Strong charge and spin fluctuations in ${\mathbf{La}}_{\mathbf{2}}{\mathbf{O}}_{\mathbf{3}}{\mathbf{Fe}}_{\mathbf{2}}{\mathbf{Se}}_{\mathbf{2}}$

The electronic structure and magnetic properties of the strongly correlated material ${\mathrm{La}}_2{\mathrm{O}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_2$ are studied by using both the density-functional theory plus $U$ $\left(\mathrm{DFT}+U\right)$ method and the DFT plus Gutzwiller (DFT + G) variational method. The ground-state magnetic structure of this material obtained with $\mathrm{DFT}+U$ is consistent with recent experiments with an appropriate $U$ parameter, but its band gap is significantly overestimated by $\mathrm{DFT}+U$, even with a small Hubbard $U$ value. In contrast, the DFT + G method yields a band gap of 0.1–0.2 eV, in excellent agreement with experiment. Detailed analysis shows that the electronic and magnetic properties of ${\mathrm{La}}_2{\mathrm{O}}_3{\mathrm{Fe}}_2{\mathrm{Se}}_2$ are strongly affected by charge and spin fluctuations which are missing in the $\mathrm{DFT}+U$ method.

Figure 1

(a) Crystal structure of LOFS where green, red, blue, and yellow balls represent ${\mathrm{La}}^{3+},{\mathrm{O}}^{2-},{\mathrm{Fe}}^{2+}$, and ${\mathrm{Se}}^{2-}$, respectively; (b) Symmetry points in the Brillouin zone; (c) ${\mathrm{FeO}}_2{\mathrm{Se}}_4$ octahedra where the Fe atom is surrounded by two axial oxide atoms and four equatorial selenide atoms, forming a tilted Fe-centered octahedron with the $D_{2h}$ point symmetry.

Figure 2

Comparison of the non-spin-polarized GGA band structures and the down-folded tight-binding band structures.

Figure 3

(a)–(g) The magnetic structures of one layer of Fe atoms on the crystalline $ab$ plane. Only the Fe atoms are shown in the figures, which is indicated by large blue circles; and the small red circle and yellow cross represent up- and down-spin orientations, respectively.

Figure 4

(a) Band structure of LOFS calculated by the $\mathrm{DFT}+U$ method under the ground-state magnetic structure AFM6 and $U_{\mathrm{eff}}=1.5\mathrm{eV}$. The Fermi energy has been set to 0 eV. (b) Relation between the band gap of LOFS and $U_{\mathrm{eff}}$ calculated by the $\mathrm{DFT}+U$ method under the ground-state magnetic structure.

Figure 5

Energy levels of Fe $3d$ states under crystal-field splitting.

Figure 6

(a) Illustration of the main atomic configurations with relatively large probability; (b) probability of the atomic configurations $|I\rangle$ in the Gutzwiller wave function $|G\rangle$, calculated with $U=6.0\mathrm{eV}$ and $J=0.25U$ under the ground-state magnetic structure. Here, the atomic configurations with occupation numbers 5–8 are represented by histograms with the colors yellow, red, blue, and green, respectively.