Magnetic Nonlinear Response of UPt$_3$: An augmented Landau approach

Several heavy fermion materials, including UPt$_3$, exhibit a rapid but gradual rise in the magnetization at a critical field, without an apparent phase transition at any temperature $T>0$, with the possibility of a first order transition at $T \equiv0$. To model such a quantum phase transition it is most appropriate to develop approaches considering the quantum nature of the spins. Within a fully classical framework, we show that it is sufficient to start from a Landau-type free energy with an added Bragg-Williams entropy term to arrive at a number of key experimental features as seen in UPt$_3$. In particular, we show that correctly arriving at the measured (low-field) higher order susceptibilities necessarily invokes an isobestic (crossing) point at a high field in the magnetization isotherms. We also present a full analysis of the angular dependence of the (low-field) linear and nonlinear susceptibilities which when extended also capture the anisotropic high field response of the magnetization. Key to this success is the proper conversion of the evaluated magnetization from constant volume to a constant pressure situation relevant at high fields in heavy fermion materials.