${\text{FeS}}_2$ monolayer: A high-valence and high-$T_C$ Ising ferromagnet

Two-dimensional (2D) magnetic materials are currently of great interest for their promising applications in spintronics. Strong magnetic coupling and anisotropy are both highly desirable for the achievement of high-temperature magnetic order. Here we propose the unusual high-valence ${\mathrm{FeS}}_2$ hexagonal monolayer as such a candidate for a strong Ising 2D ferromagnet by spin-orbital state analyses, first-principles calculations, and the renormalized spin-wave theory (RSWT). We find that, very importantly, the high-valence ${\mathrm{Fe}}^{4+}$ 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 us 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 ferromagnetic superexchange and the huge perpendicular SIA, both of which are further enhanced by a compressive strain. Then, our RSWT calculations predict that the ferromagnet $T_C$ is 261 K for the pristine ${\mathrm{FeS}}_2$ monolayer and could be increased to 409 K under −5% compressive strain. The high $T_C$ is also reproduced by our Monte Carlo simulations. Therefore, it is worth exploring high-$T_C$ Ising ferromagnets in high-valence 2D magnetic materials with degenerate orbitals.