnetic response decreases. In the inset of fig. 4(a), M instead of monotonically approaching zero becomes positive and goes through a peak before reducing to zero. This feature is similar to that observed in local measurements in fig.3(f). We also find unusual features in specific heat behavior in the regime near T c where we find evidence for magnetic fluctuations in our local measurements (cf. supplementary information, section V, at Ref. [14]). Evidence of strong pinning near T c via bulk magnetization measurements. -In recent times origin of strong pinning in pnictides has been attributed to being either chemical in nature, related to fluctuations in doping concentration on the scale of few 100 nm [25] or due to magnetic fields related to onset of magnetic ordering in the pnictides [10,11]. Our data suggests magnetic correlations as being responsible for pinning in the Co doped CaFe 2 As 2 compound. To investigate the pinning in our sample we capture bulk M-H hysteresis loops measured in the SQUID magnetometer above 10 K. Shown in fig.4(b) are the virgin and reverse runs of the 4πM vs. H hysteresis loop (upto low H = 210 Oe) measured at T = 14 K and 17 K. Here we find an unusual feature, i.e., at 17 K which is ~ 0.95 T c (with T c (0) ~ 17.8 K determined from fig.4(c)), significant amount of hysteresis persists. Figure 4(d) shows the behavior of the width of hysteresis loop (ΔM) as a function of the applied magnetic field. Note that ΔM ∝ J c , is a measure of pinning strength in a superconductor. Strong intervortex interactions in a weak pinning environment typically leads to a weak pinning scenario where J c (or equivalently ΔM) is proportional to 1/H α [26], where α is a positive constant. However, the log-log plot in fig.4(d) at 17 K shows that ΔM does not follow the weak pinning behavior, rather up to ~ 80 Oe, the ΔM is almost field independent. The strong pinning regime is expected in the limit of dilute density of vortices wherein the vortices are weakly interacting, i.e., the mean intervortex separation (a 0 ) is greater than the superconducting penetration depth (λ). In such a situation, the vortices can be easily pinned on the pin-ning sites and the vortex state enters a maximally pinned state. In this strong pinning regime, the J c or ΔM is expected to be almost field independent, as changes in H in this regime do not significantly enhance the intervortex interaction to weaken the effective pinning strength.
In fig.4(d) we find the field independent ΔM(H) regime i.e., the strong pinning regime extending up to 80 Oe and surviving at 17 K (~ 0.95 T c ). Near T c , large thermal fluctuations are expected to weaken the pinning potential significantly. In such an H -T regime, the thermal smearing effects should have been significantly weakened the pinning. Furthermore, at 80 Oe where the intervortex separation is a 0 ~ 400 nm, due to the divergence of λ(T) at T = 17 K ~ 0.95T c , it is expected that the vortices aren't weakly interacting. Therefore near 17 K ~ 0.95T c one does not expect to find a strong pinning regime. However our observation shown in fig.4(d) suggests strong pinning surviving at T close to T c which suggests the presence of strong pinning centers in the superconductor whose pinning potential is much larger than the thermal (~k B T c ) energy scale. . In fig.3 we have already argued that the positive ( z B -H) response near T c at low fields is indicative of the presence of magnetic correlations in the superconductor. Regions with magnetic correlations coexisting along with superconductivity and having ordering temperature higher than T c of the superconductor would be suitable candidates whose pinning strengths would be effective up to close to T c . Therefore, in the present pnictide system investigated, we suggest magnetic correlations as a plausible source of strong pinning surviving in the superconductor up to ~T c .
To summarize, at low T (<< T c ) while the material exhibits features like any bulk superconductor, with increasing T as the shielding response of the superconductor weakens, the presence of underlying magnetic correlations in the CaFe 1.94 Co 0.06 As 2 is uncovered. We suggest that CaFe 1.94 Co 0.06 As 2 is a rich system to investigate aspects related to the coexistence of magnetic correlations along with superconductivity.
SSB acknowledges DST, CSIR and MHRD-India, and Debanjan Chowdhury for his help during the experiments.