Six-fold crystalline anisotropic magnetoresistance in the (111) LaAlO$_3$/SrTiO$_3$ oxide interface

We measured the magnetoresistance of the 2D electron liquid formed at the (111) LaAlO$_3$/SrTiO$_3$ interface. The hexagonal symmetry of the interface is manifested in a six-fold crystalline component appearing in the anisotropic magnetoresistance (AMR) and planar Hall data, which agree well with symmetry analysis we performed. The six-fold component increases with carrier concentration, reaching 15% of the total AMR signal. Our results suggest the coupling between higher itinerant electronic bands and the crystal as the origin of this effect and demonstrate that the (111) oxide interface is a unique hexagonal system with tunable magnetocrystalline effects.