Symmetry-Driven Trimer Formation in Kagome Correlated Electron Materials

TL;DR

This paper identifies symmetry, electron filling, and correlation strength as key factors stabilizing metal trimers in kagome lattice materials, providing a design rule for quantum materials with cluster-based quantum states.

Contribution

It introduces a unified criterion based on electron count, symmetry, and correlation strength for trimer formation in kagome correlated electron materials.

Findings

Trimer formation occurs with 6-8 electrons filling molecular orbitals.

Stability is linked to avoiding antibonding orbital occupation.

The principle explains the stability of Nb₃X₈ compounds.

Abstract

Correlated electron materials with molecular orbital states extending over transition metal clusters can host multiferroicity, spin frustration, and unconventional insulating phases. However, the fundamental criteria that govern cluster formation and stability remain unclear. Here, we identify a symmetry, correlation, and electron filling driven criteria that stabilize triangular metal trimers in materials displaying transition metal kagome patterns. Using density functional theory and chemical bonding analysis, we show that trimer formation emerges when 6 to 8 electrons occupy molecular orbitals derived from transition metal d-states, achieving near complete filling of bonding states while avoiding antibonding occupation, and correlations are of intermediate strength. This principle explains the stability of Nb$_3$X$_8$ (X = Cl, Br, I), and more broadly, our findings offer a general design rule to obtain quantum materials with quantum states extended across transition metal clusters.