Quadrupolar Order and Disordered States in Spin-1 Diamond Lattice Antiferromagnets

Recent experiments have demonstrated a lack of long-range magnetic order in spin-1 diamond lattice compounds such as NiRh₂O₄ [1]. These compounds can potentially provide a rich playground for exotic quantum states such as a proposed quantum spiral spin liquid [2]. We study the phase diagram of the Heisenberg model with bilinear and biquadratic interactions between nearest and next-nearest neighbors on the diamond lattice to search for ordered and quantum spin liquid states. The phase diagram for this frustrated spin-1 model reveals ground states that lack long-range spin order, including quadrupolar states and valence-bond solids. We use variational Monte Carlo with projected fermionic states to compare energies for different candidate states within a plausible region of the phase diagram corresponding to NiRh₂O₄.

[1] J.R. Chamorro et al., Phys. Rev. Materials 2, 034404 (2018).
[2] F. L. Buessen, M. Hering, J. Reuther, S. Trebst, Phys. Rev. Lett. 120, 057201 (2018).