Signature of surface state coupling in thin films of the topological Kondo insulator SmB${}_6$ from anisotropic magnetoresistance

The temperature and thickness dependencies of the in-plane anisotropic magnetoresistance (AMR) of SmB${}_6$ thin films are reported. We find that the AMR changes sign from negative (${\rho }_{\mathrm{\mid }\mathrm{\mid }}<{\rho }_{\perp }$) at high temperatures to positive (${\rho }_{\mathrm{\mid }\mathrm{\mid }}>{\rho }_{\perp }$) at low temperatures. The temperature, T${}_s$, at which this sign change occurs, decreases with increasing film thickness $t$ and T${}_s$ vanishes for $t$ $>$ 30 nm. We interpret our results in the framework of a competition between two components: a negative bulk contribution and a positive surface AMR.