Kitaev physics beyond 4d5 and 5d5 honeycomb lattices: understanding 3d7-3d7 exchange, strategies for optimizing Kitaev couplings

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Magnetic systems with a layered honeycomb structure represent a topic of active research. The celebrated Kitaev spin liquid may be realized in such compounds, a collective state of matter displaying long-range quantum entanglement and unconventional fractionalized excitations. This has been argued to be relevant for applications in topological quantum computing.The essential feature of the Kitaev model is that there is a different type of intersite coupling for each of the three magnetic links originating from a given magnetic site of the honeycomb lattice, KSixSjx, KSiySky, and KSizSlz, where j, k, l are nearest neighbors of the reference (pseudo)spin i. Just in this form, the one initially analyzed by Kitaev, the model is exactly solvable. As potential platforms for materializing it, 5d5 and 4d5 honeycomb materials such as Na2IrO3 and RuCl3 were pointed out at the early stages. It turns out however that, even if K is large in iridates and ruthenates, there are additionally residual isotropic Heisenberg J couplings that tend to obstruct the formation of the quantum spin liquid. In the search for alternative settings, a number of 3d7 cobalt and nickel honeycomb compounds were very recently brought to the fore. Considerations based on effective-model superexchange theory, leading to the conclusion that K/J ratios superior to those realized in 5d5 iridates and 4d5 ruthenates can be in principle achieved, seem to find support in the latest experimental data. In this frame of reference, we would like to address the underlying electronic interaction mechanisms in 3d7 honeycomb systems of major present interest quantitatively and in a systematic manner, using advanced quantum-chemical electronic-structure computations. Principal aspects to be clarified are (i) the ratio between Kitaev and Heisenberg interactions (K/J) and starting from here the prospects for robust spin liquid ground states in these 3d7 compounds, (ii) the strength of off-diagonal Siα-Sjβ effective exchange couplings (so-called Γ's), (iii) what is similar and what is different between intersite virtual processes in 3d7 t2g5eg2 honeycomb oxides and t2g5-t2g5 superexchange in honeycomb 5d5/4d5 oxides/halides, (iv) the effect of O-cage trigonal distortion on the strength of the effective intersite interactions and the M-O-M bond angles that maximize the K/J ratio, (v) how the less standard chemical environment next to the M-O2-M magnetic paths (i.e., strongly covalent Pn-O and Te-O bonds) affects magnetism. The use of multiconfiguration and multireference methods from wavefunction-based quantum chemistry will enable a balanced treatment, on equal footing, of competing electron configurations and of the different superexchange processes. Our work will set the playground for new insights into the correlated electronic structures of these materials and will provide solid reference ab intio data in the context of Kitaev-Heisenberg magnetism in transition-metal compounds.