Ferromagnetic Peierls insulator state in $\mathit{A}$Mg$_4$Mn$_6$O$_{15}$ ($\mathit{A}$ = K, Rb, Cs)

Using the density-functional-theory based electronic structure calculations, we study the electronic state of recently discovered mixed-valent manganese oxides $A$Mg$_4$Mn$_6$O$_{15}$ ($A=$ K, Rb, Cs), which are fully spin-polarized ferromagnetic insulators with a cubic crystal structure. We show that the system may be described as a three-dimensional arrangement of the one-dimensional chains of a $2p$ orbital of O and a $3d$ orbital of Mn running along the three axes of the cubic lattice. We thereby argue that in the ground state the chains are fully spin polarized due to the double-exchange mechanism and are distorted by the Peierls mechanism to make the system insulating.