Theory of ferromagnetic superconductors with spin-triplet electron pairing

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.Comment: Report at Physics Congress, Sofia, Sept 2013; to appear, in: Bulg.J.Phys. (2014

Theory of ferromagnetic unconventional superconductors with spin-triplet electron pairing

A general phenomenological theory is presented for the phase behavior of ferromagnetic superconductors with spin-triplet electron Cooper pairing. The theory describes in details the temperature-pressure phase diagrams of real inter-metallic compounds exhibiting the remarkable phenomenon of coexistence of spontaneous magnetic moment of the itinerant electrons and spin-triplet superconductivity. The quantum phase transitions which may occur in these systems are also described. The theory allows for a classification of these itinerant ferromagnetic superconductors in two types: type I and type II. The classification is based on quantitative criteria.The comparison of theory and experiment is performed and outstanding problems are discussed.Comment: 25 pages, 7 figures; CP-ISSP-BAS preprint; a preliminary version of a review paper; to be submitted for a publicatio

Phase diagram of a class of spin-triplet ferromagnetic superconductors

We investigate thermodynamic phases, including the phase of coexistence of superconductivity and ferromagnetism, the possible phase transitions of first and second order, and the shape of the phase diagram in mean-field approximation for a phenomenological model of spin-triplet ferromagnetic superconductors. The results are discussed in view of application to metallic ferromagnets as UGe$_2$, ZrZn$_2$, URhGe, and Fe.Comment: 8 pages, MikTexTeX, 1 fi

Comment on "Fluctuation-induced first-order transition p-wave superconductors" by Qi Li, D. Belitz, and J. Toner [Phys. Rev. B79, 054514 (2009)]

In this Comment, we show that the paper by Qi Li, D. Belitz and J. Toner, published in Phys. Rev. B {\bf 79}, 054514 (2009), contains an incomplete mean-field analysis of a simple model of Ginzburg-Landau type. The latter contains a stable non-unitary phase, which has not been found in this study and is missing in the outlined picture of possible stable phases. In this Comment, the mean field analysis has been corrected, the errors have been explained in details and relevant topics have been discussed. Shortcomings in the mean-field-like and renormalization group studies in the mentioned paper have also been revealed.Comment: accepted in Phys. Rev.

Diamagnetic critical singularity in unconventional ferromagnetic superconductors

The scaling properties of the free energy, the diamagnetic moment, and the diamagnetic susceptibility above the phase transition from the ferromagnetic phase to the phase of coexistence of ferromagnetic order and superconductivity in unconventional ferromagnetic superconductors with spin-triplet (p-wave) electron paring are considered. The crossover from weak to strong magnetic induction is described for both quasi-2D (thin films) and 3D (bulk) superconductors. The singularities of diamagnetic moment and diamagnetic susceptibility are dumped for large variations of the pressure and, hence, such singularities could hardly be observed in experiments. The results are obtained within Gaussian approximation on the basis of general theory of ferromagnetic superconductors with p-wave electron pairing.Comment: To be published in Bulg. J. Phys (2012