  We present an improved analysis of the phase transitions in rare earth
superconductor using Ginzburg-Landau theory. Our work is based on the
systematic study of critical field and superconducting order parameter in the
presence of localized magnet due to rare-earth atom. We present the different
phases that can occur and analyze the conditions of phase transition from the
normal phase to the coexistence phase of antiferromagnetism and
super-conductivity. We calculate the critical field and Ginzburg-Landau
parameters to show the coexisting property. We compare our theoretical results
with existing experimental results.
