Induced order and collective excitations in three-singlet quantum magnets

For even $f$-electron compounds (e.g., Pr, U) the ground state may be a nonmagnetic singlet, nevertheless magnetic order appears. The moments are induced simultaneously with the ordering. This excitonic quantum magnetism is investigated by the author within a general three-singlet model. The precursor soft magnetic excitons, the transition temperature, and the induced saturation moment are derived. Furthermore, the phase diagram with possible first- and second-order transitions and critical behavior of magnetic exciton dispersions across the transition are obtained.