Induced-moment singlet-triplet model: High-temperature series expansion

We have obtained five terms in the high-temperature series expansion for the magnetic susceptibility for the singlet-triplet model, which has been used to represent, in a simplified version, the cubic induced-moment systems such as fcc Pr, ${\mathrm{Pr}}_3$Tl, and TbSb. Our high-temperature series is valid for an arbitrary energy splitting between the singlet level and the triplet level. It also allows for arbitrary range of interaction and lattice geometry. The critical temperature as a function of the crystal field to the exchange-interaction ratio is estimated for the three cubic lattices of the nearest-neighbor interaction model. We show that the molecular-field predictions are unacceptable for induced-moment systems with the crystal-field to the exchange-interaction ratio near the critical value for magnetic ordering (at $T=0\mathrm{}$) such as fcc Pr and ${\mathrm{Pr}}_3$Tl.