Competing orders in spin-1 andspin−32XXZ kagome antiferromagnets: A series expansion study

We study the competition between $\sqrt{3}\ifmmode\times\else\texttimes\fi{}\sqrt{3}$ (RT3) and $q=0$ (Q0) magnetic orders in spin-1 and $\text{spin}\ensuremath{-}\frac{3}{2}$ kagome-lattice XXZ antiferromagnets with varying XY anisotropy parameter $\mathrm{\ensuremath{\Delta}}$, 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 $\mathrm{\ensuremath{\Delta}}$. 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-1 model at the Heisenberg point ($\mathrm{\ensuremath{\Delta}}=1$), 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-1 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.