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 ($rho_{||}<rho_{perp}$) at high temperatures to positive ($rho_{||}>rho_{perp}$) 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.