  Two-dimensional structures that exhibit intriguing magnetic phenomena such as
perpendicular magnetic anisotropy and switchable magnetization are of great
interests in spintronics research. Herein, the density-functional theory
studies reveal the critical impacts of strain and external gating on
vacancy-induced magnetism and its spin direction in a graphene-like single
layer of zinc oxide (ZnO). In contrast to the pristine and defective ZnO with
an O-vacancy, the presence of a Zn-vacancy induces significant magnetic moments
to its first neighboring O and Zn atoms due to the charge deficit. We further
predict that the direction of magnetization easy axis reverses from an in-plane
to perpendicular orientation under a practically achieved biaxial compressive
strain of $\sim$1--2\% or applying an electric-field by means of the charge
density modulation. This magnetization reversal is driven by the strain- and
electric-field-induced changes in the spin-orbit coupled \emph{d} states of the
first-neighbor Zn atom to the Zn-vacancy. These findings open interesting
prospects for exploiting strain and electric-field engineering to manipulate
magnetism and magnetization orientation of two-dimensional materials.
