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

TL;DR

This paper uses massive-scale computational analysis to identify rare-earth materials with strong Kitaev interactions, revealing promising candidates like Nd$^{3+}$ and Er$^{3+}$ for quantum spin liquid research.

Contribution

Developed a parallel computational program to analyze over six million intermediate states, enabling the identification of rare-earth compounds with potential Kitaev quantum spin liquid behavior.

Findings

Kitaev interactions often compete with Heisenberg interactions.

$4f^3$ and $4f^{11}$ configurations show dominant Kitaev interactions.

Potential new materials include Nd$^{3+}$ and Er$^{3+}$ compounds.

Abstract

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. This study investigates 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 $4f^3$ and $4f^{11}$ configurations showcase the prevalence of $K$ over $J$, presenting unexpected prospects for exploring the Kitaev QSLs in compounds including Nd$^{3+}$ and Er$^{3+}$, respectively. Beyond the Kitaev model, our computational program also proves adaptable to a wide range of $4f$-electron magnets.