Common-spacer dilution in the two-current model ($m=p^2/[(1+s{)}^2-p^2]$)

Define a dimensionless channel contrast $p=(b-a)/(a+b)$ and spacer ratio $s=r/(a+b)$. Positive $a,b$ give $|p|<1$, and substitution gives the displayed expression. Equal channel responses, $p=0$, eliminate the model's magnetic-configuration signal. Increasing the common spacer resistance at fixed $a,b$ increases the denominator and decreases $m$.

This is a controlled comparison within the model. In an actual multilayer, changing a spacer thickness can change the magnetic coupling and the interfaces as well as electrical transport. Spin-flip scattering also mixes the channels that the calculation kept independent.