Ground state properties, excitation spectra and phase transitions in the $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb Lattice

TL;DR

This study investigates the ground state, excitation spectra, and phase transitions of $S=1/2$ and $S=3/2$ bilayer Heisenberg models on the honeycomb lattice, revealing how frustration influences magnetic order and relating findings to the material Bi$_3$Mn$_4$O$_{12}$NO$_3$.

Contribution

It provides a comparative analysis of $S=1/2$ and $S=3/2$ models using series expansions, highlighting the effects of frustration on phase transitions and excitation spectra.

Findings

Good agreement with Quantum Monte Carlo results for unfrustrated cases.

Frustration rapidly suppresses magnetic order in the $S=3/2$ system.

Excitation spectra in the disordered phase are characterized.

Abstract

Motivated by the observation of a disordered spin ground state in the $S=3/2$ material Bi$_3$Mn$_4$O$_{12}$NO$_3$, we study the ground state properties and excitation spectra of the $S=3/2$ (and for comparison $S=1/2$) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the N\'eel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in $1/\lambda=J_1/J_{\perp}$, where $J_1$ is an in-plane exchange constant and $J_\perp$ is the exchange constant between the layers are used to study properties of the spin singlet phase. For the unfrustrated case, our results for the phase transitions are in very good agreement with recent Quantum Monte Carlo studies. We also obtain the excitation spectra in the disordered phase and study the change in the critical $\lambda$ when frustrating exchange interactions are added to the $S=3/2$ system and find a rapid suppression of the ordered phase with frustration. Implications for the material Bi$_3$Mn$_4$O$_{12}$NO$_3$ are discussed.