This thesis will explore magnetotransport in artificial spin ice (ASI) and RuO2. Small dimension ASI samples were fabricated in order to study systems undergoing thermal fluctuations in magnetisation. Optimisation of the fabrication process for small dimension ASI is outlined. Bar dimensions of 62nm x 18nm x 5.5nm were achieved.

The magnetoresistance (MR) and Hall response of alternate geometry ASI systems were investigated in order to attempt to further understand previously observed asymmetric Hall signals in kagome ASI. The temperature dependence of the square, brickwork and Shakti arrays was investigated, in both the Hall and MR measurement configurations. Brickwork was found to exhibit the largest asymmetry, and all geometries showed a transition in behaviour below 50K. This is likely due to additional pinning of domain walls, resulting in a certain current path being favoured. The square lattice was measured with magnetic field parallel to applied current, as well as perpendicular. These measurements suggest that connected square ASI undergoes a different switching process to disconnected square ASI, which has not been previously reported (to the author's knowledge).

Finally, magnetotransport measurements were performed on RuO2 thin films, in order to probe the temperature dependence of resistivity. The variation of resistivity with respect to applied field for a range of temperatures was also studied. The obtained Hall parameters were compared to values for IrO2, due to their similar structures. The temperature dependent Hall resistivity results show the same trends as IrO2, but with a smaller magnitude. The Hall measurements are consistent with a folded Fermi surface. A large single carrier "effective" mobility observed in the [100] and [110] orientations could be caused by possible hybridisation between the d and p bands. It could also be caused by the similar exotic band structure features that RuO2 shares with graphene.