Tunnelling magnetoresistance

tunnelling magnetoresistance is the dependence of a magnetic tunnel junction's electrical resistance on the relative magnetizations of its electrodes. A common convention is $(R_{AP}-R_P)/R_P$, where the subscripts denote antiparallel and parallel alignment. Its magnitude and sign depend on effective spin-polarized transmission through the particular interfaces and barrier.

Assume spin-conserving, low-voltage tunnelling and a spin-independent matrix element. Then parallel conductance is proportional to $D_{1\uparrow }{D}_{2\uparrow }+D_{1\downarrow }{D}_{2\downarrow }$, while antiparallel conductance has the crossed products. Define $P_i=(D_{i\uparrow }-D_{i\downarrow })/(D_{i\uparrow }+D_{i\downarrow })$. The two conductances are $G_0(1\pm P_1{P}_2)$; taking their reciprocals and using the resistance-ratio convention proves the displayed formula. Orbital filtering and interface-dependent matrix elements can invalidate a bulk-density-of-states estimate.