Effect of magnetic field on the electrical properties:

This can be shown vectorially as demonstrated in Figure 27.01, where the angle ø is the Hall angle.

The only way to get MR (within free electron model) is to consider a system with two types of electrons. This is often referred as a two-band model because of its application to semiconductors where the magnetoresistance results from the presence of electrons and holes.

Figure 27.01: Vectorial representation of current density and magnetic field.

Hence, we have to treat the two types of electrons, labeled 1 and 2, separately and combine the vector diagram for j1 and j2. The net result is that to first order the normal magnetoresistance is given by

and simplifies to

Hence, normal MR is always positive, but directly proportional to square of applied magnetic field. Nevertheless, the magnitude varies widely depending on the resistivity of the sample.