We present a comparative investigation of singlet ground state induced magnetism for singlet, doublet, and triplet excited CEF states of non-Kramers $f$ electrons relevant primarily for Pr- and U-based compounds. This type of magnetic order is of the intrinsic quantum nature because it requires the superposition of singlet ground state with excited states due to nondiagonal matrix elements of the effective intersite exchange to generate local moments. In contrast to conventional magnets, the local moments and their ordering appear simultaneously at the transition temperature. It is finite only if the control parameter proportional to the ratio of exchange strength to level splitting exceeds a critical value marking the quantum critical point of the models. We determine the dependence of transition temperature, saturation moment, renormalized level splitting, specific heat jumps, and low-temperature susceptibility as a function of control parameters. Furthermore, the temperature dependence of these quantities is calculated for control parameters above and below the quantum critical point and the distinction to conventional magnetism is discussed. In addition, we investigate the dynamical properties of the three models, deriving the magnetic exciton dispersion and their critical behavior. In particular, the conditions for true and arrested soft-mode behavior at the ordering wave vector are identified.

• Received 17 November 2023
• Revised 2 February 2024
• Accepted 20 February 2024

DOI:https://doi.org/10.1103/PhysRevB.109.115110