Dipolar and quadrupolar orderings in theΓ3−Γ5magnetic system

The dipolar and quadrupolar orderings in the doublet-triplet (${\Gamma }_3-{\Gamma }_5$) system is studied on the basis of a symmetry-adapted spin-Hamiltonian under molecular-field approximation. One obtains pure quadrupolar ordering or dipolar and quadrupolar orderings either at one particular temperture or at two different temperatures depending on the ratio of the bilinear and biquadratic pair interactions. The separation between the ground ${\Gamma }_3$ and the excited ${\Gamma }_5$ levels plays an important role on the nature of the phase transitions. The cases of TmCd and TmZn are discussed.