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The crystalline electric field (CEF) is investigated inPr$_3$Pt$_{23}$Si$_{11}$ and Nd$_3$Pt$_{23}$Si$_{11}$ by neutron spectroscopy(NS). At low temperature, the number of observed CEF excitations is consistentwith the orthorhombic symmetry at the rare earth site. This agrees withprevious results on Ce$_3$Pt$_{23}$Si$_{11}$. For Pr- andNd$_3$Pt$_{23}$Si$_{11}$, the number of CEF parameters is too large to allowfor an unambiguous determination. This determination is possible forCe$_3$Pt$_{23}$Si$_{11}$, due to a reduced number of parameters and to theavailability of extensive experimental data. A specific procedure is developedfor this purpose that combines genetic algorithmics and optimization methods.An unique set of CEF parameters is found for Ce$_3$Pt$_{23}$Si$_{11}$. Itreveals a strong anisotropy at the orthorhombic site, responsible for an easythreefold magnetization axis in the cubic system. Using a microscopic,mean-field, description, the magnetization processes in the paramagnetic andferromagnetic phases of Ce$_3$Pt$_{23}$Si$_{11}$ are well reproduced.Ce$_3$Pt$_{23}$Si$_{11}$ is shown to realize a model for systems whereconflicting anisotropies are forced to cooperate.

Crystal field investigation in the light rare earth R$_3$Pt$_{23}$Si$_{11}$ compounds