Induced order and collective excitations in three-singlet quantum magnets

The quantum magnetism in a three-singlet model (TSM) with singlet crystalline electric field (CEF) states interacting on a lattice is investigated, motivated by its appearance in compounds with 4f^2 and 5f^2 electronic structure. Contrary to conventional (semi-classical) magnetism there are no preformed moments above the ordering temperature Tm. They appear spontaneously as induced or excitonic moments due to singlet-singlet mixing at Tm. In most cases the transition is of second order, however for large matrix elements between the excited states it turns into a first order transition at a critical point. Furthermore we derive the excitonic mode spectrum and its quantum critical soft mode behaviour which leads to the criticality condition for induced order as expressed in terms of the control parameters of the TSM and discuss the distinctions to the previously known two-singlet case. We also derive the temperature dependence of order parameters for second and first order transitions and the exciton spectrum in the induced magnetic phase.