${\mathrm{Fe}}_n$ ($n=1–6$) clusters chemisorbed on vacancy defects in graphene: Stability, spin-dipole moment, and magnetic anisotropy

In this work, we have studied the chemical and magnetic interactions of ${\mathrm{Fe}}_n$ ($n=1–6$) clusters with vacancy defects (monovacancy to correlated vacancies with six missing C atoms) in a graphene sheet by ab initio density functional calculations combined with Hubbard $U$ corrections for correlated Fe-$d$ electrons. It is found that the vacancy formation energies are lowered in the presence of Fe, indicating an easier destruction of the graphene sheet. Due to strong chemical interactions between Fe clusters and vacancies, a complex distribution of magnetic moments appear on the distorted Fe clusters which results in reduced averaged magnetic moments compared to the free clusters. In addition to that, we have calculated spin-dipole moments and magnetic anisotropy energies. The calculated spin-dipole moments arising from anisotropic spin density distributions vary between positive and negative values, yielding increased or decreased effective moments. Depending on the cluster geometry, the easy axis of magnetization of the Fe clusters shows in-plane or out-of-plane behavior.

Figure 1

Potential energy (P.E.) landscape as a function of simulation time. Figures (a)–(h) show the snapshots at different simulation times. These snapshots are also marked by arrow in the P.E. graph. Figure (i) shows the optimized geometry after the completion of MD simulation for 30 ps. Cyan and red balls indicate C and Fe atoms, respectively. See text in Sec. 3a for more details.

Figure 2

Geometries and spin densities of vacancy defects in graphene. Figures (a) to (f) represents the vacancy $V_1$ to $V_6$, respectively. Yellow isosurface denotes the spin density of the system. The numbers on each figure denote the bond length in Å.

Figure 3

Geometries and spin density of Fe${}_n$ clusters on $V_n$ vacancies ($n=1–3$) are shown together. Cyan and red balls indicate C and Fe atoms, respectively. Yellow and blue isosurface denotes positive and negative spin densities.

Figure 4

Geometries and spin densities of Fe${}_n$ clusters on $V_n$ vacancies ($n=4–6$) are shown together. Cyan and red balls indicate C and Fe atoms, respectively. Yellow and blue isosurface denotes positive and negative spin densities.

Figure 5

Comparison of total DOS for (a) Fe${}_1$ on $V_1$ and (b) Fe${}_6$ on $V_6$. We have plotted DOS for pure vacancy (red lines) and the Fe cluster adsorbed in vacancy without $U$ (green lines) and with $U$ (shaded region).

Figure 6

$m_l$ decomposed DOS for Fe atom for the system Fe${}_1$ in one vacancy. Figures (a) and (b) are within PBE and PBE$+U$ formalism, respectively.