Metallic islands in the Kondo insulator SmB$_{6}$

The predicted interplay between Kondo physics and non-trivial topology in SmB$_{6}$ has stimulated many experimental reports, some of which are in apparent contradiction. The origin of the dispute may lie on the fragility of the Kondo insulating phase in the presence of Sm vacancies (Kondo holes) and/or natural impurities, such as Gd$^{3+}$. In this work, we locally investigated this fragility for Al-flux grown Sm$_{1-x}$Gd$_{x}$B$_{6}$ single crystals (0 $\leq$ $x$ $\leq$ 0.02) by combining electron spin resonance (ESR) and complementary bulk measurements. The Gd$^{3+}$ ESR spectra in a highly dilute regime ($x$ $\sim 0.0004$) display the features of an insulating cubic environment. Remarkably, a metallic ESR lineshape is observed for more concentrated samples ($x$ $\geq$ 0.004), even though these systems are still in a reasonably dilute regime and show insulating $dc$ electrical resistivity. Our data indicate that the Kondo insulating state is destroyed locally around impurities before a global percolation occurs. This result not only explains the discrepancy between $dc$ and $ac$ conductivity, but also provides a scenario to explain the presence of quantum oscillations in magnetization in the absence of quantum oscillations in electrical resistivity.