# Magnetoresistance

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Magnetoresistance is the property of a material to change the value of its electrical resistance when an external magnetic field is applied to it. The effect was first discovered by William Thomson (more commonly known as Lord Kelvin) in 1856, but he was unable to lower the electrical resistance of anything by more than 5%. This effect was later called ordinary magnetoresistance (OMR). More recent researchers discovered materials showing giant magnetoresistance (GMR), colossal magnetoresistance (CMR) and magnetic tunnel effect (TMR).

## Contents

### Discovery

William Thomson (or 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).

### The Corbino disc

Figure 1 illustrates the 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 parallel to the axis of the annulus is applied, a circular component of current flows as well, due to the Lorentz force. A discussion of the disc is provided by Giuliani.[1] Initial interest in this problem began with Boltzmann in 1886, and independently was re-examined by Corbino in 1911.[1]

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 = carrier mobility. Solving for the velocity, we find:

where the reduction in mobility due to the B-field is apparent.

### Anisotropic magnetoresistance (AMR)

AMR[2] is the property of a material in which a dependence of electrical resistance on the angle between the direction of electric current and orientation of magnetic field is observed. The effect is attributed to a larger probability of s-d scattering of electrons in the direction of magnetic field. The net effect is that the electrical resistance has maximum value when the direction of current is parallel to the applied magnetic field. AMR up to 50% has been observed in some ferromagnetic uranium compounds [3].

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 or T −1) and B is the magnetic field (units teslas). 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%.