Reversible electric-field manipulation of the adsorption morphology and magnetic anisotropy of small Fe and Co clusters on graphene

First-principles electronic calculations show how the adsorption morphology, orbital magnetism, and magnetic anisotropy energy (MAE) of small ${\mathrm{Co}}_N$ and ${\mathrm{Fe}}_N$ clusters ($N\le 3$) on graphene (G) can be reversibly controlled under the action of an external electric field (EF). A variety of cluster-specific and EF-induced effects are revealed, including (i) perpendicular or canted adsorption configurations of the dimers and trimers, (ii) significant morphology-dependent permanent dipole moments and electric susceptibilities, (iii) EF-induced reversible transitions among the different metastable adsorption morphologies of ${\mathrm{Fe}}_3$ and ${\mathrm{Co}}_3$ on graphene, (iv) qualitative changes in the MAE landscape driven by structural changes, (v) colossal values of the magnetic anisotropy $\mathrm{\Delta }E\simeq 45$ meV per atom in ${\mathrm{Co}}_2/\mathrm{G}$, (vi) EF-induced spin-reorientation transitions in ${\mathrm{Co}}_3/\mathrm{G}$, and (vii) reversibly tunable coercive field and blocking temperatures, which in some cases allow a barrierless magnetization reversal of the cluster. These remarkable electric and magnetic fingerprints open new possibilities of characterizing and exploiting the size- and structural-dependent properties of magnetic nanostructures at surfaces.

Figure 1

Optimized structures of ${\mathrm{Fe}}_2$ on graphene for representative values of the external electric field $\vec{\varepsilon }={\varepsilon }_z\widehat{z}$. The dimer adsorption position is toplike in (a), whereas it is hollowlike in (b) and (c). The corresponding calculated local spin moments ${\mu }_i$, tilting angle $\delta$, and bond lengths are indicated. In the inset of (a), the coordinate system is illustrated.

Figure 2

Magnetic anisotropy energy $\mathrm{\Delta }E=E\left(\theta \right)-E_z$ of ${\mathrm{Fe}}_2$ deposited on graphene as a function of the polar angle $\theta$ between the magnetization $\vec{M}$ and the $z$ axis. Representative values of the external field $\vec{\varepsilon }={\varepsilon }_z\widehat{z}$ are considered [see the inset of Fig. 1]. Positive $\theta$ corresponds to the half-plane including the $z$ axis and the dimer bond, while negative $\theta$ corresponds to the opposite half-plane, away from the dimer. The symbols show the actual self-consistent electronic results, while the curves are fits to those data using an $l=2$ spherical harmonics expansion.

Figure 3

Illustration of the different adsorption configurations $\alpha , \beta$, and $\gamma$ of ${\mathrm{Fe}}_3$ and ${\mathrm{Co}}_3$ on graphene. In (a) the coordinate system and a different perspective to the structure $\alpha$ are illustrated. Notice that in the optimized geometries, the trimer plane is perpendicular or nearly perpendicular to the graphene layer. In the structures $\alpha$ and $\gamma$, the basis of the triangle (atoms 2 and 3) is in contact with the graphene layer, while in $\beta$ only atom 3 does.

Figure 4

Total energy $E$ of ${\mathrm{Fe}}_3$ on graphene as a function of the external electric field ${\varepsilon }_z$ for the different optimized adsorption configurations $\alpha , \beta$, and $\gamma$ illustrated in Fig. 3.

Figure 5

Magnetic anisotropy energy $\mathrm{\Delta }{E}_{xz}=E_x-E_z$ and orbital-moment anisotropy $\mathrm{\Delta }{L}_{zx}={\langle L\rangle }_z-{\langle L\rangle }_x$ of a Co atom on graphene as a function of the normal component ${\varepsilon }_z$ of the electric field $\vec{\varepsilon }={\varepsilon }_z\widehat{z}$. Positive ${\varepsilon }_z$ corresponds to $\vec{\varepsilon }$ pointing from the graphene layer toward the atom. The inset of (a) shows $\mathrm{\Delta }E\left(\theta \right)=E\left(\theta \right)-E_z$ for ${\varepsilon }_z=0$ as a function of the polar angle $\theta$ (in degrees) between $\vec{M}$ and the $z$ axis.

Figure 6

Magnetic anisotropy energy per Co atom $\mathrm{\Delta }{E}_{xz}=E_x-E_z$ and average Co orbital-moment anisotropy $\mathrm{\Delta }{L}_{zx}={\langle L\rangle }_z-{\langle L\rangle }_x$ of a Co dimer on graphene as a function of the normal component ${\varepsilon }_z$ of the electric field $\vec{\varepsilon }={\varepsilon }_z\widehat{z}$. Positive ${\varepsilon }_z$ corresponds to $\vec{\varepsilon }$ pointing from the graphene layer toward the dimer. In the inset of (a), the anisotropy energy $\mathrm{\Delta }E\left(\theta \right)=E\left(\theta \right)-E_z$ is given for ${\varepsilon }_z=0$ as a function of the polar angle $\theta$ between the magnetization $\vec{M}$ and the $z$ axis.

Figure 7

Total energy of ${\mathrm{Co}}_3$ on graphene (G) as a function of the external electric field ${\varepsilon }_z$ for the optimized adsorption configurations $\beta$ and $\gamma$ illustrated in Fig. 3.

Figure 8

Magnetic anisotropy energy and orbital-moment anisotropy of the most stable adsorption configurations of ${\mathrm{Co}}_3$ on graphene as a function of the external electric field ${\varepsilon }_z$ ($\vec{\varepsilon }={\varepsilon }_z\widehat{z}$). In (a) results are shown for $\mathrm{\Delta }{E}_{xz}=E_x-E_z$ in the configurations $\beta$ and $\gamma$, as well as for $\mathrm{\Delta }{E}_{yz}$ in the configuration $\gamma$. Full symbols highlight the most stable adsorption morphology (see Figs. 3 and 7). In (b) the EF dependence of the average orbital-moment anisotropy $\mathrm{\Delta }{L}_{zx}={\langle L\rangle }_z-{\langle L\rangle }_x$ is shown. As in (a), solid lines and full symbols (dashed lines and open symbols) refer to the most stable (second best) structure. The inset in (a) shows the MAE $\mathrm{\Delta }E\left(\theta \right)=E\left(\theta \right)-E_z$ as a function of the polar angle $\theta$ between $\vec{M}$ and the $z$ axis for representative values of ${\varepsilon }_z$. The adsorption geometries and the coordinate system are illustrated in Fig. 3.

Figure 9

Spin-polarized density of Kohn-Sham electronic states (DOS) ${\rho }_{\sigma }\left(\varepsilon \right)$ of ${\mathrm{Fe}}_3$ and ${\mathrm{Co}}_3$ on graphene in the adsorption configuration $\beta$. See also Fig. 3. The single-particle energy $\varepsilon$ is referred to the Fermi energy ${\varepsilon }_F$.