magnetotransport

Magnetotransport is the study of how charge carriers move in a material when a magnetic field is present. It encompasses phenomena such as magnetoresistance, where the resistance changes with the applied field; the Hall effect, which produces a transverse voltage proportional to the magnetic field and carrier density; and related effects like planar Hall responses and anisotropic magnetoresistance. Measurements typically determine longitudinal and transverse resistivity or conductivity as functions of field, temperature, and carrier concentration.

In the classical picture, the Drude model describes how a magnetic field modifies the motion of charge carriers, leading to a tensorial conductivity that depends on the carrier mobility and field strength. As a result, the longitudinal resistivity often increases with the square of the product of mobility and field in simple single-carrier systems, and the Hall resistivity is proportional to the field divided by the carrier density. Real materials frequently involve multiple carrier types, anisotropy, or complex band structure, producing richer and sometimes non-saturating magnetoresistance. In quantum regimes, Landau quantization gives rise to Shubnikov–de Haas oscillations and, in two-dimensional systems at low temperatures and high fields, the quantum Hall effect. Topological materials can exhibit magnetotransport features tied to Berry curvature and other topological properties.

Experimental approaches include four-terminal or Hall-bar geometries to extract ρ_xx and ρ_xy, along with angle-dependent measurements and studies at cryogenic temperatures and high magnetic fields. Magnetotransport is widely used in magnetic sensing, read heads for data storage, and spintronic devices, and is a key tool in probing electronic structure in metals, semiconductors, graphene and other two-dimensional materials, topological insulators, and Weyl or Dirac semimetals.