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

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.

5 pages, 1 figure

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• The Interplay Between Lattice Topology, Frustration, and Spin Quantum Number in Quantum Antiferromagnets on Archimedean Lattices
• Clustering of Topological Charges in a Kagome Classical Spin Liquid
• Spin--lattice coupling and the emergence of the trimerized phase in the $S=1$ Kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$
• Reentrance of disorder in the anisotropic shuriken Ising model
• Spin ordered ground state and thermodynamic behaviors of the spin-3/2 kagome Heisenberg antiferromagnet
• The route to magnetic order in the spin-$1/2$ kagome Heisenberg antiferromagnet: The role of interlayer coupling
• Structure Factors of the Kagome-Lattice Heisenberg antiferromagnets at finite temperatures
• Thermodynamics of the kagome-lattice Heisenberg antiferromagnet with arbitrary spin $S$
• Quantum half-orphans in kagome antiferromagnets
• High temperature series expansions of S = 1/2 Heisenberg spin models: algorithm to include the magnetic field with optimized complexity
• Non-perturbative linked-cluster expansions in long-range ordered quantum systems
• Absence of long-range order in a general spin-$S$ kagome lattice Ising antiferromagnet
• Emergence of magnetic long-range order in kagome quantum antiferromagnets