I don't know how to calculate magnetic scalar potential due to spherical shell with inner radius $R_1$ and outer radius $R_2$. The magentization is uniform and in $z$ direction ($\vec{M} = M_0\hat{k}$). My first attempt was the following: $$ \varphi_{ext}^* = \sum_{n=0}^{\infty}\frac{D_n}{r^{n+1}}P_n(\cos{\theta}) \\ \varphi_{int}^* = \sum_{n=0}^{\infty}C_nr^nP_n(\cos{\theta}) $$ Of course, the tangent component of $\vec{H}$ must be continuous at $r=R_2$ and the normal component of $\vec{B}$ must be continuous too.
But in the region $ R1 \le r \le R_2$ I don't know how is the expression for the scalar potential. Any comment or sugestion will be very helpful