The importance of direct exchange in Kitaev magnetism

In magnetism research, Kitaev's honeycomb spin model is one of the revelations of the 21st century: it hosts a quantum spin-liquid ground state that can be described analytically. Current scenarios for the occurrence of bond-dependent magnetic interactions as proposed by Kitaev rely on indirect exchange mechanisms based on intersite electron hopping. Analyzing the wavefunctions of Kitaev magnetic bonds at both single- and multiconfiguration levels, we find however that direct, Coulomb exchange may be at least as important in $5d$ and $4d$   $t_{2g}^5$ , $3d$   $t_{2g}^5{e}_g^2$ , and even rare-earth $4f^1$ Kitaev-Heisenberg magnets. The Coulomb exchange mechanism hints at Kitaev physics in materials that so far were not expected to host it, new ways of tuning the relative strength of the Kitaev interaction, and new design principles for Kitaev spin liquids.