An effective field theory approach for the $S = 3/2$ bilayer honeycomb antiferromagnet

TL;DR

This paper develops an effective field theory for the spin-3/2 bilayer honeycomb antiferromagnet, explaining how quantum and thermal fluctuations select a specific magnetic order near experimental parameters.

Contribution

It introduces a continuum field theory approach that captures fluctuation effects and explains order selection in the model relevant to Bi$_3$Mn$_4$O$_{12}$(NO$_3$).

Findings

Quantum and thermal fluctuations lift degeneracy and select a collinear state.

The theory aligns with experimental observations of the magnetic behavior.

A specific point in parameter space exhibits fluctuation-induced order.

Abstract

The spin-3/2 Heisenberg antiferromagnet on the bilayer honeycomb lattice is a minimal model to describe the magnetic behavior of Bi$_3$Mn$_4$O$_{12}$(NO$_3$). We study this model with frustrating inter-layer second-neighbor couplings, taking into account quantum and thermal fluctuations. We use a path integral formulation in terms of coherent states to describe the low energy physics of the model. We show that for a particular point in the parameter space, close to the experimental estimated couplings, a continuum classical degeneracy is lifted by both quantum and thermal fluctuations, and a collinear state is then selected by an order by disorder mechanism. Our results provide a global perspective in the understanding of the experimental observations.