Kondo-Ising and tight-binding models for TmB4

In ${\mathrm{TmB}}₄$, localized electrons with a large magnetic moment interact with metallic electrons in boron-derived bands. We examine the nature of ${\mathrm{TmB}}₄$ using full-relativistic ab initio density functional theory calculations, approximate tight-binding Hamiltonian results, and the development of an effective Kondo-Ising model for this system. Features of the Fermi surface relating to the anisotropic conduction of charge are discussed. The observed magnetic moment $\ensuremath{\sim}6\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_B$ is argued to require a subtle crystal field effect in metallic systems, involving a flipped sign of the effective charges surrounding a Tm ion. The role of on-site quantum dynamics in the resulting Kondo-Ising type ``impurity'' model are highlighted. From this model, elimination of the conduction electrons will lead to spin-spin (RKKY-type) interaction of Ising character required to understand the observed fractional magnetization plateaus in ${\mathrm{TmB}}₄$.