Spin-polarized electronic structure for the layered two-dimensional $\left[{\text{Fe}}^{\text{II}}\left(\text{TCNE}\right){\left(\text{NCMe}\right)}_2\right]\left[{\text{Fe}}^{\text{III}}{\text{Cl}}_4\right]$ organic-based magnet

The results of first-principles density-functional theory and the local-spin-density approximation [L(S)DA] with a Hubbard Coulombic $U$ and projector-augmented wave method electronic-structure calculations for the layered two-dimensional organic-based magnet $\left[{\text{Fe}}^{\text{II}}\left(\text{TCNE}\right){\left(\text{NCMe}\right)}_2\right]\left[{\text{Fe}}^{\text{III}}{\text{Cl}}_4\right]$ are reported. The $\text{L}\left(\text{S}\right)\text{DA}+U$ method accounted for the on-site Coulomb interaction between the ${\text{Fe}}^{\text{II}}$ and ${\mu }_4\text{−}{\left[\text{TCNE}\right]}^{•-}$ ions. The results from the spin-polarized calculations are in agreement with the antiferromagnetically coupled ferrimagnetic ground state. The magnetic moments for ${\text{Fe}}^{\text{II}}$ and ${\left[\text{TCNE}\right]}^{•-}$ are 3.70 and $0.27{\mu }_{\text{B}}$, respectively, which are reduced from the sum of the isolated ions (4 and $1{\mu }_{\text{B}}$, respectively) due to antiferromagnetic coupling, which are in accord with molecular-cluster model calculations. Spin-polarized partial density-of-states calculations reveal strongly spin-polarized ${\text{Fe}}^{\text{II}}{\left[\text{TCNE}\right]}^{•-}$ conduction and valence bands. The highest majority band primarily consists of a ${\text{Fe}}^{\text{II}}{d}_{xz}$-based band with hybridization $\left(\sim 33\%\right)$ by a ${\left[\text{TCNE}\right]}^{•-}$ $p$ band at 2.60 eV below the Fermi level $\left(E_{\text{F}}\right)$, and the highest minority band primarily consists of a ${\left[\text{TCNE}\right]}^{•-}$ $p$ band with hybridization $\left(\sim 40\%\right)$ by ${\text{Fe}}^{\text{II}}d$ bands at 0.09 eV below $E_{\text{F}}$, and the materials is an insulator.

Figure 1

(Color online) Crystal structure of $\left[\text{Fe}\left(\text{TCNE}\right){\left(\text{NCMe}\right)}_2\right]\left[{\text{FeCl}}_4\right]$ (H, white; C, gray; N, blue, Cl, green, and Fe, red) (Ref. 10). Due to structural disorder each methyl groups displays 6 H atoms.

Figure 2

(Color online) Partial density of states from LDA PAW calculation. Total DOS (—); ${\left[\text{TCNE}\right]}^{•-}$ $\text{C}p$ (—); ${\left[\text{TCNE}\right]}^{•-}$ $\text{N}p$ (—); $\text{Cl}p$ (—); ${\text{Fe}}^{\text{II}}d$ (—); and ${\text{Fe}}^{\text{III}}d$ (—).

Figure 3

(Color online) Spin-density isosurface of a ferrimagnetic layer of ${\left[{\text{Fe}}^{\text{II}}\left({\text{TCNE}}^{•-}\right){\left(\text{NCMe}\right)}_2\right]}^{+}$ calculated by the $\text{L}\left(\text{S}\right)\text{DA}+U$ method. The red isosurface indicates the spin-up electron density; the blue isosurface indicates the spin-down electron density. All atoms are black.

Figure 4

(Color online) Spin density of an antiferromagnetic ${\text{Fe}}^{\text{II}}{\text{-TCNE}}^{•-}$ fragment calculated by the LCAO molecular-cluster model. The red isosurface indicates the spin-up electron density and the blue isosurface indicates the spin-down electron density. All atoms are black.

Figure 5

(Color online) Spin-polarized partial density of states of layer ${\left[{\text{Fe}}^{\text{II}}\left({\text{TCNE}}^{•-}\right){\left(\text{NCMe}\right)}_2\right]}^{+}$. Total DOS (—); top: ${\text{Fe}}^{\text{II}}{d}_{xy}$ orbital (—); $d_{yz}$ (—); $d_{z^2}$ (—); $d_{xz}$ (—); $d_{x^2-y^2}$ (—); bottom: TCNE $\text{C}s$ (—); $p$ (—) and $\text{N}s$ (—); $p$ (—). Inset: all ${\text{Fe}}^{\text{II}}$ bands (—), all ${\left[\text{TCNE}\right]}^{•-}$ bands (—).

Figure 6

Schematic illustration of spin-polarized density of states for ${\left[{\text{Fe}}^{\text{II}}\left({\text{TCNE}}^{•-}\right)\right]}^{+}$.