We fix a monic polynomial $\bar f(x) \in \mathbb{F}_q[x]$ over a finite field
of characteristic $p$, and consider the
$\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower defined by $\bar f(x)$; this
is a tower of curves $\cdots \to C_m \to C_{m-1} \to \cdots \to C_0
=\mathbb{A}^1$, whose Galois group is canonically isomorphic to
$\mathbb{Z}_{p^\ell}$, the degree $\ell$ unramified extension of
$\mathbb{Z}_p$, which is abstractly isomorphic to $(\mathbb{Z}_p)^\ell$ as a
topological group. We study the Newton slopes of zeta functions of this tower
of curves. This reduces to the study of the Newton slopes of L-functions
associated to characters of the Galois group of this tower. We prove that, when
the conductor of the character is large enough, the Newton slopes of the
L-function asymptotically form a finite union of arithmetic progressions. As a
corollary, we prove the spectral halo property of the spectral variety
associated to the $\mathbb{Z}_{p^{\ell}}$-Artin-Schreier-Witt tower. This
extends the main result in [DWX] from rank one case $\ell=1$ to the higher rank
case $\ell\geq 1$.