Geometrical 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 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. 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 = carrier mobility. Solving for the velocity, we find:
where the reduction in mobility due to the B-field is apparent. Electric current (proportional to the radial component of velocity) will decrease with increasing magnetic field and hence the resistance of the device will increase. 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 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%.
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