  It is essential to explore two-dimensional (2D) material with magnetic
ordering in new generation spintronic devices. Particularly, the seeking of
room-temperature 2D ferromagnetic (FM) materials is a hot topic of current
research. Here, we study magnetism of the Mn-doped and electron-doped SiC
monolayer using first-principle calculations. For the Mn-doped SiC monolayer,
we find that either electron or hole could mediate the ferromagnetism in the
system and the Curie temperature ($T_C$) can be improved by appropriate carrier
doping. The codoping strategy is also discussed on improving $T_C$. The
transition between antiferromagnetic and FM phase can be found by strain
engineering. The $T_C$ is improved above room temperature (RT) under the strain
larger than $0.06$. Moreover, the Mn-doped SiC monolayer develops half-metal at
the strain range of $0.05-0.1$. On the other hand, the direct electron doping
can induce ferromagnetism due to the van Hove singularity in density of states
of the conduction band edge of the SiC monolayer. The $T_C$ is found to be
around RT. These fascinating controllable electronic and magnetic properties
are desired for spintronic applications.
