Ternary iron selenide ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$ is an antiferromagnetic semiconductor

We have studied electronic and magnetic structures of ${\mathrm{K}}_{0.8+x}$Fe${}_{1.6}$Se${}_2$ by performing the first-principles electronic structure calculations. The ground state of the Fe-vacancies ordered ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$ is found to be a quasi-two-dimensional blocked checkerboard antiferromagnetic (AFM) semiconductor with an energy gap of 594 meV and a large ordering magnetic moment of 3.37$\hspace{0.5em}{\mu }_B$ for each Fe atom, in excellent agreement with the neutron-scattering measurement. The underlying mechanism is the chemical-bonding-driven tetramer lattice distortion. ${\mathrm{K}}_{0.8+x}$Fe${}_{1.6}$Se${}_2$ with finite $x$ is a doped AFM semiconductor with low conducting carrier concentration, which is approximately proportional to the excess potassium content, consistent qualitatively with the infrared observation. Our study reveals the importance of the interplay between antiferromagnetism and superconductivity in these materials. This suggests that ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$, instead of KFe${}_2$Se${}_2$, should be regarded as a parent compound from which the superconductivity emerges upon electron or hole doping.

Figure 1

K${}_y$Fe${}_x$Se${}_2$ with the ThCr${}_2$Si${}_2$-type structure: (a) a tetragonal unit cell containing two formula units without any vacancy; (b) and (c) are schematic top views of an Fe-Fe square layer with one-fifth Fe-vacancies ($x=1.6$) ordered with the right and left chirality, respectively. In this $\sqrt{5}\times \sqrt{5}$ lattice, each Fe is coordinated with three neighboring Fe atoms. The squares enclosed by the solid lines denote the unit cells. The filled circles denote the Fe atoms while the empty circles denote the Fe vacancies. After optimizing the structure by the energy minimization, the Fe atoms go into a blocked distribution from a uniform square distribution, in which the four closest Fe atoms form a block, represented by dashed (blue) circles in (b) and (c), whose bond distance is shorter than that of the uniform Fe square lattice (green dots). Correspondingly, the angle $\theta$ decreases from 180${}^{°}$ to ${176}^{°}-{178}^{°}$.

Figure 2

Electronic structure of ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$ with one-fifth Fe vacancies ordered in a way as shown by Figs. 1b or 1c in the nonmagnetic state: (a) band structure; (b)–(i) are the Fermi surface sheets due to the bands crossing the Fermi energy denoted by 1–8 in (a), respectively. The corresponding Brillouin zone is shown in Fig. 4b. The Fermi energy sets to zero.

Figure 3

Schematic top view of eight possible magnetic orders in the Fe-Fe square layer with one-fifth Fe vacancies. Among these magnetic orders, the blocked checkerboard antiferromagnetic order in (c) is the ground state, in which the magnetic moments within each block are in parallel, but the magnetic moments for the neighboring two blocks are in antiparallel. The Fe spins are shown by arrows. The empty circles mark the Fe vacancies. The squares or rectangles enclosed by the dashed lines denote the magnetic unit cells.

Figure 4

(a) Electronic band structure of Fe vacancies ordered ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$ in the ground state with a blocked checkerboard antiferromagnetic order [Fig. 3c]. (b) Brillouin zone. Here the top of the valence band is set to zero.

Figure 5

K${}_{0.8}$Fe${}_{1.6}$Se${}_2$ in the blocked checkerboard antiferromagnetic ground state: (a) total and orbital-resolved partial density of states (spin-up part); (b) projected density of states onto the five Fe-$3d$ orbitals at an Fe atom. Here the top of the valence band sets to zero. $x$ axis is along the two next-nearest-neighbor Fe-Fe.

Figure 6

Electronic band structures and Fermi surfaces in the blocked checkerboard antiferromagnetic ground state with the left chirality: (a)–(c) for ${\mathrm{K}}_{0.7}$Fe${}_{1.6}$Se${}_2$ and (d)–(f) for ${\mathrm{K}}_{0.9}$Fe${}_{1.6}$Se${}_2$, to represent the hole doping or electron doping upon ${\mathrm{K}}_{0.8}$Fe${}_{1.6}$Se${}_2$, respectively. The Fermi energy sets to zero.