K$_2$Cr$_8$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 K$_2$Cr$_8$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.

Ab initio electronic structure calculation of hollandite vanadate K$_2$V$_8$O$_{16}$

An textit{ab initio} electronic structure calculation based on the generalized gradient approximation in the density functional theory is carried out to study the basic electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$. We find that the states near the Fermi energy consist predominantly of the three $t_{2g}$-orbital components and the hybridization with oxygen $2p$ orbitals is small. The $d_{yz}$ and $d_{zx}$ orbitals are exactly degenerate and are lifted from the $d_{xy}$ orbital. The calculated band dispersion and Fermi surface indicate that the system is not purely one-dimensional but the coupling between the VO double chains is important. Comparison with available experimental data suggests the importance of electron correlations in this system.