Abstract:
A comprehensive theory is developed that describes the coexistence of p-wave, spin-triplet superconductivity and itinerant ferromagnetism. It is shown how to use field-theoretic techniques to derive both conventional strong-coupling theory, and analogous gap equations for superconductivity induced by magnetic fluctuations. It is then shown and discussed in detail that the magnetic fluctuations are generically stronger on the ferromagnetic side of the magnetic phase boundary, which substantially enhances the superconducting critical temperature in the ferromagnetic phase over that in the paramagnetic one. The resulting phase diagram is compared with the experimental observations in UGe_2 and ZrZn_2.

Abstract:
On the basis of a two-dimensional t-t' Hubbard model in ferromagnetic and paramagnetic states, the triplet superconducting mechanism is investigated by the third-order perturbation theory with respect to the on-site Coulomb interaction U. In general, the superconducting state is more stable in the paramagnetic state than in the ferromagnetic state. As a special case, the dominant ferromagnetic superconductivity is obtained by the electron-electron correlation between the electronlike majority and holelike minority bands. Furthermore, it is pointed out that in some cases the two bands play an essential role for the coexistence of superconductivity and ferromagnetism.

Abstract:
The experimental results for ZrZn$_{2}$, URhGe, and in some pressure ranges also for UGe$_{2}$, have shown that the ferromagnetic superconductors are weak itinerant ferromagnets. Guided by these results we describe the phenomenon of coexistence between equal spin triplet pairing superconductivity (SC) and ferromagnetism (F) using the extended Stoner model, which includes in Hamiltonian the on-site Coulomb interaction, $U$, and occupation dependent hopping integral. We use Hartree-Fock (H-F) approximation and the Green functions technique. In the H-F approximation the on-site Coulomb interaction plays the role of the on-site exchange (Hund's) field. All inter-site interactions will have included the inter-site kinetic correlation, $$, within the H-F approximation. We introduce the pressure-dependence to the hopping integral. Numerical results are compared with experimental data for ZrZn$_{2}$. The kinetic correlation creates the superconductivity without help of negative values of Coulomb interactions. The model can explain stimulation of triplet SC by the weak itinerant ferromagnetism. This effect was observed experimentally in ZrZn$_{2}$. Numerical analysis also confirms the experimental effect of decrease in critical temperatures (Curie and superconducting) with increasing external pressure.

Abstract:
Ferromagnetism is usually considered to be incompatible with conventional superconductivity, as it destroys the singlet correlations responsible for the pairing interaction. Superconductivity and ferromagnetism are known to coexist in only a few bulk rare-earth materials. Here we report evidence for their coexistence in a two-dimensional system: the interface between two bulk insulators, LaAlO$_3$ (LAO) and SrTiO$_3$ (STO), a system that has been studied intensively recently. Magnetoresistance, Hall and electric-field dependence measurements suggest that there are two distinct bands of charge carriers that contribute to the interface conductivity. The sensitivity of properties of the interface to an electric field make this a fascinating system for the study of the interplay between superconductivity and magnetism.

Abstract:
In this paper we address the question of coexistence of superconductivity and ferromagnetism in the high temperature superconductor RuSr$_2$GdCu$_2$O$_{8-\delta}$. Using a field theoretical approach we study a one-fermion effective model of a ferromagnetic superconductor in which the quasiparticles responsible for the ferromagnetism form the Cooper pairs as well. We discuss the physical features which are different in this model and the standard BCS model and consider their experimental consequences.

Abstract:
The triplet superconductivity in $UGe_2$ and $URhGe$ coexists with itinerant ferromagnetism such that in the pressure-temperature phase diagram the whole region occupied by the superconducting state is situated inside a more vast ferromagnetic region. In the same family metal UCoGe the pressure dependent critical lines T_{Curie}(P) and T_{sc}(P) of the ferromagnet and the superconducting phase transitions intersect each other. The two-band multidomain superconducting ferromagnet state arises at temperatures below both of these lines. Here I describe the symmetry and the order parameters of the paramagnet as well of the multidomain ferromagnet superconducting states. The Josephson coupling between two adjacent ferromagnet superconducting domains is discussed.

Abstract:
We extend the Blonder, Tinkham and Klapwijk theory to the study of the inverse proximity effects in the normal mental/superconductor/ferromagnet structures. In the superconducting film, there are the gapless superconductivity and the spin-dependent density of states both within and without the energy gap. It indicates an appearance of the inverse-proximity-effect-induced ferromagnetism and a coexistence of ferromagnetism and superconductivity near the interface. The influence of exchange energy in the ferromagnet and barrier strength at the superconductor/ferromagnet interface on the inverse proximity effects is discussed.

Abstract:
We show the observation of the coexistence of bulk superconductivity and ferromagnetism in CeO1-xFxBiS2(x = 0 - 1.0) prepared by annealing under high-pressure. In CeO1-xFxBiS2 system, both superconductivity and two types of ferromagnetism with respective magnetic transition temperatures of 4.5 K and 7.5 K are induced upon systematic F substitution. This fact suggests that carriers generated by the substitution of O by F are supplied to not only the BiS2 superconducting layers but also the CeO blocking layers. Furthermore, the highest superconducting transition temperature is observed when the ferromagnetism is also enhanced, which implies that superconductivity and ferromagnetism are linked to each other in the CeO1-xFxBiS2 system.

Abstract:
By combining a holographic p-wave superconductor model and a holographic ferromagnetism model, we study the coexistence and competition of ferromagnetism and p-wave superconductivity. It is found that the results depend on the self-interaction of magnetic moment of the complex vector field and which phase appears first. In the case that the ferromagnetic phase appears first, if the interaction is attractive, the system shows the ferromagnetism and superconductivity can coexist in low temperatures. If the interaction is repulsive, the system will only be in a pure ferromagnetic state. In the case that the superconducting phase appears first, the attractive interaction will leads to a magnetic p-wave superconducting phase in low temperatures. If the interaction is repulsive, the system will be in a pure p-wave superconducting phase or ferromagnetic phase when the temperature is lowered.

Abstract:
A model for coexistence of p-wave spin-triplet superconductivity (SC) and itinerant ferromagnetism (FM) is presented. The Hamiltonian can be diagonalized by using the so(5) algebraic coherent state. We obtain the coupling equations of the magnetic exchange energy and superconducting gaps through the double-time Green function. It is found that the ferromagnetisation gives rise to the phase transitions of p-wave superconducting states or superfluid of $^{3}He$.