Transistors can be modelled as a barrier potential, with the voltage across them represented by different potentials on either side.
The rapid variation in transmission coefficient (current) with change in potential barrier (voltage) is the basis of the transistor The name come from ‘transfer resistor’. The resistance to motion of electrons past the barrier is determined by the voltage \(V_0\) in the barrier region more than the voltage difference across the transistor.
Actual behavior also depends on the availability of electrons for conduction, which depends in turn on the material in question, since there must be available electron states of appropriate energy on each side of the barrier.
In GMR a series of barriers are created from layers of ferromagnetic material and a spacer chosen to make the layer align antiferromagnetically (e.g. FeCrFe). Conduction electrons with spin opposite to the magnetic moment pass easily through iron (there are many state available to them). So oppositely aligned layers form a series of barriers to either spin. An external magnetic field applied to the GMR causes all the ferromagnetic layers to align, meaning there is no barrier to antialigns conduction electrons. Thus a magnetic field causes a change in resistance: GMR heads are used to “read” the magnetisation states in computer hard disks.