= GMR ratio for identical thickness-averaged layers
{c}
{title2=$(R_{AP}-R_P)/R_P=(a-b)^2/(4ab)$}
From the <four-layer CIP sheet resistance>, $R_P=ab/[2D^2(a+b)]$ and $R_{AP}=(a+b)/(8D^2)$. Subtraction gives $R_{AP}-R_P=(a-b)^2/[8D^2(a+b)]\ge0$ for positive channels. The ratio in the title normalizes by the low-resistance state; normalizing by the high-resistance state instead gives $(a-b)^2/(a+b)^2$. Common spacer scattering adds equally to $a,b$, diluting the contrast. The result assumes identical magnetic layers; arbitrary materials need not have the same sign of spin asymmetry.
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