Computational design of f-electron Kitaev magnets: Honeycomb and hyperhoneycomb compounds A2PrO3 (A = alkali metals)

The Kitaev spin model offers an exact quantum spin liquid in the ground state, which has stimulated exploration of its material realization over the last decade. Thus far, most of the candidates are found in 4d- and 5d-electron compounds, in which the low-spin d(5) electron configuration subject to strong spin-orbit coupling comprises a Kramers doublet with the effective angular momentum j(eff) = 1/2 and gives rise to the bond-dependent anisotropic interactions in the Kitaev model. Extending the recent work on another candidates in 4f-electron compounds [S.-H. Jang et al., Phys. Rev. B 99, 241106(R) (2019)], here we systematically study the Pr-based materials A(2)PrO(3) (A = alkali metals) on both quasi-two-dimensional honeycomb and three-dimensional hyperhoneycomb structures. By using the ab initio-based scheme used in the previous study, we show that the low-energy magnetic properties of A(2)PrO(3) are well described by an effective spin model with the isotropic Heisenberg, anisotropic Kitaev, and symmetric off-diagonal interactions, dubbed the J-K-Gamma' model, with systematic modulations of the exchange coupling constants for the A-site substitution; while increasing the A-site ionic radii, J is not largely modulated but the antiferromagnetic K is reduced and Gamma' is slightly increased. We analyze the systematic changes by decomposing each interaction into the contributions from different perturbation processes in terms of both virtual hoppings and intermediate states. In addition, by computing the ground states of the J-K-Gamma' model by using the exact diagonalization, we map out the systematic evolution of the model parameters in the phase diagram. Our results will stimulate material exploration of the antiferromagnetic Kitaev interaction in f-electron compounds, including the previously-synthesized honeycomb and hyperhoneycomb compounds, Na2PrO3.