We investigate spin-charge-orbital ordering in a Mn$^{ 3+}$/Mn$^{ 4+}$ mixed valence state on a hollandite-type lattice using unrestricted Hartree-Fock calculation on a multi-band Mn 3$d$-O 2$p$ lattice model. The calculations show that the Mn$^{ 3+}$-Mn$^{ 4+}$ double exchange interaction, the Mn$^{ 3+}$-Mn$^{ 3+}$ and Mn$^{ 4+}$-Mn$^{ 4+}$ superexchange interactions are ferromagnetic and play important roles to stabilize the charge and orbital ordering pattern. The most stable charge and orbital ordering pattern is consistent with the $1\times1\times1$ orthorhombic or monoclinic structure of K$_{ 1.6}$Mn$_8$O$_{ 16}$.
Categories: cond-mat.str-el
