Charge Localization and Ordering in A$_2$Mn$_8$O$_{16}$ Hollandite Group Oxides: Impact of Density Functional Theory Approaches

TL;DR

This study evaluates various density functional theory approaches to understand charge localization, ordering, and structural distortions in A$_2$Mn$_8$O$_{16}$ hollandite oxides, highlighting the importance of including van der Waals interactions and Coulomb corrections.

Contribution

It systematically compares multiple DFT functionals, including hybrid and DFT+U, to accurately model charge and structural phenomena in hollandite oxides.

Findings

Van der Waals interactions influence binding energies.

Low U approaches predict metallic behavior, high U captures charge localization.

Charge localization aligns with experimental observations.

Abstract

The phases of A$_2$Mn$_8$O$_{16}$ hollandite group oxides emerge from the competition between ionic interactions, Jahn-Teller effects, charge ordering, and magnetic interactions. Their balanced treatment with feasible computational approaches can be challenging for commonly used approximations in Density Functional Theory. Three examples (A = Ag, Li and K) are studied with a sequence of different approximate exchange-correlation functionals. Starting from a generalized gradient approximation (GGA), an extension to include van der Waals interactions and a recently proposed meta-GGA are considered. Then local Coulomb interactions for the Mn $3d$ electrons are more explicitly considered with the DFT+$U$ approach. Finally selected results from a hybrid functional approach provide a reference. Results for the binding energy of the A species in the parent oxide highlight the role of van der Waals interactions. Relatively accurate results for insertion energies can be achieved with a low $U$ and a high $U$ approach. In the low $U$ case, the materials are described as band metals with a high symmetry, tetragonal crystal structure. In the high $U$ case, the electrons donated by A result in formation of local Mn$^{3+}$ centers and corresponding Jahn-Teller distortions characterized by a local order parameter. The resulting degree of monoclinic distortion depends on charge ordering and magnetic interactions in the phase formed. The reference hybrid functional results show charge localization and ordering. Comparison to low temperature experiments of related compounds suggests that charge localization is the physically correct result for the hollandite group oxides studied here. . . .