Cubulating hyperbolic free-by-cyclic groups: the general case
  Let $\Phi:F\rightarrow F$ be an automorphism of the finite-rank free group $F$. Suppose that $G=F\rtimes_\Phi\mathbb Z$ is word-hyperbolic. Then $G$ acts freely and cocompactly on a CAT(0) cube complex. 
Mark F. Hagen and Daniel T. Wise
math.GR