Four-layer CIP sheet resistance ($G_P=2D^2(1/a+1/b),G_{AP}=8D^2/(a+b)$)

Let $D=t_1+t_2$, $a=t_1{\rho }_L+t_2{\rho }_N$ and $b=t_1{\rho }_H+t_2{\rho }_N$. A square of four layers has total thickness $2D$. For parallel moments its channel sheet resistances are $a/(2D^2)$ and $b/(2D^2)$; for antiparallel moments both are $(a+b)/(4D^2)$. Adding parallel spin conductances gives the title. The factor of four-layer thickness is essential; changing the normalization changes the prefactors. The nonmagnetic bulk resistivity would be ${\rho }_N/2$ when ${\rho }_N$ is this model's per-spin value.