Magnetoresistance


Magnetoresistance is the tendency of a material 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. Finally, in multicomponent or multilayer systems, giant magnetoresistance, tunnel magnetoresistance, colossal magnetoresistance, and extraordinary magnetoresistance 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%. Today, 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.

Discovery

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.
drives a circular component of current, and the resistance between the inner and outer rims goes up. This increase in resistance due to the magnetic field is called magnetoresistance.
In 2007, Albert Fert and Peter Grünberg were jointly awarded the Nobel Prize for the discovery of Giant Magnetoresistance.

Geometrical magnetoresistance

An example of magnetoresistance due to direct action of magnetic field on electric current can be studied on a Corbino disc.
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, 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:
where μ is the carrier mobility. Solving for the velocity, we find:
where the effective reduction in mobility due to the B-field is apparent. Electric current will decrease with increasing magnetic field and hence the resistance of the device will increase. 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, where μ is the semiconductor mobility and B is the magnetic field. Indium antimonide, an example of a high mobility semiconductor, could have an electron mobility above 4 m2·V−1·s−1 at 300 K. So in a 0.25 T field, for example the magnetoresistance increase would be 100%.

Anisotropic magnetoresistance (AMR)

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 from the simultaneous action of magnetization and spin-orbit interaction 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. The net effect 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 ferromagnetic uranium compounds.
In polycrystalline ferromagnetic materials, the AMR can only depend on the angle between the magnetization and current direction
and, it must follow
where is the resistivity of the film and are the resistivities for and, respectively. Associated with longitudinal resistivity, there is also transversal resistivity dubbed 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 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, for electric current measuring, for traffic detection and for linear position and angle sensing. The biggest AMR sensor manufacturers are Honeywell, NXP Semiconductors, STMicroelectronics, and .
As theoretical aspects, I. A. Campbell, A. Fert, and O. Jaoul 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, 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.

Footnotes