Magnetic-field tuned anisotropy in superconducting Rb${}_x$Fe${}_{2-y}$Se${}_2$

The anisotropic superconducting properties of a Rb${}_x$Fe${}_{2-y}$Se${}_2$ single crystal with $T_{\mathrm{c}}\simeq 32$ K were investigated by means of superconducting quantum interference device (SQUID) and torque magnetometry, probing the effective magnetic penetration depth ${\lambda }_{\mathrm{eff}}$ and the magnetic penetration depth anisotropy ${\gamma }_{\lambda }$. Interestingly, ${\gamma }_{\lambda }$ is found to be temperature independent in the superconducting state but strongly field dependent: ${\gamma }_{\lambda }\left(0.2\mathrm{T}\right)<4$ and ${\gamma }_{\lambda }\left(1.4\mathrm{T}\right)>8$. This unusual anisotropic behavior, together with a large zero-temperature ${\lambda }_{\mathrm{eff}}\left(0\right)\simeq 1.8$ $\mu$m, is possibly related to a superconducting state heavily biased by the coexisting antiferromagnetic phase.

Figure 1

Zero-field-cooled measurements of $m/H$ of single crystal Rb${}_x$Fe${}_{2-y}$Se${}_2$ for (a) $H\left|\right|c$ axis and (b) $H\left|\right|ab$ plane. The change of vortex penetration with temperature is very similar for both directions, consistent with an isotropic ${\mu }_0{H}_{\mathrm{c}1}\lesssim 0.3$ mT. The sharp transition at $T_{\mathrm{c}}\simeq 32$ K demonstrates the high quality of the crystal. Due to demagnetization the magnitude of $m/H$ varies by a factor of $\sim$3 for both orientations. A rough estimation of the demagnetization factors from the sample dimensions yields $0.05<N^{\left|\right|ab}<0.3$ and $N^{\left|\right|c}\sim 0.65$.

Figure 2

Angular-dependent torque of single-crystal Rb${}_x$Fe${}_{2-y}$Se${}_2$ measured at 15 K and 1.4 T. For clarity not all of the measured data are presented. (a) Comparison of magnetic torque data obtained without and with the shaking procedure as discussed in the text. The “unshaken” red data ${\tau }_{\mathrm{cw}}$ (blue data ${\tau }_{\mathrm{ccw}}$) are gathered by turning $H$ clockwise (counterclockwise) around the sample. The inset explains schematically the field configuration during the experiment. The “shaken” data are obtained by applying a transverse ac field, yielding reduced irreversibility and enhanced data quality. (b) Angular dependence of the “shaken” magnetic torque averaged for both directions. The green curve is the superconducting component of the signal, obtained after subtracting the background as explained in the text. A fit by Eq. (1) yields ${\gamma }_{\lambda }(15\mathrm{K},1.4\mathrm{T})\simeq 8.6$ (black line). For comparison, the red dotted line is calculated with a fixed ${\gamma }_{\lambda }=3$.

Figure 3

Angular dependence of the superconducting component of the magnetic torque of Rb${}_x$Fe${}_{2-y}$Se${}_2$. (a) Magnetic torque at 17 K for various magnetic fields. (b) Magnetic torque at 1.4 T for various temperatures. The insets in both panels show the evolution of ${\tau }_{\mathrm{norm}}$ close to the $ab$ plane.

Figure 4

Summary of all the results obtained by analyzing the experimental torque signal of Rb${}_x$Fe${}_{2-y}$Se${}_2$ with Eq. (1). (a) Temperature dependence of ${\lambda }_{\mathrm{eff}}^{-2}$. The line is a power law fit to the data at 1.4 T. (b) Temperature dependence of ${\gamma }_{\lambda }$ for various fields, showing that ${\gamma }_{\lambda }$ is strongly increasing with $H$ but is almost independent of $T$. The dotted lines represent the average ${\gamma }_{\lambda }$ for each field. (c) Field dependence of ${\lambda }_{\mathrm{eff}}^{-2}$ for various temperatures. (d) Field dependence of ${\gamma }_{\lambda }$ for various $T$. The black line is a guide to the eye.