Hydrogenation-induced ferromagnetism on graphite surfaces

We calculate the electronic structure and magnetic properties of hydrogenated graphite surfaces using van der Waals density functional theory (DFT) and model Hamiltonians. We find, as previously reported, that the interaction between hydrogen atoms on graphene favors adsorption on different sublattices along with an antiferromagnetic coupling of the induced magnetic moments. On the contrary, when hydrogenation takes place on the surface of graphene multilayers or graphite (Bernal stacking), the interaction between hydrogen atoms competes with the different adsorption energies of the two sublattices. This competition may result in all hydrogen atoms adsorbed on the same sublattice and, thereby, in a ferromagnetic state for low concentrations. Based on the exchange couplings obtained from the DFT calculations, we have also evaluated the Curie temperature by mapping this system onto an Ising-like model with randomly located spins. Remarkably, the long-range nature of the magnetic coupling in these systems makes the Curie temperature size dependent and larger than room temperature for typical concentrations and sizes.

Figure 1

Atomic structure of (a) single-layer and (b) bilayer graphene for a $3\times 3\times 1$ supercell.

Figure 2

Electronic band structure of monolayer, bilayer, five-layer graphene, and graphite calculated with a $100\times 100\times 2$ MP grid for a $1\times 1\times 1$ supercell.

Figure 3

Atomic structure of H on graphene. (a) Top and (b) side view for a $3\times 3\times 1$ supercell.

Figure 4

Relaxed atomic structure and spin polarization around an adsorbed H atom. Magnetic moments with opposite orientations are depicted by blue and red arrows for clarity.

Figure 5

Total density of states for a H atom on single-layer graphene calculated with a $6\times 6\times 1$ supercell.

Figure 6

Atomic view of a pair of H atoms on a graphene monolayer for a $12\times 12\times 1$ supercell.

Figure 7

Spin density (blue indicates up and red down) and spin-resolved total DOS for graphene monolayer with 2 H atoms sitting on AA [(a) and (c), respectively] and AB [(b) and (d), respectively] sublattices at far distances calculated with a $4\times 4\times 2$ MP grid for a $12\times 12\times 1$ supercell.

Figure 8

Total energy for a pair of H atoms on a graphene monolayer $(12\times 12\times 1$ supercell) relative to twice the adsorption energy of a single atom. Both AA and AB cases are shown.

Figure 9

Top view of the atomic structure of H on bilayer graphene for (a) $\alpha$ and (b) $\beta$ sites on a $4\times 4\times 1$ supercell.

Figure 10

Adsorption energy difference between the two sites $(\alpha$ and $\beta )$ of bilayer graphene against different cell sizes.

Figure 11

Total energy for two H atoms on bilayer graphene as a function of distance.

Figure 12

Relaxed atomic structure and spin polarization around an adsorbed H atom at $\beta$ site on a four-layer graphene surface. Magnetic moments are depicted by blue(red) arrows for spin-up(spin-down) for clarity.

Figure 13

Exchange energy for a pair of H atoms adsorbed on the same sublattice.

Figure 14

Absolute magnetization per spin for supercells sizes in the range $L=24.6$ nm $(L=100$ supercell units) and 123 nm $(L=500$ supercell units), using concentrations (a) $C=0.0005$ and (b) 0.0010.

Figure 15

Fourth-order cumulant for supercells sizes in the range $L=24.6$ nm $(L=100$ supercell units), and 123 nm $(L=500$ supercell units), using concentrations (a) $C=0.0005$ and (b) 0.0010.

Figure 16

Fourth-order cumulant for (a) $LC=0.2$, (b) $LC=1.0$, (c) $LC=2.0$, and (d) $LC=4$, using supercell sizes $L=80$, 160, 320, 460, and 1280.

Figure 17

Critical temperature against LC.

Figure 18

Magnetization square vs temperature over critical temperature computed with Monte Carlo and compared with the mean-field result for various concentrations and sizes.