Intrinsic and extrinsic pinning in NdFeAs(O,F): vortex trapping and lock-in by the layered structure

Fe-based superconductors (FBS) present a large variety of compounds whose properties are affected to different extents by their crystal structures. Amongst them, the REFeAs(O,F) (RE1111, RE being a rare-earth element) is the family with the highest critical temperature Tc but also with a large anisotropy and Josephson vortices as demonstrated in the flux-flow regime in Sm1111 (Tc ∼ 55 K). Here we focus on the pinning properties of the lower-Tc Nd1111 in the flux-creep regime. We demonstrate that for H//c critical current density Jc at high temperatures is dominated by point-defect pinning centres, whereas at low temperatures surface pinning by planar defects parallel to the c-axis and vortex shearing prevail. When the field approaches the ab-planes, two different regimes are observed at low temperatures as a consequence of the transition between 3D Abrikosov and 2D Josephson vortices: one is determined by the formation of a vortex-staircase structure and one by lock-in of vortices parallel to the layers. This is the first study on FBS showing this behaviour in the full temperature, field, and angular range and demonstrating that, despite the lower Tc and anisotropy of Nd1111 with respect to Sm1111, this compound is substantially affected by intrinsic pinning generating a strong ab-peak in Jc.

the 4.2 K data). A much weaker deviation due to correlated defects is also noticed for the data near the caxis at intermediate and high temperatures in the low-field region (few examples are marked by coloured arrows on the 25 K data).
In order to investigate the nature of the different pinning mechanisms in the two principal field configurations, two different approaches have been followed. For the c-axis pinning, the shape of the F p (H//c) curves has been analysed by a modified Dew-Hughes model, 25 but we did not follow a similar approach for F p (H//ab) because it is unable to reveal a possible 3D/2D transition of the vortices.
Moreover, since the Josephson vortices, unlike the Abrikosov vortices, have no normal cores they have little interaction with pinning defects. In order to reveal the nature of the ab-pinning, we instead performed an analysis of the n-values of the I-V curves in the flux-creep regime (n ∼ U p /k B T, where U p is the pinning potential and k B is the Boltzmann constant, in the case of logarithmic current density dependence of U p ). 22,26 Fitting F p (H//c) in Figure 1 25 generates unphysical p and q values because of the superposition of different pinning mechanisms. However, using constant p and q according to different possible pinning scenarios does not reproduce the curves well either, although the best fits were obtained with (p,q) = (0.5,2) at low temperature and (p,q) = (1,2) at high temperature. According to ref. 25, these parameters correspond to surface pinning [(0.5,2)] and point defect (PD) pinning [ (1,2)]. However, vortex shearing generates the same functional dependence as surface pinning and its possible effect has to be considered and will be discussed ahead (surface pinning or vortex shearing contribution will be marked by S in the following). 27,28 Considering that this is a thin film, the surface contribution could be provided by planar defects parallel to the c-axis such as domain, antiphase/twin boundaries or dislocation array, whereas PD pinning is probably induced by atomic defects such as vacancies or disorder. To reproduce the experimental data taking into account the superposition of two contributions we used the expression The first two parameters represent the amplitudes of the PD and S contributions while the latter two describe the maximum fields of their effectiveness. As shown in Figure 1, this equation well reproduces the F p (H//c) data at all temperatures. In all cases H S > H PD implying that H S actually corresponds to the experimental irreversibility field. The fitting parameters reported in Figure 3(a) reveal a crossover in the dominant mechanism at about 20 K: the S contribution dominates at low T, whereas PD pinning is stronger at high T. Figure 3(b) also shows that the S contribution has a wider in-field effectiveness with H S exceeding 50 T at 4.2 K whereas PD pinning is limited to ∼20 T.
The I-V curves, from which J c was determined, were analysed with the power-law relation V ∼ I n in order to determine the n-value that carries information about the pinning potential. In general, in case of random isotropic pinning, n scales with J c independently of temperature, field or angle [in ref. 29 a relation (n-1) ∼ J c α is suggested, whereas here we found n ∼ J c α ]. As a consequence the J c (H,θ) and n(H,θ) plots should have similar trends. This is roughly the case observed in Figure 4 at 30 K (and above, not shown) where n presents a maximum along ab. However, this trend changes with decreasing temperature.
A small dip in n-value starts forming at 25 K (it is more visible for increasing field) revealing an inverse n-J c correlation. At 20 K the dip becomes deeper and wider but there is a point exactly at 180° where the n-value peaks with respect to its neighbouring angles. At 15 K both the dip and the peak become more when the ab-direction is approached. At 25 K, where the dip in n(θ) starts to appear, the data deviate downward from the n ∼ J c α trend-line and J c increases despite the n-value drops. This initial behaviour is visible also at 20, 15 and 10 K but the emerging peak inside the dip of n(θ) produces a second deviation toward high n-values. Although less evident, a similar double-deviation behaviour is also observed at 4.2 K.

Discussion
The critical current density and the pinning properties of the Nd1111 thin film can be compared with other films of the same family. Of particular interest is the comparison with Sm1111 which has the same structure but higher T c . The self-field J c (4.  Figure   6(b). Since in this case the whole vortex is parallel to the ab-planes, the Lorentz force is always directed along the c-axis. This generates very strong pinning and an increased n-value (Figure 4 and 5). L ϕ seems to have a weaker dependence (∼H -1/2 ) than the theoretical prediction ( L ϕ ∼ H T / ϕ ) 22 and an amplitude larger than previously observed in YBCO (0.1-1°) 22,39 which has a slightly higher intrinsic anisotropy.
However, here the reduced temperature is much lower than for YBCO and the multiband nature of FBS and the temperature dependence of the superconducting parameters could also play a role in determining the vortex lock-in. Another factor to take into account is the sample mosaicity: despite the high crystalline quality, the vortex lock-in likely occurs over the domain-size, not the entire sample, enhancing L ϕ . Awaji et al. 38

characterized YBCO films down to 4.2 K and observed that the n-value for H//ab first increases on
going below T c , has a plateau from 70 to 40 K and then increases again below 20 K. The authors explained this behaviour by vortex kink excitation in the plateau region, followed by its suppression below 20 K. In our Nd1111 sample we observed the same trend when the reduced temperature is taken into account. Clear evidence of locked-in vortices have never been reported before for FBS, however Iida et al. 20 did observe a small peak emerging from the n-value dip at 4 K in Fe(Se,Te). It is quite striking that even a material with such a low T c reveals itself to have such strong intrinsic pinning.
To conclude, in this paper we investigated the intrinsic and extrinsic pinning properties of an

Additional information
Competing financial interests: The authors declare no competing financial interests.            The NdFeAs(O,F) thin film was characterized by XRD. The θ-2θ scan in Fig. S1(a) shows only the   The angular dependencies of J c were measured in a wide 35-4.2 K temperature range up to 35 T at 4.2 K and up to 16 T at higher temperatures. The data are reported in Fig. S2.