The recent conjecture of a topologically-protected surface state in SmB$_6$ and the verification of robust surface conduction below 4 K have prompted a large effort to understand the surface states. Conventional Hall transport measurements allow current to flow on all surfaces of a topological insulator, so such measurements are influenced by contributions from multiple surfaces of varying transport character. Instead, we study magnetotransport of SmB$_6$ using a Corbino geometry, which can directly measure the conductivity of a single, independent surface. Both (011) and (001) crystal surfaces show a strong negative magnetoresistance at all magnetic field angles measured. The (011) surface has a carrier mobility of $122text{ cm}^2/text{V}cdottext{sec}$ with a carrier density of $2.5times10^{13} text{ cm}^{-2}$, which are significantly smaller than indicated by Hall transport studies. This mobility value can explain a failure so far to observe Shubnikov-de Haas oscillations. Analysis of the angle-dependence of conductivity on the (011) surface suggests a combination of a field-dependent enhancement of the carrier density and a suppression of Kondo scattering from native oxide layer magnetic moments as the likely origin of the negative magnetoresistance. Our results also reveal a hysteretic behavior whose magnitude depends on the magnetic field sweep rate and temperature. Although this feature becomes smaller when the field sweep is slower, does not disappear or saturate during our slowest sweep-rate measurements, which is much slower than a typical magnetotransport trace. These observations cannot be explained by quantum interference corrections such as weak anti-localization, but are more likely due to an extrinsic magnetic effect such as the magnetocaloric effect or glassy ordering.
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