Generalized Ginzburg-Landau theory for the magnetostatics of ferromagnetic superconductors

The phase diagram of ferromagnetic superconductors is investigated on the basis of a semimacroscopic free-energy functional. A self-consistent decoupling of the fourth-order term in the magnetization sigma-arrow-right and the assumption of a homogeneous modulus psi0 of the superconducting order parameter psi allows one to integrate out the fluctuating parts of magnetization and magnetic induction B as well as the phase of psi. The resulting free-energy function depends only on the homogeneous parts psi0, sigma-arrow-right0, and B0. The thermodynamically stable states can be found by minimization. We present model calculations for the phase diagram and discuss the order of the transitions involved. Good agreement with recent measurements including specific-heat data is obtained. The possible occurrence of a coexisting phase is discussed in the frame of our model