Role of quantum fluctuations on spin liquids and ordered phases in the Heisenberg model on the honeycomb lattice

TL;DR

This study maps the phase diagram of the J1-J2-J3 Heisenberg model on the honeycomb lattice, revealing a quantum spin liquid for S=1/2 that diminishes as S increases, and provides insights into magnetic properties relevant for experiments.

Contribution

It introduces a fully unrestricted Schwinger boson approach to analyze magnetic phases and quantum fluctuations in the honeycomb J1-J2-J3 model for different spin values.

Findings

Quantum spin liquid exists for S=1/2 but is destroyed for S=1.

Phase diagrams are mapped using SU(2) and SU(3) Schwinger boson representations.

Results suggest experimental tests via neutron scattering and susceptibility measurements.

Abstract

Motivated by the rich physics of honeycomb magnetic materials, we obtain the phase diagram and analyze magnetic properties of the spin-1/2 and spin-1 J1-J2-J3 Heisenberg model on the honeycomb lattice. Based on the SU(2) and SU(3) symmetry representations of the Schwinger boson approach, which treats disordered spin liquids and magnetically ordered phases on an equal footing, we obtain the complete phase diagrams in the (J2,J3)plane. This is achieved using a fully unrestricted approach which does not assume any pre-defined Ansatze. For S=1/2, we find a quantum spin liquid (QSL) stabilized between the N\'eel, spiral and collinear antiferromagnetic phases in agreement with previous theoretical work. However, by increasing S from 1/2 to 1, the QSL is quickly destroyed due to the weakening of quantum fluctuations indicating that the model already behaves as a quasi-classical system. The dynamical structure factors and temperature dependence of the magnetic susceptibility are obtained in order to characterize all phases in the phase diagrams. Moreover, motivated by the relevance of the single-ion anisotropy, D, to various S=1 honeycomb compounds, we have analyzed the destruction of magnetic order based on a SU(3) representation of the Schwinger bosons. Our analysis provides a unified understanding of the magnetic properties of honeycomb materials realizing the J1-J2-J3 Heisenberg model from the strong quantum spin regime at S=1/2 to the S=1 case. Neutron scattering and magnetic susceptibility experiments can be used to test the destruction of the QSL phase when replacing S=1/2 by S=1 localized moments in certain honeycomb compounds.