From the triangular to the kagome lattice: Following the footprints of the ordered state

TL;DR

This study explores the transition from triangular to kagome lattices in a spin-1/2 Heisenberg model, revealing how antiferromagnetic order diminishes and the kagome phase destabilizes as the lattice interpolates.

Contribution

It provides a detailed analysis of the evolution of magnetic properties and excitations during the lattice transition, highlighting the instability of the kagome phase for any non-zero J' value.

Findings

Antiferromagnetic order persists down to J'/J ~ 0.2.

The kagome phase is destabilized for any J' > 0.

Low-energy spectra show no continuity to the kagome limit.

Abstract

We study the spin-1/2 Heisenberg model in a lattice that interpolates between the triangular and the kagome lattices. The exchange interaction along the bonds of the kagome lattice is J, and the one along the bonds connecting kagome and non-kagome sites is J', so that J'=J corresponds to the triangular limit and J'=0 to the kagome one. We use variational and exact diagonalization techniques. We analyze the behavior of the order parameter for the antiferromagnetic phase of the triangular lattice, the spin gap, and the structure of the spin excitations as functions of J'/J. Our results indicate that the antiferromagnetic order is not affected by the reduction of J' down to J'/J ~ 0.2. Below this value, antiferromagnetic correlations grow weaker, a description of the ground state in terms of a Neel phase renormalized by quantum fluctuations becomes inadequate, and the finite-size spectra develop features that are not compatible with antiferromagnetic ordering. However, this phase does not appear to be connected to the kagome phase as well, as the low-energy spectra do not evolve with continuity for J'-> 0 to the kagome limit. In particular, for any non-zero value of J', the latter interaction sets the energy scale for the low-lying spin excitations, and a gapless triplet spectrum, destabilizing the kagome phase, is expected.