Tunability of magnetic anisotropy of Co on two-dimensional materials by tetrahedral bonding

Pairing of $\pi$ electronic state structures with functional or metallic atoms makes them possible to engineer physical and chemical properties. Herein, we predict the reorientation of magnetization of Co on hexagonal BN ($h\text{−}\mathrm{BN}$) and graphene multilayers. The driving mechanism is the formation of the tetrahedral bonding between $s{p}^3$ and $d$ orbitals at the interface. More specifically, the intrinsic $\pi$ bonding of $h\text{−}\mathrm{BN}$ and graphene is transformed to $s{p}^3$ as a result of strong hybridization with metallic $d_{z^2}$ orbital. The different features of these two tetrahedral bondings, $s{p}^2$ and $s{p}^3$, are well manifested in charge density and density of states in the vicinity of the interface, along with associated band structure near the $\overline{K}$ valley. Our findings provide an approach to tailoring magnetism by means of degree of the interlayer hybrid bonds in two-dimensional layered materials.

Figure 1

Top- and side view of three kinds of $h\text{−}\mathrm{BN}$ stacking: (a) ${\mathrm{AA}}^{\prime }$, (b) AA, and (c) AB stacking, where orange and blue sphere denote B and N atoms, respectively.

Figure 2

Side views of the optimized atomic structures of a Co monolayer on the (a) $s{p}^2$ and (b) $s{p}^3$ BN bilayers. Red, blue, orange, and gray spheres represent the Co, N, B, and F atom, respectively. The arrows through the Co atoms denote the direction of Co magnetic moments. (c) The formation energy $H_f$ of the physisorbed and chemisorbed $\mathrm{Co}|\mathrm{BN}$. The case of metal-free chemisorbed BN bilayer is shown in open circle. Total energy of Co adatoms on functional-free $h$-BN is taken as reference energy.

Figure 3

The $d$-orbital PDOS of the Co atom (a) physisorbed and (b) chemisorbed on BN bilayer. (c),(d) The corresponding $p$-orbital PDOS of the N atom underlying the Co atom. The blue and red areas denote the spin-up and spin-down states, respectively. The Fermi level is set to zero energy.

Figure 4

(a) Isosurface plot of the charge density difference $\mathrm{\Delta }\rho$, where red (blue) corresponds to charge accumulation (depletion) in units of $5\times {10}^{-2}e/{\mathrm{bohr}}^3$. (b) The planar average of the $\mathrm{\Delta }\rho$ ($e$) along the $z$ axis in the case of Co/BN with $s{p}^3$ bonding (chemisorbed). The notation of the atomic symbol is the same as used in Figs. 1 and 2. In (b), the planar average of the $\mathrm{\Delta }\rho$ for the physisorption is also shown in red line.

Figure 5

Difference of $d$-orbital projected SOC energies, $\mathrm{\Delta }{E}_{\mathrm{soc}}$, between in- and out-of-plane magnetization orientation of the Co atom (a) physisorbed and (b) chemisorbed on bilayer BN. Positive and negative contributions are denoted by orange and blue bars, respectively.

Figure 6

Energy- and $k$-resolved distribution of the orbital character of the (a) and (b) majority- and (c) and (d) minority-spin bands of the physisorbed and chemisorbed Co/BN, respectively. The symbols superimposed over the band lines with black, blue, green, red, and orange colors represent the $d_{xy}$, $d_{xz}$, $d_{yz}$, $d_{z^2}$, and $d_{x^2-y^2}$ orbitals of the Co adatom, where the size of the symbols is proportional to their weights. The Fermi level is set to zero in energy.

Figure 7

Schematic diagram of the interlayer bond splitting of the Co $d$- and N $p$-orbital levels at the $\overline{\mathrm{K}}$ point in the 2D BZ. The metal $d$-orbital states are not much perturbed upon the physisorption with $h$-BN (middle panel). The interlayer bonds at the $\mathrm{Co}|s{p}^3\text{−}\mathrm{BN}$ interface splits the Co $d_{z^2}$ and N $p_z$ into the hybrid bonding states across the Fermi level ($E_F$), denoted as $p_z\otimes d_{z^2}$ in the right panel. The upward blue and downward red arrows represent the majority- and minority-spin states, respectively.