Direct observation of in-plane anisotropy of the superconducting critical current density in $\mathbf{Ba}{\left({\mathbf{Fe}}_{1-x}{\mathbf{Co}}_x\right)}_2{\mathbf{As}}_2$ crystals

The phase diagram of iron-based superconductors exhibits structural transitions, electronic nematicity, and magnetic ordering, which are often accompanied by an electronic in-plane anisotropy and a sharp maximum of the superconducting critical current density ($J_{\text{c}}$) near the phase boundary of the tetragonal and the antiferromagnetic-orthorhombic phase. We utilized scanning Hall-probe microscopy to visualize the $J_{\text{c}}$ of twinned and detwinned $\mathrm{Ba}{\left({\mathrm{Fe}}_{1-x}{\mathrm{Co}}_x\right)}_2{\mathrm{As}}_2$ ($x=5\%–8\%$) crystals to compare the electronic normal state properties with superconducting properties. We find that the electronic in-plane anisotropy continues into the superconducting state. The observed correlation between the electronic and the $J_{\text{c}}$ anisotropy agrees qualitatively with basic models, however, the $J_{\text{c}}$ anisotropy is larger than predicted from the resistivity data. Furthermore, our measurements show that the maximum of $J_{\text{c}}$ at the phase boundary does not vanish when the crystals are detwinned. This shows that twin boundaries are not responsible for the large $J_{\text{c}}$, suggesting an exotic pinning mechanism.

Figure 1

Sketch of (a) a free-standing crystal with twin boundaries and (b) a detwinned crystal after applying pressure with the spin configuration of the iron atoms in the center, and (c) a sketch of the device used for detwinning (c).

Figure 2

Scanning Hall-probe microscopy measurements of the remanent field profile of (a) twinned and (b) detwinned $\mathrm{Ba}{\left({\mathrm{Fe}}_{0.95}{\mathrm{Co}}_{0.05}\right)}_2{\mathrm{As}}_2$ single crystals at 5 K. The absolute value of the field gradient calculated from the field maps of (a) and (b) are displayed in (c) and (d). The color scale indicates the magnitude of the field and field gradient. The triangles in (b) and (d) indicate the direction of the applied pressure, which was 2–3 MPa, while the current flow is indicated by arrows (see text).

Figure 3

Phase diagram (a) with the antiferromagnetic and orthorhombic (AFO) and the superconducting transition temperature ($T_{\text{c}}$), (b) critical current density of twinned and detwinned crystals, and (c) in-plane anisotropies of the critical current density. The bend of the AFO phase in the superconducting dome was adopted from Ref. [8] and not measured directly. $J_{\text{c}}$ is the critical current density of the twinned and $J_{\text{c},i}$, where $i=a,b$ are the critical current densities parallel to the crystal axes of the detwinned crystals. The error bars indicate the uncertainty of the doping level and three times the standard variants of the critical current density of the fit (cf. Appendix pp2). The error bars lie within the markers if they are not clearly visible. The dashed lines are guides to the eye. $J_{\text{c},a}^{\text{max}}$ and $J_{\text{c},b}^{\text{min}}$ denote the maximum and minimum values observed for the respective axes. The measurements were carried out at 5 K with an applied pressure of about 5–6 MPa, except for 5% where the pressure was 2–3 MPa because of a larger sample cross section.

Figure 4

Sketch of the critical current densities and geometry for modeling the current flow (a) and the comparison of a scanning Hall-probe microscopy (SHPM) measurement (solid lines) and the fit to this data (b). The solid contours refer to the SHPM data, while the dotted contours show the field profile that would result from the idealized current flow assumed in the model.