Quantum paramagnetic ground states on the honeycomb lattice and field-induced Neel order

Bi3Mn4O12(NO3) is a recently synthesized spin-3/2 bilayer honeycomb antiferromagnet which behaves as a spin liquid down to very low temperatures. Beyond a magnetic field of about 5 T, it develops long-range Neel order. Motivated by this observation, we have studied spin-S Heisenberg models with next neighbor frustrating interactions as well as bilayer couplings on the honeycomb lattice. For a model with frustrating second-neighbor exchange, J(2), we use a Lindemann-like criterion within spin-wave theory to show that Neel order melts beyond a critical J(2). The critical J(2) is found to increase in the presence of a magnetic field, implying the existence of a field-induced paramagnet-Neel transition over a range of parameters. For the bilayer model, we use a spin-S generalization of bond operator mean-field theory to show that there is a Neel-dimer transition for various spin values with increasing bilayer coupling and that the resulting interlayer dimer state undergoes a field-induced transition into a state with transverse Neel order. Motivated by a broader interest in such paramagnets, we have also studied a spin-3/2 model which interpolates between the nearest-neighbor Heisenberg model and the Affleck-Kennedy-Lieb-Tasaki (AKLT) parent Hamiltonian. Using exact diagonalization, we have found that there is a single Neel-AKLT quantum phase transition in this model. Computing the fidelity susceptibility and assuming a transition in the O(3) universality class, we have located the critical point of this model. In addition, we have obtained the spin gap of the AKLT parent Hamiltonian. Our numerics indicate that the AKLT state also undergoes a field-induced Neel ordering transition. We discuss implications of some of our results for experiments on Bi3Mn4O12(NO3) and for numerics on the honeycomb lattice Hubbard model.