| We consider the competition of superconductivity (S) and itinerant ferromagnetism (F) due to a Stoner-type exchange or spin bandwidth asymmetry in different cases: intrinsic systems with singlet/triplet type pairing, S/F bilayer with chiral triplet p- or singlet d-wave pairing. In the former situation, we present the analysis on the competition between pairing and magnetic exchange by explicitly taking into account the role of various key aspects like the system size, the symmetry breaking, as well as the nature of spin polarizing interactions. The basic problem is related to individuate the best conditions for the coexistence of singlet type superconductivity and ferromagnetism. In this context, the exact solution of a model Hamiltonian that contains the above features is exploited to determine the overall phase diagram in presence of different type of magnetic exchange. The focus is on the general conditions for the stability of coexisting superconductivity and magnetism together with that for having inhomogeneous structure of the paired configurations. We show that the occurrence of ground states with a non uniform energy profile can be related to exchange mechanisms that soften the competition between pairing and depairing processes. Bridging such knowledge to the field of asymmetric superfluids in harmonic traps, we will also address some issues about the current debate on phase separated and/or mixture of normal/polarized superfluids in ultra cold Fermi gas. For the hetero-structures, we consider the proximity effect within a junction made of an unconventional superconductor (US) and a ferromagnet (F) in the limit of high barrier transparency. Superconductivity of chiral p-wave or singlet d-wave form in the US side is described by an extended Hubbard model with intersite attractive interaction, while metallic ferromagnetism in the F side is assumed to be originated by a relative change in the bandwidths of electrons with opposite spin. The effect of this mass-split mechanism is analyzed in conjunction with the usual Stoner-like one where one band is rigidly shifted with respect to the other band due to the presence of a constant exchange field. Starting from the numerical solution of the Bogoliubov-de Gennes equations, we show that the two above-mentioned mechanisms for ferromagnetism lead to different features as concerns the propagation of singlet and triplet superconducting components in the F side of the junction as well as the formation of bound states at the interface. This considerably affects the opening of gap-like structures in the local density of states at the interface for majority and minority spin electrons, leading to distinct effects as one moves towards the half-metallic regime where the density of the minority carriers becomes vanishing. |
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