Quantum paramagnets on the honeycomb lattice and field-induced Néel order: Possible application to Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$)

Abstract

Motivated by recent experiments on the spin-3/2 frustrated bilayer honeycomb antiferromagnet Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$), we study the spin-S Heisenberg model on the honeycomb lattice with various additional exchange interactions which frustrate Néel order. Using spin wave theory, exact diagonalization, and bond operator theory, we consider the effects of (i) second-neighbor exchange, (ii) biquadratic exchange for $S=3/2$ which leads to an AKLT valence bond solid, and (iii) bilayer coupling which leads to an interlayer dimer solid. We show that the resulting paramagnetic states undergo a transition to Néel order beyond a critical magnetic field. We discuss experimental implications for Bi${}_3$Mn${}_4$O${}_{12}$(NO${}_3$).

5 pages, 4 figures; 2 page supplementary material with 1 figure; Longer, updated version: arXiv:1104.0691

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• Bose-Einstein Condensation in Magnetic Insulators
• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Affleck-Kennedy-Lieb-Tasaki State on a Honeycomb Lattice is a Universal Quantum Computational Resource
• Disordered Ground State and Magnetic Field-Induced Long-Range Order in an S=3/2 Antiferromagnetic Honeycomb Lattice Compound Bi3Mn4O12(NO3)
• Spin-gap phase of a quantum spin system on a honeycomb lattice
• Bond-operators and triplon analysis for spin-S dimer antiferromagnets
• Variational RVB wave function for the spin-1/2 Heisenberg Model on honeycomb lattice

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