  Three two-dimensional phosphorus nitride (PN) monolayer sheets (named as
$\alpha$-, $\beta$-, and $\gamma$-PN, respectively) with fantastic structures
and properties are predicted based on first-principles calculations. The
$\alpha$-PN and $\gamma$-PN are buckled structure, whereas $\beta$-PN shows
puckered characteristics. Their unique structures endows these atomic PN sheets
with high dynamic stabilities and anisotropic mechanical properties. They are
all indirect semiconductors and their band gap sensitively depends on the
in-plane strain. Moreover, the nanoribbons patterned from these three PN
monolayers demonstrate remarkable quantum size effect. Particularly, the Zigzag
$\alpha$-PN nanoribbon shows size-dependent ferromagnetism. Their significant
properties show potential in nano-electronics. The synthesis of the three
phases of PN monolayer sheets is proposed theoretically, which is deserved to
further study in experiments.
