${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ is a promising candidate to realize the Kitaev spin liquid phase since the large Kitaev spin exchange interaction is tunable via the change in electronic structure, such as the trigonal crystal field splitting (${\mathrm{\Delta }}_{\text{TCF}}$). Here, we show that the uncorrelated electronic structure of ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ is rather insensitive to the strain effect due to the low crystal symmetry accompanied by oxygen displacements and the presence of Sb $s$ orbitals. Using density functional theory plus dynamical mean field theory, we find that the correlated electronic structure of ${\mathrm{Na}}_3{\mathrm{Co}}_2{\mathrm{SbO}}_6$ is an orbital-selective Mott insulating state where the trigonal $a_{1g}$ orbital is insulating due to the nearly full occupation, while other $d$ orbitals behave as typical Mott insulators, resulting in the effective tunability of ${\mathrm{\Delta }}_{\text{TCF}}$ under the strain effect. The sign change of ${\mathrm{\Delta }}_{\text{TCF}}$ can occur as the in-plane tensile strain is applied, and the Kitaev spin liquid phase could possibly be realized due to the strongly suppressed ${\mathrm{\Delta }}_{\text{TCF}}$ under tensile strain. Our results show that the local Co-site symmetry and dynamical correlation effects will play an important role in engineering the novel magnetic phase in this and related materials.

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• Electronic structure
• Jahn-Teller effect
• Magnetism
• Quantum spin liquid
• Honeycomb lattice
• Strongly correlated systems
• Density functional theory
• Dynamical mean field theory
• Kitaev-Heisenberg model
• Wannier function methods