Crystal field investigation in the light rare earth R$_3$Pt$_{23}$Si$_{11}$ compounds
The crystalline electric field (CEF) is investigated in Pr$_3$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 consistent with the orthorhombic symmetry at the rare earth site. This agrees with previous results on Ce$_3$Pt$_{23}$Si$_{11}$. For Pr- and Nd$_3$Pt$_{23}$Si$_{11}$, the number of CEF parameters is too large to allow for an unambiguous determination. This determination is possible for Ce$_3$Pt$_{23}$Si$_{11}$, due to a reduced number of parameters and to the availability of extensive experimental data. A specific procedure is developed for this purpose that combines genetic algorithmics and optimization methods. An unique set of CEF parameters is found for Ce$_3$Pt$_{23}$Si$_{11}$. It reveals a strong anisotropy at the orthorhombic site, responsible for an easy threefold magnetization axis in the cubic system. Using a microscopic, mean-field, description, the magnetization processes in the paramagnetic and ferromagnetic 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 where conflicting anisotropies are forced to cooperate.