  Two-dimensional (2D) half-metallic materials that have sparked intense
interest in advanced spintronic applications are essential to the developing
next-generation nanospintronic devices. Here we have adopted a first-principles
calculation method to predict the magnetic properties of intrinsic, Se-doped,
and biaxial strain tuning Cr$_2$AsP monolayer. The Janus Cr$_2$AsP monolayer is
proved to be an intrinsic ferromagnetic (FM) semiconductor with a exchange
splitting bandgap of 0.15 eV at the PBE+U level. Concentration-dependent Se
doping such as Cr$_2$As$_{1-x}$Se$_x$P (x = 0.25, 0.50, 0.75) can regulate
Cr$_2$AsP from FM semiconductor to FM half-metallicity. Specifically, the
spin-up channel crosses the Fermi level, while the spin-down channel has a
bandgap. More interestingly, the wide half-metallic bandgaps and spin bandgaps
make them have important implications for the preparation of spintronic
devices. At last, we also explore the effect of biaxial strain from -14% to 10%
on the magnetism of the Cr$_2$AsP monolayer. There appears a transition from FM
to antiferromagnetic (AFM) at a compressive strain of -10.7%, originating from
the competition between the indirect FM superexchange interaction and the
direct AFM interaction between the nearest-neighbor Cr atoms. Additionally,
when the compressive strain to -2% or the tensile strain to 6%, the
semiconducting Cr$_2$AsP becomes a half-metallic material. These charming
properties render the Janus Cr$_2$AsP monolayer with great potential for
applications in spintronic devices.
