Frustrated trimer chain model and ${\mathrm{Cu}}_3{\mathrm{Cl}}_6{(\mathrm{H}}_2{\mathrm{O})}_2{\mathrm{\cdot }2\mathrm{H}}_8{\mathrm{C}}_4{\mathrm{SO}}_2$ in a magnetic field

Recent magnetization and susceptibility measurements on ${\mathrm{Cu}}_3{\mathrm{Cl}}_6{(\mathrm{H}}_2{\mathrm{O})}_2{\mathrm{\cdot }2\mathrm{H}}_8{\mathrm{C}}_4{\mathrm{SO}}_2$ by Ishii et al. [J. Phys. Soc. Jpn. 69, 340 (2000)] have demonstrated the existence of a spin gap. In order to explain the opening of a spin gap in this copper-trimer system, Ishii et al. have proposed a frustrated trimer chain model. Since the exchange constants for this model have not yet been determined, we develop a 12th-order high-temperature series for the magnetic susceptibility and fit it to the experimentally measured one. We find that some of the coupling constants are likely to be ferromagnetic. The combination of several arguments does not provide any evidence for a spin gap in the parameter region with ferromagnetic coupling constants, but further results, e.g., for the magnetization process are in qualitative agreement with the experimental observations.