Half-metallicity induced by charge injection in hexagonal boron nitride clusters embedded in graphene

We study the electronic structure and magnetic properties of h-BN triangular clusters embedded in graphene supercells. We find that, depending on the sizes of the clusters and the graphene separation region between them, spin polarization can be induced through charge doping or can be observed even in the neutral state. For these cases, half-metallicity is observed for certain charged states, which are otherwise metallic. In these half-metallic states, the spin density is concentrated near the edges of the clusters, in analogy to the more common predictions for half-metals in zigzag graphene nanoribbons and h-BN/graphene intercalated nanoribbons. Since experimental realizations of h-BN domains in graphene have already been reported, these heterostructures can be suitable candidates for nanoelectronics and spintronics applications.

Figure 1

(Top) An $11\times 11$ supercell containing two triangular $B_{15}{N}_{10}$ and $B_{10}{N}_{15}$ ($\Delta =5$) clusters, being a representative of all cells used in this work. The triangular clusters are facing opposite directions, with two parallel edges. Notice that one cluster contains only B atoms on the edges, whereas the other contains only N atoms. (Bottom) The same supercell pictured with three periodical images, showing the regular spacing of the clusters by $N_z=4$ graphene zigzag chains in all directions.

Figure 2

Selected results of the three general types of band structures observed in this system, as described in the text. These results are for a constant $N_z=4$ graphene separation, but different values of $N_z$ show similar trends. Energies are in eV and the Fermi level is set to zero in all panels. Note that the energy scale is different in each row. Spin-up (-down) bands are represented by black (red) lines. (a)–(c) Type 1, $B_6{N}_3+B_3{N}_6$ ($\Delta =3$) and $N_s=9$; (d)–(f) type 2, $B_{15}{N}_{10}+B_{10}{N}_{15}$ ($\Delta =5$) and $N_s=11$; (g)–(i) type 3, $B_{45}{N}_{36}+B_{36}{N}_{45}$ ($\Delta =9$) and $N_s=15$. All the bands on the left column are for neutral states, while the middle column are for $-$1 charged states and the right column for $+1$ charged states. Note that the $+1$ type 2 and $\pm 1$ type 3 charged states are half-metallic.

Figure 3

Selected results for the $N_z=2$ family. The units, lines and column organization are the same as in Fig. 2. (a)–(c) $B_{15}{N}_{10}+B_{10}{N}_{15}$ ($\Delta =5$) and $N_s=8$. (d)–(f) $B_{45}{N}_{36}+B_{36}{N}_{45}$ ($\Delta =9$) and $N_s=12$. We have only observed the type 2 band structure in this family in the range of values of $\Delta$ considered in this work. Nevertheless, since the band gap decreases with increasing $\Delta$, we expect to see a type 3 behavior for larger cluster sizes. Note also that all the charged states shown in this picture are half-metallic.

Figure 4

Spin density results for the $N_z=4$ family. The selected configurations are the same as in Fig. 2. Spin-up values are shown in red and spin-down in blue. Maximum absolute value for the spin density is $\approx$${10}^{-5}$ bohr${}^{-3}$ for type 1 (a)–(c) and neutral type 2 (d), and $5\text{--}10\times {10}^{-4}$ bohr${}^{-3}$ for charged type 2 (e),(f) and type 3 (g)–(i). Note the increasing intensity and degree of localization of the spin density on the carbon atoms near the edges of each cluster with increasing cluster size, with electrons tending to localize near the N terminated cluster and holes around the B terminated one.

Figure 5

Projected density of states for ${\pi }_z$ orbitals of selected atoms in the $B_{15}N10+B_{10}{N}_{15}$, $N_s=11$, $N_z=4$ configuration (type 2). (a) Neutral state; (b) $-$1 charged state; (c) $+$1 charged state. The color codes for the different curves is shown in panel (a) and the notation is described as follows: B (N): boron (nitrogen) atom on the edge of one cluster; C(B) [C(N)]: carbon atom bonded to the B (N) atom on the edge. For the edge atoms we choose those on the central region of the edge, because spin polarization is reduced near the vertexes. As always, the Fermi level is set to zero in all cases.