We present a general thermodynamic theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory is based on extended Ginzburg-Landau expansion in powers of superconducting and ferromagnetic order parameters. We propose a simple form for the dependence of theory parameters on the pressure that allows correct theoretical outline of the temperature-pressure phase diagram for which, at low temperatures, a stable phase of coexistence of $p$-wave superconductivity and itinerant ferromagnetism appears. We demonstrate that the theory is in agreement with the experimental data for some intermetallic compounds that are experimentally proven to be itinerant ferromagnetic exhibiting spin-triplet superconductivity. Some basic features of quantum phase transitions in such systems are explained and clarified. We propose to group the spin-triplet ferromagnetic superconductors in two different types of thermodynamic behavior, on the basis of quantitative criterion deduced from the present theory and the analysis of experimental data.

• Received 9 November 2008

DOI:https://doi.org/10.1103/PhysRevB.79.064501