Magnetoresistance

Magnetoresistance is the tendency of a material (preferably ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance: some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions), giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed. Magnetoresistance is the tendency of a material (preferably ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field. There are a variety of effects that can be called magnetoresistance: some occur in bulk non-magnetic metals and semiconductors, such as geometrical magnetoresistance, Shubnikov de Haas oscillations, or the common positive magnetoresistance in metals. Other effects occur in magnetic metals, such as negative magnetoresistance in ferromagnets or anisotropic magnetoresistance (AMR). Finally, in multicomponent or multilayer systems (e.g. magnetic tunnel junctions), giant magnetoresistance (GMR), tunnel magnetoresistance (TMR), colossal magnetoresistance (CMR), and extraordinary magnetoresistance (EMR) can be observed. The first magnetoresistive effect was discovered by William Thomson, better known as Lord Kelvin, in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. Nowadays, systems, e.g. semimetals or concentric ring EMR structures, are known where a magnetic field can change resistance by orders of magnitude. As the resistance may depend on magnetic field through various mechanisms, it is useful to separately consider situations where it depends on magnetic field directly, e.g. geometric magnetoresistance and multiband magnetoresistance, and those where it does so indirectly through magnetisation, e.g. AMR, TMR. William Thomson (Lord Kelvin) first discovered ordinary magnetoresistance in 1856. He experimented with pieces of iron and discovered that the resistance increases when the current is in the same direction as the magnetic force and decreases when the current is at 90° to the magnetic force. He then did the same experiment with nickel and found that it was affected in the same way but the magnitude of the effect was greater. This effect is referred to as anisotropic magnetoresistance (AMR). In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of Giant Magnetoresistance. An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc (see Figure).It consists of a conducting annulus with perfectly conducting rims. Without a magnetic field, the battery drives a radial current between the rims. When a magnetic field perpendicular to the plane of the annulus is applied, (either into or out of the page) a circular component of current flows as well, due to Lorentz force. Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911. In a simple model, supposing the response to the Lorentz force is the same as for an electric field, the carrier velocity v is given by: