Topological Kondo insulators (TKIs) are a new class of topological materials in which topological surface states dominate the transport properties at low temperatures. They are also an ideal platform for studying the interplay between strong electron correlations and topological order. Here, hysteretic magnetoresistance (MR) is observed in TKI SmB6 thin nanowires at temperatures up to 8 K, revealing the strong magnetism at the surface of SmB6. It is also found that such MR anomaly exhibits an intriguing finite size effect and only appears in nanowires with diameter smaller than 58 nm. These nontrivial phenomena are discussed in terms of the latest Kondo breakdown model, which incorporates the RKKY magnetic interaction mediated by surface states with the strong electron correlation in SmB6. It would provide new insight into the nature of TKI surface states. Additionally, a non‐monotonically temperature dependent positive magnetoresistance is observed at intermediate temperatures, suggesting the possible impurity‐band conduction in SmB6, other than the surface state transport at low temperatures and the bulk‐band transport at high temperatures.

P-type ferromagnetic Cr1-δTe thin films with the Curie temperature of 170K were epitaxially grown on GaAs substrate. Low-temperature magnetotransport study reveals that the film has a strong perpendicular magnetic anisotropy (PMA) and an anisotropic magnetoresistance (AMR) ratio up to 8.1%. Furthermore, reduced anomalous Hall effect is observed at low temperatures in Cr1-δTe, suggesting the possible crossover of the contribution to AHE from the intrinsic mechanism to extrinsic skew scattering. Distinctive from conventional transition metal ferromagnets, the AMR ratio is also greatly suppressed at low temperatures. Our work demonstrates that epitaxial Cr1-δTe films are interesting platforms for studying the physics underlying the strong PMA and large AMR.