Dehn functions of subgroups of right-angled Artin groups

We show that for each positive integer k there exist right-angled Artin groups containing free-by-cyclic subgroups whose monodromy automorphisms grow as nk\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n^k$$\end{document}. As a consequence we produce examples of right-angled Artin groups containing finitely presented subgroups whose Dehn functions grow as nk+2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$n^{k+2}$$\end{document}.