Magnetic moment formation in metal-organic monolayers

We investigate the electronic and magnetic properties of a two-dimensional polymeric manganese phthalocyanine (Mn-Pc) network and its derivative, the metal-ligand network Mn-TCNB formed by the transition-metal atom Mn and the organic ligand TCNB (1,2,4,5-tetracyanobenzene), using first-principles calculations on the basis of density functional theory (DFT) with the Hubbard-like Coulomb term. Our calculations show that Mn-Pc and Mn-TCNB are metallic. It is found that the Mn-Pc network is more stable than the Mn-TCNB one, and both have a total magnetic moment of about $3{\mu }_B$. In the case of Mn-Pc, also the local Mn moment is close to $3{\mu }_B$. But in Mn-TCNB, we find a high spin state $S=5/2$ at Mn that is partially screened by unpaired electrons at the ligands. That screening is static in the $\mathrm{DFT}+U$ results, but we argue in favor of a dynamical screening in reality. Using our proper model calculation on the basis of a suitable model Hamiltonian, we explain the ab initio calculations, analyze the partial screening effect that exists in the two-dimensional Mn-TCNB network, and compare both systems.

Figure 1

Structure of the 2D Mn-TCNB network. The Mn, N, C, and H atoms are highlighted in red, blue, gray, and white, respectively. The square represents the unit cell.

Figure 2

Structure of the 2D Mn-Pc polymer network. It can be obtained from the Mn-TCNB network (Fig. 1) by a polymerization reaction which turns the benzene hexagons by ${30}^{\circ }$ and creates additional chemical bonds that are indicated by black bars.

Figure 3

Total energy as a function of the lattice parameter for Mn-Pc. The energies indicated by blue circles are obtained by the fixed-spin-moment method to complete the parabola for the $S=5/2$ solution. The stable state has $S=3/2$.

Figure 4

Total DOS of Mn-Pc in the ground state with the $\text{PAW-SGGA}+U$ method.

Figure 5

Projected DOS of the $d$ orbitals on the Mn atom in the 2D Mn-Pc monolayer with the $\text{PAW-SGGA}+U$ method.

Figure 6

Total energy of Mn-TCNB as a function of lattice parameter; $S=3/2$ is the ground state of the system. Both spin states correspond to local minima of the $\mathrm{SGGA}+U$ functional for the given lattice constant; the fixed-spin-moment method was not necessary.

Figure 7

Total DOS of the Mn-TCNB sheet.

Figure 8

DOS projected onto the Mn $3d$ orbitals in the 2D Mn-TCNB monolayer.

Figure 9

Energy-level diagram of the ground-state manifold (18 states) of the local model for a filling of $n=4$ for fixed values of $t_{pd}=1.5\mathrm{eV}$ and $\mathrm{\Delta }=4\mathrm{eV}$ as a function of $t_{pp}$ (results of perturbation theory). The zero of the energy corresponds to $E_G$. The total spin of the eigenstates is indicated ($S=0$, solid line; $S=1$, dashed lines; and $S=2$, dotted line). The level crossing between the $S=0$ state (screening of the Mn moment) and the $S=1$ state (absence of screening) occurs at $t_{pp}=0.56\mathrm{eV}$ for the chosen parameter values.