Thomson's experiments are an example of AMR,  a property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and direction of magnetization is observed. The effect arises in most cases from the simultaneous action of magnetization and spin-orbit interaction (exceptions related to non-collinear magnetic order notwithstanding, see Sec. 4(b) in the review ) and its detailed mechanism depends on the material. It can be for example due to a larger probability of s-d scattering of electrons in the direction of magnetization (which is controlled by the applied magnetic field). The net effect (in most materials) is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. AMR of new materials is being investigated and magnitudes up to 50% have been observed in some uranium (but otherwise quite conventional) ferromagnetic compounds.  Very recently, materials with extreme AMR have been identified driven by unconventional mechanisms such as a metal-insulator transition triggered by rotating the magnetic moments (while for some directions of magnetic moments, the system is semimetallic, for other directions a gap opens).
In polycrystalline ferromagnetic materials, the AMR can only depend on the angle  between the magnetization and current direction
and (as long as the resistivity of the material can be described by a rank-two tensor), it must follow
where  is the (longitudinal) resistivity of the film and   are the resistivities for  and , respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed (somewhat confusingly[1]) the planar Hall effect. In monocrystals, resistivity  depends also on  individually.
To compensate for the non-linear characteristics and inability to detect the polarity of a magnetic field, the following structure is used for sensors. It consists of stripes of aluminum or gold placed on a thin film of permalloy (a ferromagnetic material exhibiting the AMR effect) inclined at an angle of 45°. This structure forces the current not to flow along the “easy axes” of thin film, but at an angle of 45°. The dependence of resistance now has a permanent offset which is linear around the null point. Because of its appearance, this sensor type is called barber pole.
The AMR effect is used in a wide array of sensors for measurement of Earth's magnetic field (electronic compass), for electric current measuring (by measuring the magnetic field created around the conductor), for traffic detection and for linear position and angle sensing. The biggest AMR sensor manufacturers are Honeywell, NXP Semiconductors, STMicroelectronics, and [http://www.sensitec.com Sensitec GmbH].
As theoretical aspects, I. A. Campbell, A. Fert, and O. Jaoul (CFJ)  derived an expression of the AMR ratio for Ni-based alloys using the two-current model with s-s and s-d scattering processes, where s is a conduction electron and d is 3d states with the spin-orbit interaction. The AMR ratio is expressed as
with  and , where , , and  are a spin-orbit coupling constant (so-called ), an exchange field, and a resistivity for spin , respectively. In addition, recently, Satoshi Kokado et al. have obtained the general expression of the AMR ratio for 3d transition-metal ferromagnets by extending the CFJ theory to a more general one. The general expression can also be applied to half-metals.