Order-by-disorder from Schwinger bosons in a frustrated honeycomb ferromagnet

TL;DR

This paper investigates the origin of a double-zigzag magnetic order in a honeycomb magnet using a Schwinger-boson mean-field approach, revealing quantum fluctuation-driven order-by-disorder effects consistent with experiments.

Contribution

It introduces a generalized Schwinger-boson mean-field theory to explain the double-zigzag phase in a frustrated honeycomb magnet, aligning with recent numerical and experimental findings.

Findings

Double-zigzag phase emerges in a narrow parameter range due to quantum fluctuations.

Order-by-disorder mechanism stabilizes the magnetic order.

Results agree with density-matrix renormalization-group and neutron scattering data.

Abstract

The cobalt-based honeycomb magnet BaCo$_2$(AsO$_4$)$_2$ (BCAO) has recently emerged as a promising platform for frustrated magnetism beyond conventional paradigms. Neutron-scattering experiments and first-principles calculations have revealed an unexpected double-zigzag (dZZ) magnetically ordered ground state, whose microscopic origin remains under active debate. Here, we revisit this problem within a ferro--antiferromagnetic $J_1$--$J_3$ Heisenberg model on the honeycomb lattice using a generalized Schwinger-boson mean-field theory (gSBMFT) that treats ferromagnetic and antiferromagnetic interactions on equal footing. This approach, combined with exact diagonalization (ED), allows us to demonstrate the emergence of the dZZ phase in a narrow parameter range, stabilized by quantum fluctuations through an order-by-disorder mechanism, in good agreement with recent density-matrix renormalization-group (DMRG) results. We further characterize the associated magnetic excitations and discuss their relevance to recent inelastic neutron-scattering (INS) measurements on BCAO.