Let $S=Spec R$, $s=Spec\: k$ and $\eta=Spec\:K$, where $R$ is a d.v.r. with fraction field $K$. Let $j:\eta\rightarrow S$

Now how to computer the sheaf $R^1j_*(\mathbb{G}_{m,\eta})$ in the fppf topology?

The case for etale topology is zero by considering the stalks and use the Hilbert 90.