Strain control of magnetism in graphene decorated by transition-metal atoms

We report a strain-controlled tuning of magnetism in graphene decorated by transition-metal (TM) atoms. Our first-principles calculations demonstrate that strain can lead to a sudden change in the magnetic configuration of a TM adatom and the local atomic structure in the surrounding graphene layer. A strong spin-dependent hybridization between TM $d$ and graphene $\pi$ orbital states, derived from the orbital selection rule of the local lattice symmetry, is responsible for the determination of the local electronic and magnetic structure. Our results indicate that the strain can be an effective way to control the magnetism of atomic-scale nanostructures, where the reliable control of their magnetic states is a key step for the future spintronic applications.

Figure 1

(a) Magnetic moments of Mn atoms adsorption on PG and defective graphene with a SV as a function of strain. (b) The heights between Mn atoms and the nearest C atoms as a function of strain for Mn-PG and Mn-SV systems. (c) The average bond lengths between Mn atoms and the nearest C atoms as a function of strain for Mn-PG and Mn-SV systems. (d) The binding energies of Mn atoms on graphene as a function of strain for Mn-PG and Mn-SV systems. (e) The local structure transition for Mn-SV system from $\eta$ $=$ 0 (up structure) to $\eta =-0.04$ (down structure).

Figure 2

Schematic drawings of the energy diagrams of Mn atom and graphene electronic states near the Fermi level ($E_F$) for (a) Mn atom on PG under $\eta$ $=$ 0, (b) Mn atom on PG under $\eta$ $=$ 0.05, (c) Mn atom on graphene with SV under $\eta$ $=$ 0, and (d) Mn atom on graphene with SV under $\eta =-0.04$. The local electronic structure of graphene is represented by the occupied $\pi$ and unoccupied ${\pi }^{☆}$ levels arising from C $p_{\pi }$ bands, which touch at the $K$ point in the orignal Brillouin zone of graphene. In (c), three dangling bond orbitals of C atoms near SV form one bonding state, labeled as $D_a$, and two degenerate nonbonding states, labeled as $D_e$. While the bonding $D_a$ level is close to $\pi$, the nonbonding $D_e$ level is located just above $E_F$. In (d), the distortion and formation of C-C pair gives rise to the bonding and antibonding states $D_B$ and $D_{AB}$, which stay far away from the Fermi level, and one nonbonding dangling bond state $D_N$ just above $E_F$.

Figure 3

The range of magnetic moments of TM atoms adsorption on graphene (a) without vacancy, (b) with SV, (c) with DV under $-0.05⩽\eta ⩽0.10$. The intrinsic magnetic moments of TM-graphene without strain are shown as green lines, while the maximum and minimum magnetic moments of TM-graphene caused by compressive (or tensible) strain (in unit of %) are shown by blue (or red) line.