Theoretical study of the electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$

Details Theoretical study of the electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$ Theoretical study of the electronic states of hollandite vanadate K$_2$V$_8$O$_{16}$

2008-03-14

arxiv.org/abs/0803.2089v1

Phys. Rev. B 77, 155120 (2008)

Physics

Condensed Matter

Strongly Correlated Electrons

7 pages, 8 figures

Scientific paper

10.1103/PhysRevB.77.155120

We consider electronic properties of hollandite vanadate K$_2$V$_8$O$_{16}$, a one-dimensional zigzag-chain system of $t_{2g}$ orbitals in a mixed valent state. We first calculate the Madelung energy and obtain the relative stability of several charge-ordering patterns to determine the most stable one that is consistent with the observed superlattice structure. We then develop the strong-coupling perturbation theory to derive the effective spin-orbit Hamiltonian, starting from the triply-degenerate $t_{2g}$ orbitals in the VO$_6$ octahedral structure. We apply an exact-diagonalization technique on small clusters of this Hamiltonian and obtain the orbital-ordering pattern and spin structures in the ground state. We thereby discuss the electronic and magnetic properties of K$_2$V$_8$O$_{16}$ including predictions on the outcome of future experimental studies.

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