  Condensed matter systems that simultaneously exhibit superconductivity and
ferromagnetism are rare due the antagonistic relationship between conventional
spin-singlet superconductivity and ferromagnetic order. In materials in which
superconductivity and magnetic order is known to coexist (such as some
heavy-fermion materials), the superconductivity is thought to be of an
unconventional nature. Recently, the conducting gas that lives at the interface
between the perovskite band insulators LaAlO$_3$ (LAO) and SrTiO$_3$ (STO) has
also been shown to host both superconductivity and magnetism. Most previous
research has focused on LAO/STO samples in which the interface is in the (001)
crystal plane. Relatively little work has focused on the (111) crystal
orientation, which has hexagonal symmetry at the interface, and has been
predicted to have potentially interesting topological properties, including
unconventional superconducting pairing states. Here we report measurements of
the magnetoresistance of (111) LAO/STO heterostructures at temperatures at
which they are also superconducting. As with the (001) structures, the
magnetoresistance is hysteretic, indicating the coexistence of magnetism and
superconductivity, but in addition, we find that this magnetoresistance is
anisotropic. Such an anisotropic response is completely unexpected in the
superconducting state, and suggests that (111) LAO/STO heterostructures may
support unconventional superconductivity.
