Two-dimensional ferromagnetism with strong magnetic interactions induced by Janus-type hydrogenation in $\mathrm{Fe}{\mathrm{Se}}_2$

In this paper, using first-principles calculations, we find that single-face (Janus-type) hydrogenation induces a magnetic transition from a ${120}^{\circ }$ noncollinear antiferromagnet (AFM) to a robust ferromagnet (FM) with high Curie temperature $\left(T_{\mathrm{c}},\sim 345\mathrm{K}\right)$ and large perpendicular magnetic anisotropy (MA, $\sim 2$ meV) in two-dimensional (2D) $\mathrm{Fe}{\mathrm{Se}}_2$. This hydrogenation results in a shift of spin-down states of in-plane orbitals $\left(d_{xy}/d_{x^2-{\mathrm{y}}^2}\right)$ to the Fermi level, which is crucial in inducing the high $T_{\mathrm{c}}$ and large perpendicular MA. To clarify the strong FM, we proposed a mechanism, i.e., FM direct exchange interaction of spin-down half-filled in-plane orbitals. This interaction is different from the traditional direct exchange interactions in most 2D magnets, which tend to form AFM coupling. As the inversion symmetry is broken, a significant Dzyaloshinskii-Moriya interaction (DMI; $\sim 2.6$ meV) is also induced by the Janus-type hydrogenation. It is found that tuning the exchange integral of orbitals can change the sign of its component of the DMI, providing an approach to manipulate the chirality of magnetic order.

Figure 1

(a) Atomic structure of monolayers of $\mathrm{Fe}{\mathrm{Se}}_2, \mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ (one-face hydrogenation), and $\mathrm{Fe}{\mathrm{Se}}_2$-2H (two-face hydrogenation), the optimized structure parameters are shown in Table 1; right is the top view of $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$. Calculated band structures of (b) $\mathrm{Fe}{\mathrm{Se}}_2$, (c) $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$, and (d) $\mathrm{Fe}{\mathrm{Se}}_2$-2H.

Figure 2

(a) Schematics of magnetic ground state transition induced by the Janus-type hydrogen adsorption. (b) The magnetic moment and specific heat capacity as functions of temperature for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$. (c) Angular dependence of the magnetic anisotropic energy (MAE) for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$.

Figure 3

(a) Hydrogen height ($h$, Fe-H distance) dependence of energy difference $\mathrm{\Delta }E=E_{\mathrm{FM}}-E_{\mathrm{AFM}}$. Insert shows the schematic of the definition of $h$. (b) Variation of bond angle θ as function of $h$. (c) Spin-polarized partial density of states (PDOS) of $d$ orbitals for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ with hydrogen at $h_0, h_1$, and $h_2$. (d) Schematics of exchange interactions between Fe atoms for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ with hydrogen at different $h$.

Figure 4

(a) Dependence of magnetic anisotropic energy (MAE) for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ on $h$. Insert shows the illustration of mechanism of perpendicular magnetic anisotropy induced by the in-plane $d$ orbitals, $d_{xy}$ and $d_{x^2-y^2}$. (b) and (c) Orbital-resolved MAE for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ with hydrogen at $h_0$ and $h_2$. (d) and (f) $k$-resolved MAE for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ with hydrogen at $h_0$ and $h_2$. (e) and (g) Spin-down band structures of $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$ with hydrogen at $h_0$ and $h_2$, in-plane $d$-orbital components of each band are shown by colors.

Figure 5

(a) In-plane Dzyaloshinskii-Moriya interaction (DMI) component $d_{\parallel }$ as function of $h$ for $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$. Inset shows the DMI vectors $D_{ij}$ between the nearest neighbors of Fe atoms. (b) $h$ dependence of atomic-resolved spin-orbit coupling (SOC) energy difference $\mathrm{\Delta }{E}_{\mathrm{SOC}}$ between spin configurations with opposite chiralities. (c)-(e) Schematics of effects of types of magnetic exchange on the chiralities in $\mathrm{Fe}{\mathrm{Se}}_2\text{-H}$.