Single-molecule magnet ${\mathrm{Mn}}_{12}$ on graphene

We study energetics, electronic and magnetic structures, and magnetic anisotropy barriers of a monolayer of single-molecule magnets (SMMs), ${\left[{\mathrm{Mn}}_{12}{\mathrm{O}}_{12}(\mathrm{COO}R\right)}_{16}]{\left({\text{H}}_2\text{O}\right)}_4$ (abbreviated as ${\mathrm{Mn}}_{12}$, with $R=\mathrm{H}$, ${\mathrm{CH}}_3$, ${\mathrm{C}}_6{\mathrm{H}}_5$, and ${\mathrm{CHCl}}_2$), on a graphene surface using spin-polarized density-functional theory with generalized gradient corrections and the inclusion of van der Waals interactions. We find that ${\mathrm{Mn}}_{12}$ molecules with ligands -H, ${\text{-CH}}_3$, and -${\mathrm{C}}_6{\mathrm{H}}_5$ are physically adsorbed on graphene through weak van der Waals interactions, and a much stronger ionic interaction occurs using a -${\mathrm{CHCl}}_2$ ligand. The strength of bonding is closely related to the charge transfer between the molecule and the graphene sheet and can be manipulated by strain in the graphene; specifically, tension enhances $n$ doping of graphene, and compression encourages $p$ doping. The magnetic anisotropy barrier is computed by including the spin-orbit interaction within density-functional theory. The barriers for the ${\mathrm{Mn}}_{12}$ molecules with ligands -H, -${\mathrm{CH}}_3$ and -${\mathrm{C}}_6{\mathrm{H}}_5$ on graphene surfaces remain unchanged (within $1\mathrm{K}$) from those of isolated molecules because of their weak interaction, and a much larger reduction ($10\mathrm{K}$) is observed when using the ${\text{-CHCl}}_2$ ligand on graphene due to a substantial structural deformation as a consequence of the much stronger interaction. Neither strain in graphene nor charge transfer affects the magnetic anisotropy barrier significantly. Finally, we discuss the effect of strong correlation in the high-spin state of a ${\mathrm{Mn}}_{12}$ SMM and the consequence of SMM-surface adsorption.

Figure 1

Schematic (a) top and (b) side views of a ${\mathrm{Mn}}_{12}$ molecule with $R={\text{-CHCl}}_2$ adsorbed onto a graphene surface. The Mn ions in three symmetry positions are denoted as I, II, and III. In supercell calculations, a vacuum layer of more than $12\AA$ is placed above the ${\mathrm{Mn}}_{12}$ molecule. Green arrows indicate strain for both tension and compression. Strain is applied uniformly in graphene along both the zigzag and armchair directions. (c1) Top view of two ligands in contact with graphene and (c2) 12 Mn ions on graphene.

Figure 2

(a) Charge transfer between the graphene surface and ${\mathrm{Mn}}_{12}$ molecules with different ligands and the total magnetic moment of the combined systems. Positive charge transfer means graphene is $p$ doped, and negative charge transfer means it is $n$ doped. Under tension, graphene has a 5% uniform tensile strain, and compression means graphene is uniformly compressed by 3%. (b) Projected density of state (PDOS) of graphene under different strains for ligand -${\mathrm{CHCl}}_2$.

Figure 3

Total spin-resolved DOS and PDOS of Mn $d$ and O $p$ orbitals (top) in a ${\mathrm{Mn}}_{12}$ molecule with the ligand -${\mathrm{CHCl}}_2$ adsorbed on a graphene system and (bottom) in the isolated ${\mathrm{Mn}}_{12}$ molecule with the ligand -${\mathrm{CHCl}}_2$. The total DOS for both spin up and spin down are scaled by a factor of $\frac{1}{3}$ for the combined system (top) and a factor of $\frac{1}{2}$ for the isolated molecule (bottom). The zero of the energy denotes the Fermi level for the combined system and the midpoint between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) for the isolated molecule system. The smearing parameter is $\sigma =0.05\mathrm{eV}$.

Figure 4

Bonding energy of ${\mathrm{Mn}}_{12}$ with different ligands adsorbed on the graphene surface and the magnitude of charge transfer between the graphene surface and the molecule.

Figure 5

Total spin-resolved DOS and PDOS of Mn $d$ and O $p$ orbitals in an isolated high-spin-state ${\mathrm{Mn}}_{12}$ molecule with ligand -${\mathrm{CHCl}}_2$ (top row) and in the molecule adsorbed on graphene (bottom row) from GGA calculations (left column) and GGA + $U$ calculations (right column). Again, the total DOS is scaled by a factor of $\frac{1}{3}$ for the combined system and $\frac{1}{2}$ for the isolated molecule. The zero of the horizontal scale denotes the midpoint between HOMO and LUMO for isolated molecules (top row) and the Fermi level for molecules adsorbed on graphene (bottom row). The smearing parameter is $\sigma =0.05\mathrm{eV}$.

Figure 6

The HOMO-LUMO gap and total magnetization (M) as a function of the Hubbard $U$ values for an isolated ${\mathrm{Mn}}_{12}$ molecule with ligands -${\mathrm{CHCl}}_2$ and -${\mathrm{CH}}_3$ in (a) high-spin and (b) low-spin states.