Exploring Kitaev Physics in Honeycomb Magnets A₃Ni₂XO₆ (A = Li, Na; X = Bi, Sb): Insights from First-Principles Calculations

Magnets exhibiting the Kitaev interaction, a bond-dependent magnetic interaction in honeycomb lattices, are generally regarded as promising candidates for hosting novel phenomena like quantum spin liquid states. However, realizing such magnets remains a significant challenge. Recently, some studies have suggested honeycomb magnets A₃Ni₂XO₆ (A = Li, Na; X = Bi, Sb) with a high spin S = 1 could serve as potential candidates for realizing strong Kitaev interactions. In this work, we systematically investigate their magnetic properties, with a particular emphasis on their Kitaev interactions, using first-principles calculations and Monte Carlo simulations. Our results indicate that all A₃Ni₂XO₆ compounds are zigzag antiferromagnets, and their magnetic moments almost tend to be out of plane. We find that their dominant magnetic interactions are the nearest-neighbor ferromagnetic and third-nearest-neighbor antiferromagnetic Heisenberg interactions, while their Kitaev interactions are extremely weak. By analyzing their electronic structures and the mechanism of generating their magnetic interactions, we reveal that either artificially tuning spin-orbit coupling or applying strain cannot produce sufficient spin-orbit entangled states to realize the intriguing Kitaev interactions. Our work advances the understanding of the magnetism in A₃Ni₂XO₆ compounds and provides insights for further exploration of Kitaev physics in honeycomb magnets.