  The crystalline electric field (CEF) of Ce3+ in trigonal symmetry has
recently become of some relevance, for instance, in the search of frustrated
magnetic systems. Fortunately, it is one of the CEF case in which a manageable
analytic solution can be obtained. Here, we present this solution for the
general case, and use this result to determine the CEF scheme of the new
compound CeIr3Ge7 with the help of T-dependent susceptibility and isothermal
magnetization measurements. The resulting CEF parameters B20 = 34.4 K, B40 =
0.82 K and B43 = 67.3 K correspond to an exceptional large CEF splittings of
the first and second excited levels, 374 K and 1398 K, and a large mixing
between the +-|5/2> and the -+|1/2> states. This indicates a very strong easy
plane anisotropy with an unusual small c-axis moment. Using the same general
expressions, we show that the properties of the recently reported system
CeCd3As3 can also be described by a similar CEF scheme, providing a much
simpler explanation for its magnetic properties than the initial proposal.
Moreover, a similar strong easy plane anisotropy has also been reported for the
two compounds CeAuSn and CePdAl4Ge2, indicating that the CEF scheme elaborated
here for CeIr3Ge7 corresponds to an exemplary case for Ce3+ in trigonal
symmetry.
