Exploring rare-earth Kitaev magnets by massive-scale computational analysis

The Kitaev honeycomb model plays a pivotal role in the quest for quantum spin liquids, in which fractional quasiparticles would provide applications in decoherence-free topological quantum computing. The key ingredient is the bond-dependent Ising-type interactions, dubbed the Kitaev interactions, which require strong entanglement between spin and orbital degrees of freedom. Here we investigate the identification and design of rare-earth materials displaying robust Kitaev interactions. We scrutinize all possible 4f electron configurations, which require up to 6+ million intermediate states in the perturbation processes, by developing a parallel computational program designed for massive-scale calculations. Our analysis reveals a predominant interplay between the isotropic Heisenberg J and anisotropic Kitaev K interactions across all realizations of the Kramers doublets. Remarkably, instances featuring 4f3 and 4f11 configurations showcase the prevalence of K over J, presenting unexpected prospects for exploring the Kitaev quantum spin liquids in compounds, including Nd3+ and Er3+, respectively. Kitaev magnets are interesting as they can host quantum spin liquid phases and fractional quasiparticles for decoherence-free topological quantum computing. Here, a parallel computational program explores all possible 4f electron configurations of rare-earth Kitaev materials, identifying those configurations, such as 4f3 and 4f11 in Nd3+ and Er3+ compounds, where anisotropic Kitaev interactions prevail over isotropic Heisenberg exchange.