What Is Ordinary Magnetoresistance?

Ordinary magnetoresistance (OMR) is the change in electrical resistance that a non-magnetic conductor or semiconductor exhibits when placed in an applied magnetic field. The effect arises from the Lorentz force acting on charge carriers, which deflects their paths and increases the effective distance they must travel between scattering events, thereby raising resistance. OMR is quantified as MR(B) = [ρ(B) − ρ(0)] / ρ(0), where ρ(0) is the resistivity in zero field and ρ(B) is the resistivity under applied field B. In most common metals at room temperature and modest field strengths, the effect is small, typically well below one percent, placing it in a distinct category from giant magnetoresistance (GMR), colossal magnetoresistance (CMR), and tunneling magnetoresistance (TMR), which are associated with magnetic multilayers or strongly correlated oxides.

The physical origin of OMR was analyzed using the Drude free-electron model, which predicts a quadratic dependence of resistivity on field strength. Quantum mechanical treatments using Boltzmann transport theory and Fermi surface geometry reproduce the classical prediction in simple cases while explaining deviations in materials with complex multi-sheet Fermi surfaces.

Physical Mechanism and the Lorentz Force

When a magnetic field B is applied perpendicular or at an angle to the current direction, the Lorentz force deflects moving electrons (or holes) into curved cyclotron orbits. In a steady state, the build-up of a transverse charge imbalance (the Hall effect) partially compensates the transverse Lorentz force. In materials where carrier mobilities are high, the deflection is large enough to measurably lengthen carrier paths and reduce their net contribution to longitudinal conductivity. WannierTools documentation on ordinary magnetoresistance and Fermi surface topology explains how semiclassical Boltzmann transport calculations use Fermi surface cross-sections to compute the conductivity tensor under field, capturing the field-squared growth expected from Drude theory and deviations driven by topology.

Kohler's Rule and Field Dependence

In metals obeying Kohler's rule, the fractional change in resistivity scales as a universal function of B/ρ(0), reflecting the fact that the dominant parameter is the product of field and scattering time (Bτ). This implies that lower-resistivity (cleaner) metals show larger magnetoresistance at a given field, since electrons complete more cyclotron arc before scattering. The Drude model predicts strictly quadratic growth at low fields, saturating at high fields when cyclotron orbits become closed. Deviations from Kohler's rule, including linear magnetoresistance over a wide field range, have been reported in semimetals and topological materials, linking OMR research to active investigations in quantum materials. The Royal Society Proceedings A paper on the theory of magnetoresistance effects in metals by Sondheimer and Wilson (1947) remains a foundational reference for the semiclassical theoretical framework.

Measurement and Material Dependence

OMR is typically measured in a four-probe (Van der Pauw or Hall bar) geometry to eliminate contact resistance contributions, with field applied perpendicular to the sample (transverse geometry) or along the current direction (longitudinal geometry). The magnitude depends on carrier mobility: high-mobility semiconductors and semimetals such as bismuth, graphite, and InAs show much larger OMR than ordinary metals. Temperature affects OMR by changing the scattering time: lower temperatures increase mobility and thus amplify the effect. The ScienceDirect overview of magnetoresistance phenomena surveys measurement methodologies and the material classes where OMR is practically significant.

Applications

Ordinary magnetoresistance has applications in a wide range of fields, including:

• Magnetic field sensing in low-noise instrumentation where linear-range OMR serves as a calibration reference
• Semiconductor characterization for extracting carrier mobility and density via magnetotransport
• Research into topological materials and semimetals, where anomalous OMR signatures indicate non-trivial band topology
• Benchmarking magnetotransport models against simple geometries before applying them to GMR or CMR devices