Theory of Ferromagnetic Superconductors with Spin-Triplet Electron Pairing *

Abstract. A general quasi-phenomenological theory that describes phases and phase transitions of ferromagnetic superconductors with spin-triplet electron Cooper pairing is presented. The theory is based on extended Ginzburg-Landau expansion in powers of superconducting and ferromagnetic order parameters. A simple form for the dependence of theory parameters on the pressure ensures a correct theoretical outline of the temperature-pressure phase diagram where a stable phase of coexistence of p-wave superconductivity and itinerant ferromagnetism appears. This new theory is in an excellent agreement with the experimental data for intermetallic compounds, for example, UGe2, URhGe, UCoGe, and UIr that are experimentally proven to be itinerant ferromagnets exhibiting spin-triplet superconductivity. The mechanism of appearance of superconductivity due to itinerant ferromagnetism (M -trigger effect) is established and demonstrated. On the basis of the same theory, basic features of quantum phase transitions in this type of ferromagnetic superconductors are explained in agreement with the experimental data. The theory allows for a classification of the spin-triplet ferromagnetic superconductors in two different types: type I and type II. The classification is based on quantitative criteria, i.e., on simple relations between theory parameters. Both theory and experiment indicate that the two types of p-wave ferromagnetic superconductors are well distinguished by essential differences in their physical properties