Effect of the iron valence in the two types of layers in ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$

We perform electronic structure calculations for the recently synthesized iron-based superconductor ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. In contrast to other iron-based superconductors, this material comprises two different iron atoms in $3d^5$ and $3d^6$ configurations. In band theory, both contribute to the low-energy electronic structure. Spin-polarized density functional theory calculations predict an antiferromagnetic metallic ground state with different moments on the two Fe sites. However, several other almost degenerate magnetic configurations exist. Due to their different valences, the two iron atoms behave very differently when local quantum correlations are included through the dynamical mean-field theory. The contributions from the half-filled $3d^5$ atoms in the ${\mathrm{LiFeO}}_2$ layer are suppressed and the $3d^6$ states from the FeSe layer restore the standard iron-based superconductor fermiology.

Figure 1

Nonmagnetic unit cell of ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. The two different iron atoms are shown with two different colors, ${\mathrm{Fe}}_{\text{Li}}$ in green and ${\mathrm{Fe}}_{\text{Se}}$ in red. The ${\mathrm{Fe}}_{\text{Li}}$ and ${\mathrm{Fe}}_{\text{Se}}$ planes are shaded in green and red, respectively.

Figure 2

Left: DFT band structure of nonmagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ (solid black lines), isolated ${\mathrm{LiFeO}}_2$ (dashed green lines), and isolated FeSe (red dotted lines). Right: (p)DOS of nonmagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. The pDOS of ${\mathrm{Fe}}_{\text{Li}}$ is shown in green and the pDOS of ${\mathrm{Fe}}_{\text{Se}}$ in red. The contributions from Se and O are plotted in blue and brown, respectively, on the negative axis. The units are st/eV (two spins) per atom for the pDOS; the total DOS is in st/eV f.u. (two spins) and has been rescaled by a factor of 2 to improve the readability of the figure.

Figure 3

Left: Zoom of Fig. 2 with the bands of ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ in solid black. The dominant character of the ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ bands is shown by the symbols. The band without special character markers is a mixture of all characters. Right: Band structure of bulk FeSe calculated for the experimental crystal structure at ambient pressure from Ref. [11].

Figure 4

Top view of the Fermi surface at $k_z=0$ (left) and $k_z=\pi /c$ (right) of nonmagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. Different colors indicate different bands.

Figure 5

Static bare susceptibility ${\chi }^0$ for isolated FeSe (red), isolated ${\mathrm{LiFeO}}_2$ (green), and the full ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ compound (black). The dotted blue line results when summing ${\chi }^0$ for the two isolated layers. The dashed brown line depicts the summed ${\chi }^0$ of the isolated layers, where we performed a rigid-band shift in order to account for the charge transfer. All susceptibilities are given per spin and for all Fe atoms in the respective unit cells. The blue and brown curves have been shifted up (down) by 1.5 ${\mathrm{eV}}^{-1}$ to improve readability. For details on the susceptibility calculation see Ref. [31].

Figure 6

Top view of the Fe lattices in ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ for the three most preferable magnetic configurations in terms of energy. The circles represent the ${\mathrm{Fe}}_{\text{Se}}$ and the triangles ${\mathrm{Fe}}_{\text{Li}}$. Blue signifies an up-spin on that particular Fe atom and green a down-spin.

Figure 7

(a) (p)DOS of nonmagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. The total DOS is shown in black and the pDOS of ${\mathrm{Fe}}_{\text{Li}}$ in green and of ${\mathrm{Fe}}_{\text{Se}}$ in red (same as Fig. 2). (b) (p)DOS of cb-ss ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$. The total DOS is shown in black and the pDOS of ${\mathrm{Fe}}_{\text{Li}}$ in green and of ${\mathrm{Fe}}_{\text{Se}}$ in red, where we summed over majority and minority spins. (c) (p)DOS of cb-ss ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ and $U=2.7$ eV. Otherwise the same as (b). Units are the same as in Fig. 2.

Figure 8

Magnetic moment of Fe in ss isolated FeSe (red), cb isolated ${\mathrm{LiFeO}}_2$ (green) and of ${\mathrm{Fe}}_{\text{Li}}$ (dotted black, $+$) and ${\mathrm{Fe}}_{\text{Se}}$ (dash-dotted black, $\times$) in cb-ss ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$.

Figure 9

Left: DFT + DMFT spectral function of paramagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ for $U=4$ eV and $J=0.9$ eV. Right: DFT + DMFT DOS of paramagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ for the same $U$ and $J$ parameters. The pDOS of ${\mathrm{Fe}}_{\text{Li}}$ is shown in green and the pDOS of ${\mathrm{Fe}}_{\text{Se}}$ in red. The contributions from Se and O are plotted on the negative axis and are displayed in blue and brown, respectively. For the definition of units, see Fig. 2.

Figure 10

DFT + DMFT spectral function of paramagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ for $U=4$ eV and $J=0.9$ eV. The ${\mathrm{Fe}}_{\text{Li}}$ $3d_{z^2}$ contributions are drawn in green and the DFT band structure is overlaid in white.

Figure 11

Contributions of ${\mathrm{Fe}}_{\text{Se}}$ to the spectral function of paramagnetic ${\mathrm{LiFeO}}_2{\mathrm{Fe}}_2{\mathrm{Se}}_2$ for $U=4$ eV and $J=0.9$ eV separated into orbital contributions. Top left: ${\mathrm{Fe}}_{\text{Se}}$ $3d_{z^2}$ orbital, top right: ${\mathrm{Fe}}_{\text{Se}}$ $3d_{x^2+y^2}$, bottom left: ${\mathrm{Fe}}_{\text{Se}}$ $3d_{xy}$, bottom right: ${\mathrm{Fe}}_{\text{Se}}$ $3d_{xz+yz}$.