${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ predicted as a half-metallic ferromagnet: Scenario for a metal-insulator transition

Based on the first-principles electronic structure calculations, we predict that a chromium oxide ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ of hollandite type should be a half-metallic ferromagnet where the Fermi level crosses only the majority-spin band, whereas the minority-spin band has a semiconducting gap. We show that the double-exchange mechanism is responsible for the observed saturated ferromagnetism. We discuss possible scenarios of the metal-insulator transition observed at low temperature and we argue that the formation of the incommensurate long-wavelength density wave of spinless fermions caused by the Fermi-surface nesting may be the origin of the opening of the charge gap.

Figure 1

(Color online) Schematic representation of (a) the unit cell of the body-centered tetragonal lattice (solid lines) and (b) Brillouin zone of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$. In (a), the primitive unit cell is also shown in the thin dotted lines. In (b), the symbols represent $\Gamma \left(0,0,0\right)$, $M\left(2\pi /a,0,0\right)$, $X\left(\pi /a,\pi /a,0\right)$, $P\left(\pi /a,\pi /a,\pi /c\right)$, $K_1\left[0,0,\pi \left(1/c+c/a^2\right)\right]$, and $K_2\left[2\pi /a,0,\pi \left(1/c-c/a^2\right)\right]$, where $K_1$ and $K_2$ are equivalent.

Figure 2

(Color online) Schematic representations of the local structure of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$, together with the three $t_{2g}$ orbitals $d_{xy}$, $d_{yz}$, and $d_{zx}$ of Cr ions in the $xyz$-coordinate system. There are two inequivalent O sites, O(1) and O(2). All the Cr sites are equivalent.

Figure 3

(Color online) Calculated result for the DOS [per spin per formula unit (f.u.)] of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ in a wide energy range for the ferromagnetic state. The Fermi level is set to be the origin of energy.

Figure 4

(Color online) Calculated orbital-decomposed DOS [per spin per formula unit (f.u.)] of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ near the Fermi level for the (a) paramagnetic and (b) ferromagnetic states. The Fermi level is indicated by the vertical line. Contributions from the $d_{yz}$ and $d_{zx}$ orbitals (thin dashed and dotted lines) are exactly degenerate.

Figure 5

(Color online) Calculated majority-spin band dispersion of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ near the Fermi level. There are 12 $t_{2g}$ bands of the $\text{Cr}3d$ orbitals, three of which cross the Fermi level. The line width is in proportion to the weight of the $d_{xy}$ component of Cr in (a) and to that of the $2p_z$ component of O(2) in (b).

Figure 6

(Color online) Calculated Fermi surfaces of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$ in the ferromagnetic state. The 61st–63rd bands counted from the lowest are shown in (a)–(c), respectively.

Figure 7

(Color online) Generalized susceptibility ${\chi }_0\left(\mathit{q}\right)$ for the noninteracting band structure of ${\text{K}}_2{\text{Cr}}_8{\text{O}}_{16}$. Contribution from only the 61st band is shown.