Geometric Magnetoresistance
Science, vol. 289, page 1530 (2000).
Scientific American, July 2004, page 70, "Magnetic field nanosensors"

   Magnetic sensors not only display interesting physical phenomena, but also find important applications in information storage and position or speed sensing. Magnetoresistance may originate from the magnetic field dependence of the materials parameters, or may be geometric in origin. An example of the former is found in layered metal structures such as spin valves (exhibiting phenomena related to GMR, or giant magnetoresistance), or in the manganite perovskites. Both of these require magnetic materials. Geometrical magnetoresistance does not require magnetic materials, and originates instead from the effect of the Lorentz force on the current and potential distribution in the geometry, taking into account appropriate boundary conditions. Geometrical magnetoresistance is thus akin to the Hall effect. Due to differences in geometry, the Hall effect is antisymmetric in the magnetic field, whereas the geometrical magnetoresistance is symmetric. Geometries can be created that exhibit a superposition of Hall and geometrical magnetoresistance effects. The Hall effect and the geometrical magnetoresistance have technological advantages over layered metal magnetoresistance: they are not subject to hysteresis and magnetic noise, and are not as sensitive to electrostatic discharge. In semiconductors, the mobility determines the magnitude of the Hall or geometrical magnetoresistance effect (linear and quadratic in mobility respectively). A high mobility is associated with high speed operation, another advantage in information storage technologies.

   Our work has extended the geometrical magnetoresistance effect to hybrid metal/semiconductor structures, where the altered boundary conditions give rise to unprecedented levels of magnetoresistance. The geometry is illustrated in the picture: a metal (Au) disc is embedded in a high-mobility semiconductor (InSb). Typical magnetoresistance traces (at RT) are illustrated at right for different ratios of Ra/Rb (0 to 15). The large magnetoresistance can be seen as resulting from current deflection by the embedded metal inhomogeneity. At low magnetic fields, the current density vector and electric field vector are close to parallel, and both perpendicular to the Au plug, which thus acts as a short. At higher magnetic fields, the current develops a Hall angle w.r.t. the electric field, the Au plug rejects the current, and the Au plug acts as an open circuit. This work, performed in collaboration with Stuart Solin (Washington University, St. Louis. MO), was published in Science, vol. 289, page 1530 (2000).

   Geometrical magnetoresistors have turned out to maintain their properties when scaled down to nanoscale dimensions, and present work is focused on such nanoscale sensors. An accessible review can be found in a recent Scientific American article (July 2004, page 70, "Magnetic field nanosensors").