Torsion graded pieces of Nyggard filtration for crystalline representation

Let $K$ be a unramified $p$-adic field with the absolute Galois group $G_K$ and $T$ a crystalline ${\mathbb{Z}}_p$-representation of $G_K$. We study the graded pieces of integral filtration on $D_{\mathrm{d}\mathrm{R}}(T)$ given by Nyggard filtration of the attached Breuil-Kisin module of $T$. We show that the $i$-graded piece has nontrivial $p$-torsion only if $i=r_j+mp$ for a Hodge-Tate weight $r_j$ of $T$ and $m$ a positive integer.