= Density-of-states tunnelling magnetoresistance model
{title2=$\mathrm{TMR}=2P_1P_2/(1-P_1P_2)$}
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 $G_0(1\pm P_1P_2)$; 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.
Back to article page
