Vortex pinning by intrinsic correlated defects in Fe1−ySe

We present a study on the transport and magnetic properties of superconducting Fe1−ySe single crystals. In the superconducting state, the in-plane electrical resistivity of the crystal is measured for fields up to 16 T and as a function of field direction, in order to understand how the vortex dynamics is affected by the presence of defects. A strong deviation from the slightly anisotropic crystal (electronic anisotropy constant 7 ∼ 1.08) is observed as a steep angular dependence, which is interpreted as a signature of the presence of correlated defects. The influence of the correlated defects on the critical current is studied through the angular dependence of the magnetization, and compared to numerical simulations.


Introduction
Recently, a new iron-based superconductor family was found, of which F eSe, the compound focused on here, is a member [1]. In all cases, the samples present a tetragonal layered structure and a slight anisotropy, γ = m c /m ab , with m c and m ab the effective electronic masses in the c axis and the ab plane, respectively [2].
It is common to find spurious phases in the crystals mixed with the superconducting tetragonal F eSe since the latter only spans a very narrow region of the thermodynamic phase diagram [3]. The spurious phases could include metallic F e, in excess of this element, or F e 7 Se 8 , in its defect. In this work we identify how the presence of F e 7 Se 8 affects the superconducting vortex dynamics in F e 1−y Se single crystals.
2. Crystal characterization F e 1−y Se single crystals were grown from 1/4 KCl:3/4 N aCl flux in evacuated double quartz ampoules. Structural characterization was made by X Ray diffraction (XRD). Chemical composition was quantified by Energy Dispersive Spectroscopy (EDS). The crystals have a platelet shape and present F e deficiency. XRD shows the presence of two phases, the superconducting tetragonal F eSe, and the ferrimagnetic hexagonal F e 7 Se 8 . Tetragonal F eSe shows two preferential orientations of the c axis, one parallel and the other at 57 • from the platelet normal. Hexagonal F e 7 Se 8 grows only with the c axis parallel to the normal [4] and presents an ordered array of F e vacancies [5]. Figure 1 shows in plane electrical resistivity, ρ, measurements for an F e 0.92 Se crystal with magnetic field, H, perpendicular to the crystal plane. The onset of the transition temperature for H = 0 is T c = (11.9 ± 0.1) K. The transition width is broadened by about 35% when H varies from 0 to 16 T. This is a signature for the presence of vortex liquid.

Results and discussion
In order to study the influence of correlated defects on the dynamics of the vortex lattice we measured the angular dependence of ρ in terms of the orientation of H. The angle of H is measured with respect to the normal to the platelet, see θ in Fig. 2a). We used a constant Lorentz force configuration, i.e. the external field is always at a right angle to the applied current. This avoids spurious angular dependencies of the pinning force related to the nonperpendicularity between current density and magnetic field.   results for a F e 0.92 Se crystal at H =12 T and for T = (9.58 ± 0.01) K and T = (6.07 ± 0.01) K. The continuous line shows the expected behavior for a slightly anisotropic material with point defects. This dependence was evaluated in base to a thermally activated ρ [6] and to the scaling for the angular dependence proposed by Blatter and co-workers [7]. The final equation is: (1) where ε(θ) = cos 2 θ + γ −2 sen 2 θ, U is the activation energy for the movement of the vortices, ρ 0 is a constant and q is a parameter that takes values between 0.5 and 2. In figure 2, we use H = 12 T, T c = (11.9 ± 0.1) K and the corresponding temperature. The parameters ρ 0 = (13±2) mΩ.cm.K, q = (1.1±0.2), U (9.58 K, 12 T, 0 • ) = (51±4) K and U (6.07 K, 12 T, 0 • ) = (141 ± 6) K were obtained adjusting ρ(T, H, θ = 0 • ) in Fig. 1. Finally, for both temperatures, we get γ = (1.08 ± 0.05) fitting Eq. 1 to the data in Fig. 2, and using the former values for the other parameters.
Notice that at temperatures near T c the angular dependence is very well described by the equation above. However, for lower temperature, the resistivity presents strong deviations from this behavior. This is observed in all samples, and can be understood in terms of vortex dynamics. At low temperature, the extra minimum at ±33 • (Fig. 2c)) could signal vortex pinning by correlated defects. The absence of this minimum near the critical temperature ( Fig.   11th  2b)) is consistent with the idea that vortices move in the flux flow regime and the pinning is less effective. It is also expected for the correlated defect pinning to be observed in the critical current which should in turn, be observable with magnetization measurements. In order to assess these effects, we measured the longitudinal (M L H) and transversal (M T ⊥ H) magnetization of the crystals as a function of the rotation angle θ around an horizontal axis, while keeping the modulus of H constant, for H = 0.15 T at 2 K, well below T c , and at 20 K, around 10 K above T c .
In these crystals, there are two contributions to the magnetization, one coming from the superconducting F eSe, and the other coming from the ferrimagnetic F e 7 Se 8 . In order to separate both signals, we assume that they are independent, and that the magnetization of F e 7 Se 8 is approximately constant in our measurements, given that the Neel temperature is much higher (T N ∼ 455 K) [5]. Consequently, we obtain the superconducting F eSe contribution to the magnetization by simply subtracting the 20 K curve from the 2 K one. Figure 3 depicts the results in a plot of M i = ± M 2 L + M 2 T as a function of the field component normal to the platelet, H z = Hcosθ, showing the superconducting magnetization loop. The curve has a rich structure due to the contribution of anisotropy, correlated defect pinning and crystal shape. In particular, at the angles where extra minima are observed in ρ, i.e. 33 • , 147 • , 213 • and 327 • , the magnetization loop also presents distinctive structure. Theoretically, this structure can be understood in terms of a critical current density with anisotropic behavior. Figure 4 summarizes the main facts in a number of simulations that were performed by a critical state modelling [8]. A θ-rotation experiment for an isotropic platelet-like superconductor would produce a bumped cycle as compared to the conventional Bean-like behavior for a standard H z experiment. An extra magnetic moment occurs at θ ≈ 90 • . This is a purely geometric effect related to the force free configuration (due to the zones with induced current parallel to the magnetic field). On the other hand, when an anisotropic    In relation to the crystal microstructure, the correlated defects observed in transport and magnetic measurements may be linked to the phase mixture and the growth directions of the tetragonal phase. Figure 5 presents the crystal structure scheme of our samples, panel a) shows the possible directions of the c axis of the tetragonal phase compatible with our XRD measurements. The direction of the ab plane at ∼ 34 • from the normal of the crystal is coincident with a dense plane of vacancies in F e 7 Se 8 as can be inferred from the structural study of ref. [5] (see Fig. 5b)). This plane is, possibly, the phase boundary between the tetragonal and hexagonal phases and it could behave as a correlated defect for the vortex lattice.

Conclusion
Electrical resistivity and magnetization results in F e 1−y Se crystals show clear evidence for the existence of superconducting pinning by correlated defects. At the same time, the structural characterization of the samples shows the existence of different phases and orientations. One of the crystalline orientations of the F eSe phase coincides with the direction in which the correlated defects increase the pinning, evidencing that the origin of the defects could be related to phase matching in the samples.