Hydrogen adsorption induced nanomagnetism at the Si(111)-$\left(7\times 7\right)$ surface

The creation of magnetism on nonmagnetic semiconductor surfaces is of importance for the realization of spintronics devices. In particular, the coupling of electron spins within quantum nanostructures can be utilized for nanomagnetism applications. Here, we demonstrate, based on first-principles density-functional theory calculations, that the adsorption of H atoms on the Si(111)-$\left(7\times 7\right)$ surface induces the spin polarization of surrounding Si dangling bonds (DBs) and their spin orderings. It is revealed that the H adsorption on a rest-atom site exhibits a Jahn-Teller-like distortion that accompanies a charge transfer from the rest atom to the nearest-neighboring adatoms. This charge transfer increases the local density of states of three such adatoms at the Fermi level, thereby inducing a Stoner-type instability to produce a ferrimagnetic order of adatom DBs around the adsorbed H atom. Meanwhile, the H adsorption on an adatom site cannot induce spin polarization, but, as adsorbed H atoms increase, the ferrimagnetic order of rest-atom DBs emerges through the charge transfer from rest atoms to adatoms. Our findings provide a microscopic mechanism of the H-induced spin orderings of Si DBs at the atomic scale, which paves the way for the design of nanoscale magnetism in the representative semiconductor surface.

Figure 1

(a) Top and side views of the optimized structure of the Si(111)-$\left(7\times 7\right)$ surface. The colored large, medium, and small circles represent the adatoms $\left(A\right)$, rest atoms $\left(R\right)$, and corner-hole atoms $\left(C\right)$, respectively. F and UF represent the faulted and unfaulted half-cells, respectively. The adatoms and rest atoms in the F half-cell are numbered. The calculated band structure of the Si(111)-$\left(7\times 7\right)$ surface is given in (b). Here, the bands originating from $A,R$, and $C$ atoms are distinguished with the same colors as used in (a), and the energy zero represents the Fermi level. The surface Brillouin zone of the $7\times 7$ unit cell is drawn in the inset of (b). The LDOS obtained at $R_1,A_1$, and $A_2$ is given in (c).

Figure 2

(a) Calculated LDOS of the $R_1,A_1$, and $A_2$ atoms for the adsorption of a single H atom on the rest atom $R_1$, obtained using the spin-unpolarized DFT calculation. In (b), the schematic diagram for the interaction of an adsorbed H atom with the rest atom is displayed. The filled (open) circles represent the full (partial) occupation of spin-up or -down electrons, while the arrow indicates charge transfer. The top view of spin density is displayed in (c), together with the side view taken in the cross section along the dashed line. The majority (minority) spin density is displayed by a bright (dark) color with an isosurface of 0.$014\left(-0.014\right)e$/Å${}^3$. The numbers in (c) represent the spin moments (in ${\mu }_{\mathrm{B}})$ for the $A_1,A_2$, and $A_6$ atoms. The spin-polarized LDOS of $A_1$ and $A_2$ is given in (d). $E_{\mathrm{ex}}$ represents the exchange splitting of majority and minority bands.

Figure 3

(a) Calculated LDOS of the $R_1,A_1$, and $A_2$ atoms for the adsorption of a single H atom on the adatom $A_2$, obtained using the spin-unpolarized DFT calculation. In (b), the schematic diagram for the interaction of an adsorbed H atom with the adatom is displayed. The filled (open) circles represent the full (partial) occupation of spin-up or -down electrons, while the arrow indicates charge transfer. $A_{\mathrm{sur}}$ represents the surrounding adatoms around $A_2$.

Figure 4

(a) Spin-unpolarized and (b) spin-polarized LDOS of the $R_1$ atom for $n_A=5$. Spin densities for $n_A=5$, 6, and 12 are displayed in (c), while those for $n_R=2$, 3, and 6 are displayed in (d). Here, the majority (minority) spin density is drawn with an isosurface of 0.$014\left(-0.014\right)e$/Å${}^3$. In (c) and (d), the numbers represent the spin moments (in ${\mu }_{\text{B}})$ for rest atoms and adatoms, respectively.