The quantum magnetism in a three-singlet model (TSM) with singlet crystalline electric field states interacting on a lattice is investigated, motivated by its appearance in compounds with $4f^2$ and $5f^2$ electronic structures. Contrary to conventional (semiclassical) magnetism, there are no preformed moments above the ordering temperature $T_m$. They appear spontaneously as induced or excitonic moments due to singlet-singlet mixing at $T_m$. 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 behavior, 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.

• Received 23 January 2021
• Revised 25 March 2021
• Accepted 5 April 2021

DOI:https://doi.org/10.1103/PhysRevB.103.144435

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Published by the American Physical Society