Calculated impact of ferromagnetic substrate on the spin crossover in a ${\mathrm{Fe}(1,10-\text{phenanthroline})}_2{\left(\mathrm{NCS}\right)}_2$ molecule

Spin crossover in the ${\mathrm{Fe}(1,10-\text{phenanthroline})}_2{\left(\mathrm{NCS}\right)}_2$ (Fephen) molecule adsorbed on ferromagnetic cobalt (001) and (111) surfaces as well as a gold (001) surface has been studied using the projector augmented wave method in conjunction with the density functional theory within the generalized gradient approximation, including a Hubbard interaction $U$ at the iron site and a van der Waals weak interaction between the molecule and the surface. It is shown that the energy difference between the high-spin (HS) and the low-spin (LS) states and the energy barrier of Fephen/Co(111) are significantly reduced compared to those of the adsorbed molecule on Cu(001) and Au(001). This makes the switching of the molecule from the HS to the LS state much easier than when the molecule is adsorbed on a copper or gold substrate. It is also shown that an indirect exchange mechanism is responsible for the ferromagnetic coupling between the Fe center of Fephen and the cobalt substrate and that, in the LS state, the Fephen/Co interface remains magnetically active due to small induced magnetic moments in the NCS group and iron center. This magnetic coupling between the molecule and the substrate decreases in an oscillatory fashion as a function of the number of copper layers inserted between the molecule and the cobalt substrate, in a manner similar to that of the interlayer magnetic exchange coupling. Finally, scanning tunneling microscopy images at the Fermi level show that the separation between the phen lobes is larger in the HS state than in the LS state and the work functions of cobalt, gold, and copper substrates are strongly reduced upon adsorption of the Fephen molecule.

Figure 1

Upper panels: Majority-spin (positive scale) and minority-

spin (negative scale) DOSs of iron of the Fephen/Co(001) system (green curve), Fephen/Co(111) (blue curve), and Fephen/Au(001) (red curve) for the HS state (right side) and LS state (left side). Lower panels: Similar DOSs, but for N-NCS (blue curve), N-phen (cyan curve), and S-NCS (orange curve).

Figure 2

Isosurface plot of the magnetization density of Fephen on Co(001). The color red represents spin up, and blue represents spin down, as indicated by the arrows. Calculated magnetic moments for Fe, N, C, and S atoms of Fephen/Co(001) in both the HS state (top) and the LS state (bottom) are shown.

Figure 3

$\mathrm{GGA}+U$ calculated nudged elastic band (NEB) of the energy barrier as a function of the intermediate images between the HS ($\mathrm{image}=0$) and the LS ($\mathrm{image}=4$) magnetic states for the free molecule (dashed squares) compared to a direct calculation where the distance between the sulfur-sulfur atoms is varied between the value of the HS state and that of the LS state (dashed circles), and solid curves are polynomial fits to the data. The HS ($S=2$) and LS ($S=0$) crystal-field splittings are also shown.

Figure 4

Right: $\mathrm{GGA}+U$ (dashed circles)– and $\mathrm{GGA}+U+\mathrm{vdW}$ (filled circles)–calculated HS-to-LS energy barrier of Fephen/Co(111) as a function of the sulfur-sulfur distance $d_{\mathrm{S}-\mathrm{S}}$. Solid and dashed curves are polynomial fits to the data. Spin state $S=2, S=1$, and $S=0$ crystal-field splittings along the MEP are also shown. Left: The Fephen molecule on the Co(111) substrate. The HS total energy is set to 0 in both calculations.

Figure 5

Upper panel: Calculated constant-current STM images for the two HS (left) and LS (right) states at the Fermi level for Fephen/Au(001). Lower panel: Similar STM images, but for Fephen/Co(001).

Figure 6

$\mathrm{GGA}+U+\mathrm{vdW}$ energy difference $\mathrm{\Delta }E$ between the ground-state energies of the ferromagnetic and the antiferromagnetic coupled molecule and substrate. This oscillatory $\mathrm{\Delta }E$ is plotted as a function of the number $n$ of copper interlayers between the Co(001) and the molecule. Error bar: $\sim 1$ meV.

Figure 7

Electrostatic potential $V\left(z\right)$ along the direction perpendicular to the interface for Fephen/Co(111). Here ${\mathrm{\Phi }}_0$ and $\mathrm{\Phi }$ are the work functions of the free surface and the surface with the Fephen molecule, respectively.

Figure 8

Left panel: Difference in the charge density $\mathrm{\Delta }n\left(\mathbf{r}\right)$ in the $xy$ plane. Right panels: From left to right, $\mathrm{\Delta }n\left(z\right), n\left(z\right)$, the difference in the charge density $\mathrm{\Delta }n\left(\mathbf{r}\right)$ along the two planes, (1) and (2), parallel to $z$ shown in the left panel, and the ensuing electric dipole $\delta \mu \left(z\right)$ (see text).