Magnetoresistance
Magnetoresistance is the tendency of a material (often ferromagnetic) to change the value of its electrical resistance in an externally-applied magnetic field.
The first magnetoresistive effect was discovered in 1856 by William Thomson, better known as Lord Kelvin, but he was unable to lower the electrical resistance of anything by more than 5%.
Today, systems including semimetals[3] and concentric ring EMR structures are known.
Since different mechanisms can alter the resistance, it is useful to separately consider situations where it depends on a magnetic field directly (e.g. geometric magnetoresistance and multiband magnetoresistance) and those where it does so indirectly through magnetization (e.g. AMR and TMR).
William Thomson (Lord Kelvin) first discovered ordinary magnetoresistance in 1856.
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.
In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of giant magnetoresistance.
[5] An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc (see Figure).
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.
[6] 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:
where the effective reduction in mobility due to the B-field (for motion perpendicular to this field) is apparent.
Critically, this magnetoresistive scenario depends sensitively on the device geometry and current lines and it does not rely on magnetic materials.
In a semiconductor with a single carrier type, the magnetoresistance is proportional to (1 + (μB)2), where μ is the semiconductor mobility (units m2·V−1·s−1, equivalently m2·Wb−1, or T −1) and B is the magnetic field (units teslas).
The effect arises in most cases from the simultaneous action of magnetization and spin–orbit interaction (exceptions related to non-collinear magnetic order notwithstanding)[8] and its detailed mechanism depends on the material.
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.
[9] AMR of new materials is being investigated and magnitudes up to 50% have been observed in some uranium (but otherwise quite conventional) ferromagnetic compounds.
[10] Materials with extreme AMR have been identified[11] 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 φ = ψ − θ 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[12]
In monocrystals, resistivity ρ depends also on ψ and θ 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.
The biggest AMR sensor manufacturers are Honeywell, NXP Semiconductors, STMicroelectronics, and Sensitec GmbH.
A. Campbell, A. Fert, and O. Jaoul (CFJ) [13] 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.
In addition, recently, Satoshi Kokado et al.[14][15] have obtained the general expression of the AMR ratio for 3d transition-metal ferromagnets by extending the CFJ theory to a more general one.
