Manipulation of Jeff=32 states by tuning the tetragonal distortion

The spin-orbit entangled quantum states in $4d/5d$ compounds, e.g., the ${J}_{\mathrm{eff}}=\frac{1}{2}$ and ${J}_{\mathrm{eff}}=\frac{3}{2}$ states, have attracted great interests for their unique physical roles in unconventional superconductivity and topological states. Here, the key role of tetragonal distortion is clarified, which determines the ground states of $4{d}¹/5{d}¹$ systems to be the ${J}_{\mathrm{eff}}=\frac{3}{2}$ one (e.g., ${\mathrm{K}}₂{\mathrm{NbCl}}₆$) or the $S=\frac{1}{2}$ one (e.g., ${\mathrm{Rb}}₂{\mathrm{NbCl}}₆$). By tuning the tetragonal distortion via epitaxial strain, the occupation weights of ${d}_xy/{d}_yz/{d}_xz$ orbitals can be subtly modulated, competing with the spin-orbit coupling. Consequently, quantum phase transitions between the $S=\frac{1}{2}$ state and the ${J}_{\mathrm{eff}}=\frac{3}{2}$ state, as well as between different ${J}_{\mathrm{eff}}=\frac{3}{2}$ states, can be achieved, resulting in significant changes of local magnetic moments. Our prediction points out a reliable route to engineer new functionality of ${J}_{\mathrm{eff}}$ states in these quantum materials.