  We have successfully synthesized the novel antiferromagnets with Ir$^{4+}$
honeycomb lattice ZnIrO$_3$ and MgIrO$_3$ and investigated their magnetic and
thermodynamic properties. The two iridates are isomorphic but exhibit
qualitatively different magnetic properties. ZnIrO$_3$ shows antiferromagnetic
ordering below 46.6 K, whereas MgIrO$_3$ displays weak ferromagnetic behavior
below 31.8 K owing to formation of a canted antiferromagnetic ordering. The
measurement of magnetic susceptibility with using an oriented powder sample
revealed the presence of an XY-like magnetic anisotropy and a tilting magnetic
structure which is possibly stabilized by the Kitaev interaction. Moreover,
magnetization curves of MgIrO3 and ZnIrO3 up to 60 T show different behaviors,
demonstrating that each magnetic ground state is different with each other. We
discuss the difference in the ground state between MgIrO$_3$ and ZnIrO$_3$ from
the viewpoint a magnetic model consisting of the Kitaev and
Dzyaloshinskii-Moriya interactions with the spin frustration effect on the
honeycomb lattice.
