Resonant magnetic proximity hot spots in Co/hBN/graphene

TL;DR

This work addresses the spatial variability of magnetic proximity effects in Co/hBN/graphene van der Waals heterostructures. Using first-principles DFT and transport calculations across more than twenty stackings, it shows graphene Dirac-band spin splittings spanning $1$ to $100$ meV, governed by local orbital hybridization among $d_{z^2}$, $p_z$ on N, and $p_z$ on C, with strong proximity hot spots at specific registries. The authors reveal energy-dependent, locally concentrated spin polarization and demonstrate that pseudospin-breaking proximity effects emerge near resonances, whereas a pseudospin-preserving picture is restored away from them. They further show that adding hBN or graphene layers and introducing twist angles modulates proximity exchange and tunneling spin polarization, offering design rules for engineering spin transport in vdW spintronic devices.

Abstract

Magnetic proximity effects in Co/hBN/graphene heterostructures are systematically analyzed via first-principles calculations, demonstrating a pronounced localized spatial variation of the induced spin polarization of graphene's Dirac states. The proximity-induced exchange coupling, magnetic moments, and tunneling spin polarization (TSP) are shown to depend sensitively on the atomic registry at the interfaces. We analyze more than twenty distinct stackings, including high- and low-symmetry configurations, and reveal that the spin splittings of graphene's Dirac bands span a wide range from 1 to 100 meV, depending on the local hybridization of Co $d_{z^2}$, hBN $p_z$, and graphene $p_z$ orbitals. The strongest proximity effects emerge at geometric resonances, or "proximity hot spots", where the three orbital states overlap maximally. The local spin polarization also depends sensitively on energy: Dirac states aligned with resonant Co orbitals experience the most pronounced exchange interaction. At these energies, the pseudospin Hamiltonian description of magnetic proximity effects breaks down. Outside these resonances, the pseudospin picture is restored. Our findings highlight the intrinsically local nature of proximity effects, governed by the spectral resonance and interlayer wavefunction overlap. We further quantify how additional hBN layers, interlayer twist, and multilayer graphene modify the proximity exchange and TSP, offering microscopic insight for designing spintronic van der Waals heterostructures with engineered interfaces and optimized spin transport.

Figures (9)

• Figure 1: Sketch of the geometries, showing the different stacking configurations S$_{1,1}$ -- S$_{3,6}$, of the 18 lattice-matched high-symmetry commensurate structures. The colors of the spheres correspond to different atoms (black = C, green = B, blue = N, red = Co). Within each row, the graphene/hBN stacking is fixed. Within each column, the hBN/Co stacking is fixed. Labels $\alpha$ and $\beta$ represent the graphene sublattices, while labels $1-3$ represent the different Co layers. The rippling of hBN, if present, is indicated. Structures S$_{4,1}$ -- S$_{4,6}$ in the last row have lowered symmetry and are derived from geometries S$_{1,2}$ and S$_{1,1}$. Further details are summarized in Table \ref{['Tab:Structures']}.
• Figure 2: Setup for the transmission calculations. For the transmission calculations with PWCOND, we consider a Co/hBN/graphene/hBN/Co stack as the scattering region, with semi-infinite bulk Co leads.
• Figure 3: (a) Side views of exemplary high-symmetry stacking configurations S$_{1,2}$, S$_{2,2}$, S$_{3,2}$, and S$_{4,2}$. The hybridization channels from Co $d_{z^2}$ to C $p_z$ orbitals via N $p_z$ orbitals are sketched. (b) Zoom to the proximitized low energy Dirac bands ($E_F = 0$) and the corresponding spin- and atom-resolved density of states of the S$_{1,2}$ configuration. The open circles on the bands represent the projection on graphene orbitals. Positive (negative) DOS corresponds to majority (minority) spin channels. (c,d,e) The same as (b), but for the corresponding stacking configuration as labeled in the dispersion.
• Figure 4: (a) Medium-sized Co/hBN/graphene supercell. The different colored spheres emphasize the different local high-symmetry stackings. The dashed line represents the unit cell. (b) The proximity-induced calculated magnetic moments on C atoms, overlayed on the geometry. (c) DFT-calculated spin-resolved band structure in the vicinity of the K point. The open circles on the bands represent projections onto graphene orbitals. (d) DFT-calculated spin polarization. We cut through the $p_z$-orbital polarization slightly above the C atoms. Yellow/Red corresponds to positive polarization, while Cyan/Blue corresponds to negative polarization, in line with the magnetic moments shown in (b). (e) Spin polarization, taking into account states below the Dirac point at $E-E_F =-0.4 \textrm{eV}$ and energy window of $\pm 10$meV. The polarization is positive, highly non-uniform, and mainly localized around the S$_{3,2}$ configuration. (f) Same as (e), but above the Dirac point at $E-E_F =-0.2 \textrm{eV}$. The polarization is negative and uniformly distributed.
• Figure 5: Zoom to the proximitized low energy bilayer-graphene bands ($E_F = 0$) and the corresponding spin- and atom-resolved density of states of selected configurations of bilayer-graphene/hBN/Co. The open circles on the bands represent the projection on bilayer-graphene orbitals. Positive (negative) DOS corresponds to the majority (minority) spin channels. The stackings are sketched in the inset.