  Two-dimensional (2D) magnetic materials are of current great interest for
their promising applications in spintronics. Strong magnetic coupling and
anisotropy are both highly desirable for the achievement of a high temperature
magnetic order. Here we propose the unusual high valent FeS$_2$ hexagonal
monolayer as such a candidate for a strong Ising 2D ferromagnet (FM), by
spin-orbital state analyses, first-principles calculations, and the
renormalized spin-wave theory (RSWT). We find that very importantly, the high
valent Fe$^{4+}$ ion is in the low-spin state ($t_{2g}^{4}$, $S$=1) with
degenerate $t_{2g}$ orbitals rather than the high-spin state
($t_{2g}^{3}e_g^{1}$, $S$=2). It is the low-spin state that allows to carry a
large perpendicular orbital moment and then produces a huge single ion
anisotropy (SIA) of 25 meV/Fe. Moreover, the negative charge transfer character
associated with the unusual high valence, strong Fe $3d$-S $3p$ hybridization,
wide bands, and a small band gap all help to establish a strong superexchange.
Indeed, our first-principles calculations confirm the strong FM superexchange
and the huge perpendicular SIA, both of which are further enhanced by a
compressive strain. Then, our RSWT calculations predict that the FM $T_{\rm C}$
is 261 K for the pristine FeS$_2$ monolayer and could be increased to 409 K
under the compressive --5\% strain. The high $T_{\rm C}$ is also reproduced by
our Monte Carlo (MC) simulations. Therefore, it is worth exploring the
high-$T_{\rm C}$ Ising FMs in the high valent 2D magnetic materials with
degenerate orbitals.
