Calculation of magnetic exchange couplings in S=3/2 honeycomb system Bi$_3$Mn$_4$O$_{12}$(NO$_3$)} from first principles

TL;DR

This study uses first-principles calculations to determine the magnetic exchange interactions in the honeycomb-layered Bi$_3$Mn$_4$O$_{12}$(NO$_3$), revealing dominant antiferromagnetic couplings and weak frustration, explaining its lack of magnetic order.

Contribution

First-principles calculation of magnetic exchange couplings in BMNO, identifying dominant interactions and their magnitudes, clarifying the magnetic frustration in the system.

Findings

Dominant interlayer interaction J_c exceeds nearest-neighbor J_1.

Longer-range interactions are antiferromagnetic but weakly frustrating.

No magnetic ordering observed despite strong antiferromagnetic couplings.

Abstract

Absence of magnetic ordering in Bi$_3$Mn$_4$O$_{12}$(NO$_3$), (BMNO) which has a magnetic subsystem that consists of honeycomb bi-layers of Mn$^{4+}$ ions with spin S=3/2, has raised the expectation that its ground state is strongly frustrated due to longer-range antiferromagnetic interactions. We calculate the magnetic exchange coupling constants of the BMNO complex within a density functional approach and find that the dominating interactions between Mn spins are the antiferromagnetic nearest-neighbor $J_1$ and interlayer interaction $J_c$. The largest interaction is $J_c$, which substantially exceeds $J_1$. Longer-range interactions are antiferromagnetic, but only weakly frustrating.