Origin of ferromagnetism of ${\text{MnSi}}_{1.7}$ nanoparticles in Si: First-principles calculations

The origin of the magnetism of ${\text{MnSi}}_{1.7}$ nanoparticles in Si is investigated using the first-principles calculations: bulk and interface effects are considered. The bulk magnetic property is expected to be affected by stoichiometry, strain, and charge accumulation. Stoichiometry and charge accumulation induce a ferromagnetic state, and strain stabilizes the ferromagnetic state. Another factor, the ${\text{MnSi}}_{1.7}/\text{Si}$ interface formation, is seen as triggering ferromagnetism strongly localized at the interface. These two mechanisms are shown to be related to the experimentally determined hard and soft components, respectively.

Figure 1

Atomic images of (a) unit cell, (b) side view, (c) top view, (d) Mn subcell, and (e) Si arrangement, of ${\text{Mn}}_4{\text{Si}}_7$ crystal. The large and small circles are Mn and Si atoms, respectively. The numbers shown in (b) indicate the symmetry type of Mn atoms. ${\text{I}}_{54}$ indicates one of the (001) planes.

Figure 2

Calculated band dispersion relations of (a) bulk ${\text{Mn}}_4{\text{Si}}_7$ and (b)–(c) bulk ${\text{Mn}}_{11}{\text{Si}}_{19}$. (d) Calculated density of states (DOS) of bulk ${\text{Mn}}_{11}{\text{Si}}_{19}$. The region near the Fermi energy is closed up in (a) and (b). Energy zero corresponds to the Fermi energy in all figures.

Figure 3

The strain effects on the total energy difference of ${\text{Mn}}_{11}{\text{Si}}_{19}$ as a function of the occupation difference between the up-spin and the down-spin states, $N_{\text{up}}-N_{\text{down}}$.

Figure 4

Schematic picture of (a) DOS for nonmagnetic ${\text{MnSi}}_{1.7}$, (b) the partial DOS of the up- and down-spin states for nonmagnetic ${\text{MnSi}}_{1.7}$, and (c) the partial DOS of the up-spin and down-spin states for ferromagnetic (half metallic) ${\text{MnSi}}_{1.7}$. The horizontal lines indicate the Fermi energy positions.

Figure 5

Total energy difference of ${\text{Mn}}_4{\text{Si}}_7$ as a function of the occupation difference of the up-spin and the down-spin states. Open circles, open diamonds, and open squares indicate hole-doped cases with the density of $+4/\text{cell}$, $+3/\text{cell}$, and $+1/\text{cell}$, respectively. Closed circles and closed diamonds indicate electron-doped cases with the density of $-7/\text{cell}$ and $-2/\text{cell}$, respectively. Closed triangle indicates neutral case.

Figure 6

Total magnetic moment as a function of the number of Mn atoms in a ${\text{Mn}}_4{\text{Si}}_7$ slab for the calculated ${\text{Mn}}_4{\text{Si}}_7/\text{Si}\left(100\right)$ interface models. The corresponding index of the interface is also shown.

Figure 7

(a) Atomic structure of the calculated ${\text{Mn}}_4{\text{Si}}_7/\text{Si}\left(100\right)$ interface model, (b) cross-sectional view of the up-spin state density distribution, (c) cross-sectional view of the down-spin state density distribution, and (d) the difference between the up-spin and the down-spin density distributions. The light and dark circles indicate Mn and Si atoms, respectively. The surface light circles denoted as hydrogen indicate H atoms.

Figure 8

Experimentally obtained mean particle size dependence of the saturation magnetization and the theoretical curves for (a) the soft and (b) the hard magnetic components. $M_{\text{s}-\text{R}}^{\text{expt}}$ and $M_{\text{s}-\text{SW}}^{\text{expt}}$ are the experimental saturation magnetization plots (Ref. 11) and the solid lines are the theoretical ones. The derivation of the theoretical curves is detailed in the paper.