We will theoretically explore how the spin-orbit coupling could give rise to the unusual ordered, amorphous or liquid states of the spin-orbital and the spin-lattice degrees of freedom depending on the local d-electron counting and the lattice geometry.
From this perspective, I will discuss d^1 and d^2 correlated transition metal compounds, such as molybdenum oxides with double perovskite or pyrochlore structures and layered honeycomb materials, and provide a brief overview of the available experimental results.
