Quadrupolar transition in CeB₆: A new theoretical description

The well-separated ground state of the 4-fold degeneracy (Γ₈ quartet) of a Ce³⁺ ion is an important prerequisite of the quadrupolar ordering in CeB₆. A new description for the Γ₈ quartet is proposed in terms of spin-like and orbital-like Pauli matrices, σ and τ. A unusual dependence of orbital ordering on magnetic field H and temperature T is explained in terms of mode-coupling effects. The theory naturally explains the orbitally modulated structure, the transition temperature behaviour, T_Q 1 vs H, as well as the growing anomaly of the specific heat at T_Q(H) with H increasing. Similar approach in terms of σ and τ matrices is available for the one f-hole compounds, e.g., TmTe.