Vortex Redistribution below the First-Order Transition Temperature in the $\beta$-Pyrochlore Superconductor ${\mathrm{KOs}}_2{\mathrm{O}}_6$

A miniature Hall-sensor array was used to detect magnetic induction locally in the vortex states of the $\beta$-pyrochlore superconductor ${\mathrm{KOs}}_2{\mathrm{O}}_6$. Below the first-order transition at $T_p\sim 8\mathrm{K}$, which is associated with a change in the rattling motion of K ions, the lower critical field and the remanent magnetization both show a distinct decrease, suggesting that the electron-phonon coupling is weakened below the transition. At high magnetic fields, the local induction shows an unexpectedly large jump at $T_p$ whose sign changes with position inside the sample. Our results demonstrate a novel redistribution of vortices whose energy is reduced abruptly below the first-order transition at $T_p$.

Figure 1

Local magnetic induction $B_{\mathrm{local}}$ (right axis) and magnetization (left axis) measured at 6.4 K near the sample center as a function of field $H$. The numbers and thin solid arrows indicate the order and direction of the field sweeps. At the first penetration field $H_{\mathrm{fp}}$, a sharp dip is observed. The remnant magnetization $\Delta M_{\mathrm{rem}}$ is defined by the hysteresis width at $H=0\mathrm{Oe}$ (thick solid arrow). Inset: the temperature dependence of local magnetization ($H=40\mathrm{Oe}$) shows a clear kink at the first penetration temperature $T_{\mathrm{fp}}$.

Figure 2

Lower critical field as a function of temperature in ${\mathrm{KOs}}_2{\mathrm{O}}_6$ obtained form the Hall-sensor magnetometry. Inset: the temperature dependence of the remanent magnetization. The dotted and dashed lines represent linear and quadratic temperature dependences, respectively.

Figure 3

Temperature dependence of the local induction change $\delta B_{\mathrm{local}}$ with respect to the value in the normal state, for different applied fields near the crystal center (a) and away from the center (b). The insets show the magnitude of the jump $\Delta B_{\mathrm{local}}$ at $T_p$ as a function of $H$.

Figure 4

(a) Contour image of local induction change $\delta B_{\mathrm{local}}$ inside the sample at 18 kOe, constituted from interpolations and plotted in the temperature-position plane. This highlights an abrupt change of the vortex distribution near $T_p$. The position dependence of $\delta B_{\mathrm{local}}$ at several fields is plotted just above (b) and below $T_p$ (c). The dotted lines indicate the approximate positions of the sample edges, and dashed lines are guides to the eye.