Competeing orders in spin-1 and spin-3/2 XXZ Kagome antiferromagnets: A series expansion study

TL;DR

This study uses series expansion methods to analyze the competition between different magnetic orders in spin-1 and spin-3/2 Kagome XXZ antiferromagnets, revealing phase preferences and the potential for a trimerized ground state.

Contribution

It introduces a series expansion approach to compare magnetic orders in Kagome antiferromagnets and predicts phase behavior, including the possibility of a trimerized phase.

Findings

Ground state energy series for RT3 and Q0 are identical up to sixth order.

Results suggest no magnetic order at the Heisenberg point for spin-one.

Ground state energy in the trimerized phase is lower, indicating its stability.

Abstract

We study the competition between $\sqrt{3} \times \sqrt{3}$ (RT3) and $q=0$ (Q0) magnetic orders in spin-one and spin-$3/2$ Kagome-lattice XXZ antiferromagnets with varying XY anisotropy parameter $\Delta$, using series expansion methods. The Hamiltonian is split into two parts: an $H_0$ which favors the classical order in the desired pattern and an $H_1$, which is treated in perturbation theory by a series expansion. We find that the ground state energy series for the RT3 and Q0 phases are identical up to sixth order in the expansion, but ultimately a selection occurs, which depends on spin and the anisotropy $\Delta$. Results for ground state energy and the magnetization are presented. These results are compared with recent spin-wave theory and coupled-cluster calculations. The series results for the phase diagram are close to the predictions of spin-wave theory. For the spin-one model at the Heisenberg point ($\Delta=1$), our results are consistent with a vanishing order parameter, that is an absence of a magnetically ordered phase. We also develop series expansions for the ground state energy of the spin-one Heisenberg model in the trimerized phase. We find that the ground state energy in this phase is lower than those of magnetically ordered ones, supporting the existence of a spontaneously trimerized phase in this model.