Effective field theory approach for the S=32 bilayer honeycomb antiferromagnet

Abstract

The spin-$\frac{3}{2}$ Heisenberg antiferromagnet on the bilayer honeycomb lattice is a minimal model to describe the magnetic behavior of ${\mathrm{Bi}}_{3}{\mathrm{Mn}}_{4}{\mathrm{O}}_{12}({\mathrm{NO}}_{3})$. We study this model with frustrating interlayer 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.