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The prospect of realizing quantum spin-liquid ground states in layered honeycomb materials with strong spin-orbit interactions has triggered intense research activity in the condensed matter community [1]. Of particular interest is the Kitaev Hamiltonian on the honeycomb lattice [2]. In this work, we study the recently synthesized rare-earth Kitaev magnet YbCl₃. Our many-body wavefunction-based quantum chemistry calculations establish that this quasi-two-dimensional system is a highly anisotropic material with the anisotropy arising not only from magnetic exchange but also from ligand field on the Yb³⁺ ions. We find that the ground state is magnetically frustrated with an antiferromagnetic Kitaev exchange coupling, approximately four times as large as the isotropic Heisenberg couplings. By using exact diagonalization based on the generalized anisotropic effective Hamiltonian, we reveal a rich magnetic phase diagram with sizable second and third neighbor coupling stabilizing the system in a long range antiferromagnetic order, which is confirmed by experiments [3].

[1] K. Kitagawa et al., Nature 554, 341 (2018).
[2] A. Kitaev, Ann. Phys. 321, 2 (2006).
[3] J. Xing et al., Phys. Rev. B 102, 01442717 (2020)