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 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. See also Giant magnetoresistance Tunnel magnetoresistance Colossal magnetoresistance Extraordinary magnetoresistance Magnetoresistive random-access memory Footnotes 1. The (ordinary) Hall effect changes sign upon magnetic field reversal and it is an orbital effect (unrelated to spin) due to the Lorentz force. Transversal AMR (planar Hall effect) does not change sign and it is caused by spin-orbit interaction. References Magnetic ordering Spintronics Articles containing video clips