 GMR ratio for identical thickness-averaged layers

From the four-layer CIP sheet resistance, $R_P=ab/[2D^2(a+b)]$ and $R_{AP}=(a+b)/(8D^2)$. Subtraction gives $R_{AP}-R_P=(a-b{)}^2/[8D^2(a+b)]\ge 0$ 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.