Ferrimagnetic Kitaev spin liquids in mixed spin-$\frac{1}{2}$ and spin-$\frac{3}{2}$ honeycomb magnets
Abstract
We explore the phase diagram of a mixed-spin Kitaev model, where spin-$1/2$ and spin-$3/2$ ions form a staggered pattern on a honeycomb lattice. Enabled by an exact mapping of local conserved flux operators onto $Z_2$ gauge fields, we perform a parton mean-field theory for the model with a single-ion anisotropy. The phase diagram contains four types of quantum spin liquids distinguished by quadrupolar parameters. These analytical results are quantitatively confirmed by state-of-the-art DMRG simulations. We also explore the potential experimental realization of the mixed-spin Kitaev model in materials such as Zr${}_{0.5}$Ru${}_{0.5}$Cl${}_{3}$. By developing a superexchange theory specifically for this mixed-spin system, we identify the conditions under which dominant Kitaev-like interactions emerge. Our findings highlight the importance of spin-orbital couplings and quadrupolar order parameters in stabilizing exotic phases, providing a foundation for exploring mixed-spin Kitaev magnets.