Magnetoresistance (MR) in materials arises from two properties of the system. One is the physical MR that is dependent on the intrinsic properties of the materials in the physical system. The second source originates in the geometric structure and distribution of the materials in the physical system. In this review, we focus on the geometric MR and show how it can be altered and dramatically enhanced in two cases. First, in metal–semiconductor hybrid (MSH) structures, the judicious distribution of metal and semiconductor leads to a dramatic increase in the MR due to the rerouting of the current passing preferentially through the metallic regions at low fields, due to their high conductivity, into the semiconductor regions in the presence of a magnetic field. This phenomenon is now known as
extraordinary magnetoresistance
(EMR), with observed room‐temperature EMR in excess of 100% at 0.05 T and reaching values of 10
6
% at 5 T. This property of the MSH has been shown to be scalable down to structure dimensions on the order of ∼50 nm with a measured EMR of 35% at a signal field of 0.05 T. The details of the diffusive transport mechanism leading to the enhancements in MR are presented. Second, in nanocontacts between ferromagnetic wires, the quantum point contact leads to a ballistic magnetoresistance (BMR) that is due to the development of a domain wall (DW) between the wires when they are magnetized in an antiparallel configuration. The scattering of electrons by the DW in the nanochannels between the wires changes the conductance of the channel, and BMR of ∼300–3000% and higher have been observed. Here again the geometric origin of the MR is evident. The various aspects of the nanochannel governing BMR are discussed. Both geometric enhancements show great promise for technological applications in the area of reliable nanoscale sensors for computer read heads, magnetic actuators and switches, and biological sensors.