Ginzburg-Landau theory for the magnetic and structural transitions in La$_{1-y}$(Ca$_{1-x}$Sr$_{x}$)$_{y}$MnO$_{3}$

We present a phenomenological theory for the ferromagnetic transition temperature, the magnetic susceptibility at high temperatures, and the structural distortion in the La$_{1-y}$(Ca$_{1-x}$Sr$_{x}$)$_{y}$MnO$_{3}$ system. We construct a Ginzburg-Landau free energy that describes the magnetic and the structural transitions, and a competition between them. The parameters of the magnetic part of the free energy are derived from a mean-field solution of the magnetic interaction for arbitrary angular momentum. The theory provides a qualitative description of the observed magnetic and structural phase transitions as functions of Sr-doping level ($x$) for $y=0.25$.