Emergent Berezinskii-Kosterlitz-Thouless and Kugel-Khomskii Physics in the Triangular Lattice Bilayer Colbaltate

Motivated by the experiments on the triangular lattice bilayer colbaltate K_{2}Co_{2}(SeO_{3})_{3}, we consider an extended XXZ model to explore the underlying physics. The model is composed of interacting Co^{2+} dimers on the triangular lattice, where the Co^{2+} ion provides an effective spin-1/2 local moment via the spin-orbit coupling and the crystal field effect. The intradimer interaction is dominant and would simply favor the local spin singlet, and the interdimer interactions compete with the interdimer interaction, leading to rich behaviors. With the easy-axis anisotropy, it is shown that, in the ground state manifold of the intradimer Ising interaction, the system realizes an effective quantum Ising model, where the ground state is either a three-sublattice order with a mixture of antiferromagnetic Ising order and a valence-bond spin singlet or Ising disordered. The finite temperature regime realizes the Berezinskii-Kosterlitz-Thouless physics. To explore the full excitations, we incorporate the excited state manifold of the intradimer Ising interaction and establish the emergent Kugel-Khomskii physics. Thus, the triangular lattice bilayer colbaltate is an excellent platform to explore the interplay between geometrical frustration and anisotropic interactions as well as the emergent effective models and the resulting physics.