Modulating superexchange interactions in the two-dimensional high Curie temperature ferromagnetic semiconductors $\mathrm{Mo}XY (X=\mathrm{S},\mathrm{Se};Y=\mathrm{Br},\mathrm{I})$

Two-dimensional ferromagnetic semiconductors are gaining increasing interest because of their promising applications in spintronics. However, the applications are greatly hindered by the weak ferromagnetic couplings and low Curie temperatures. Therefore, rationally designing two-dimensional ferromagnetic semiconductors with high Curie temperatures and enhancing their Curie temperatures are highly desirable, which inevitably requires a fundamental understanding of modulating superexchange interactions. Here, we propose two-dimensional intrinsic ferromagnetic semiconductors $\mathrm{Mo}\mathit{XY}$ $(X\hspace{0.17em}=\hspace{0.17em}\mathrm{S},\mathrm{Se};Y\hspace{0.17em}=\hspace{0.17em}\mathrm{Br},\mathrm{I})$. They are predicted to have unique quasi-1D transport behavior, high Curie temperatures (ranging from 290 K to 322 K), and large magnetic anisotropy energy. Based on the Kanamori's mechanism, we propose a general path-resolved indicator of the superexchange interaction strength to unravel how ferromagnetic superexchange interactions are modulated by two heavily used strategies, namely, ligand substitution and strain engineering. Our paper could provide a fundamental understanding of modulating superexchange interactions in two-dimensional ferromagnetic semiconductors.

Figure 1

(a) Top and side view of the $\mathrm{Mo}\mathit{XY}$ monolayers; (b) the relations between the Cartesian axes and the crystallographic axes, (c) electronic band structure of MoSeI, and (d) PDOS of MoSeI.

Figure 2

Schematic representations for (a) the superexchange interactions according to Kanamori's superexchange mechanism and the direct exchange interactions (b) for $J_1$ and $J_2$ and (c) for $J_3$.

Figure 3

Superexchange interaction strength indicators and virtual exchange gaps for $\mathrm{Mo}\mathit{XY}$ monolayers.

Figure 4

(a) Exchange interaction parameters, Curie temperatures, and (b) superexchange interaction strength indicators and virtual exchange gaps in MoSeI as functions of the uniaxial strain along the $a$ axis.

Figure 5

(a) Exchange interaction parameters, Curie temperatures, and (b) superexchange interaction strength indicators and virtual exchange gaps in MoSeI as functions of the uniaxial strain along the $b$ axis.