Spin-charge-orbital ordering in hollandite-type manganites studied by model Hartree-Fock calculation

TL;DR

This study uses Hartree-Fock calculations on a multi-band model to analyze the spin-charge-orbital ordering in hollandite-type manganites, revealing the roles of various exchange interactions in stabilizing specific charge and orbital patterns.

Contribution

It introduces a multi-band Hartree-Fock approach to model spin-charge-orbital ordering in hollandite manganites, highlighting the importance of exchange interactions in pattern stabilization.

Findings

Ferromagnetic double exchange and superexchange interactions stabilize charge and orbital order.

The most stable pattern matches the structure of K$_{1.6}$Mn$_8$O$_{16}.

The model explains the observed charge and orbital arrangements.

Abstract

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$_{16}$.