  The two-dimensional 1T-CrTe$_2$ has been an attractive room-temperature van
der Waals magnet which has a potential application in spintronic devices.
Although it was recognized as a ferromagnetism in the past, the monolayer
1T-CrTe$_2$ was recently found to exhibit zigzag antiferromagnetism with the
easy axis oriented at $70^\circ$ to the perpendicular direction of the plane.
Therefore, the origin of the intricate anisotropic magnetic behavior therein is
well worthy of thorough exploration. Here, by applying density functional
theory with spin spiral method, we demonstrate that the Kitaev interaction,
together with the single-ion anisotropy and other off-diagonal exchanges, is
amenable to explain the magnetic orientation in the metallic 1T-CrTe$_2$.
Moreover, the Ruderman-Kittle-Kasuya-Yosida interaction can also be extracted
from the dispersion calculations, which explains the metallic behavior of
1T-CrTe$_2$. Our results demonstrate that 1T-CrTe$_2$ is potentially a rare
metallic Kitaev material.
