Hybrid quantum anomalous Hall effect at graphene-oxide interfaces

Interfaces are ubiquitous in materials science, and in devices in particular. As device dimensions are constantly shrinking, understanding the physical properties emerging at interfaces is crucial to exploit them for applications, here for spintronics. Using first-principles techniques and Monte Carlo simulations, we investigate the mutual magnetic interaction at the interface between graphene and an antiferromagnetic semiconductor ${\mathrm{BaMnO}}_3$. We find that graphene deeply affects the magnetic state of the substrate, down to several layers below the interface, by inducing an overall magnetic softening, and switching the in-plane magnetic ordering from antiferromagnetic to ferromagnetic. The graphene-${\mathrm{BaMnO}}_3$ system presents a Rashba gap 300 times larger than in pristine graphene, leading to a flavor of quantum anomalous Hall effect (QAHE), a hybrid QAHE, characterized by the coexistence of metallic and topological insulating states. These findings could be exploited to fabricate devices that use graphene to control the magnetic configuration of a substrate.

Figure 1

Spin texture in real space for ${\mathrm{BaMnO}}_3$ bulk (a), (b) and slab without (c), (d) and with graphene (e)–(h), in side and top views. Red and blue colors indicate the spin directions in subsequent Mn layers. AFM coupling between layers is predicted in all cases. The magnetization in the bulk and slab without graphene has an easy plane perpendicular to [0001], characterized by anticlockwise spin spirals (b), (d). The interface with graphene results in a FM alignment in the surface, with the in-plane configuration (e), (f) still slightly favored with respect to the out-of-plane one (g), (h).

Figure 2

Relaxed atomic structure for the graphene-${\mathrm{BaMnO}}_3$ (gBMO) slab seen from the top (a) and from the side (b). Definition of the exchange coupling parameters between Mn atoms in plane ($J_{\parallel }$) (a) and between planes ($J_{\perp }$) (b) for the BMO and the gBMO slabs.

Figure 3

Side (left panels) and top (right panels) views of the spins on Mn atoms (yellow spheres), obtained from Monte Carlo simulations at 5 K for the ${\mathrm{BaMnO}}_3$ slab without (top panels) and with (bottom panels) graphene. The presence of graphene changes the spin direction of the surface layer from mostly in plane to mostly out of plane. The other half of the slab is symmetric.

Figure 4

Average magnetization per atom and magnetic susceptibility for the ${\mathrm{BaMnO}}_3$ and graphene-${\mathrm{BaMnO}}_3$ slabs. The presence of graphene makes the transition temperature increase from $T_C=220\mathrm{K}$ (BMO) to 250 K (gBMO).

Figure 5

Electronic band structure of graphene-${\mathrm{BaMnO}}_3$ computed without (“collinear” spins, top left) and with spin-orbit coupling (top right and bottom panels) with the siesta code. In the top left panel, red and black lines denote the electronic bands of majority and minority spins, respectively. Rashba spin-orbit gaps open at band crossing points to the right and left of the $\overline{K}$ point. A $\sim 8$ meV gap opens at the the $\overline{K}$ point due to the spin-diagonal part of the SOC operator.

Figure 6

(Left) Band structure of the 44-atom model system calculated with spin-orbit coupling with the fleur code. The Fermi level of the model system $E_{\mathrm{F}}$ was shifted to match the calculations of the entire slab. (Right) Anomalous Hall conductivity as a function of the position of the band filling with respect to $E_{\mathrm{F}}$.

Figure 7

Berry curvature distribution of the occupied bands at $-0.9$ eV (a) and $-1.1$ eV (b) in momentum space. It is very localized at the crossing points of the bands, as can be seen in panel (c): The band shown in blue shows a significant contribution to the Berry curvature (red) just around the K-point near the gap opening at $-0.9$ eV.

Figure 8

Schematic representation of the band offset between graphene and ${\mathrm{BaMnO}}_3$ slabs computed from first principles (siesta).

Figure 9

Electronic band structure of graphene-${\mathrm{BaMnO}}_3$ projected on the C and surface Mn atoms for collinear spins. The spin-up component of C and Mn present a considerable hybridization which leads to the Rashba spin-orbit splitting at K. The bands originating from the spin-down components, instead, present a smaller C-Mn hybridization and maintain mostly the graphene character. For this, no gap at $K$ is observed for the corresponding band in SOC calculations.

Figure 10

Projected density of states for the ${\mathrm{BaMnO}}_3$ and graphene-${\mathrm{BaMnO}}_3$ slabs, for each layer from the surface (top panel) to the center (bottom panel) of the slab computed for collinear spins. Red and blue lines correspond to Mn $3d$ and graphene $2p$ states, respectively. The PDOS show that Mn $3d$ states are localized around $E_F$ only for the surface layer. This results in an out-of-plane component of the Mn magnetic moment, which is enhanced after interaction with graphene (right panels). As a consequence, the FM in-plane alignment is favored at the surface of the slabs, in contrast with bulk ${\mathrm{BaMnO}}_3$ which is characterized by an AFM in-plane alignment (see Tables 1 and 3).