We present the derivation of an ab initio and parameter-free effective electron-electron interaction that goes beyond the screened random phase approximation and accounts for superconducting pairing driven by spin fluctuations. The construction is based on many-body perturbation theory and relies on the approximation of the exchange-correlation part of the electronic self-energy within time-dependent density functional theory. This effective interaction is included in an exchange-correlation kernel for superconducting density functional theory in order to achieve a completely parameter free superconducting gap equation. First results from applying the new functional to a simplified two-band electron gas model are consistent with experiments.

We report the first-principles study of superconducting critical temperature and superconducting properties of Fe-based superconductors taking into account on the same footing phonon, charge and spin-fluctuation mediated Cooper pairing. We show that in FeSe this leads to a modulated s± gap symmetry, and that the antiferromagnetic paramagnons are the leading mechanism for superconductivity in FeSe, overcoming the strong repulsive effect of both phonons and charge pairing.

The magnetic excitations in FeSe are studied from first principles applying linear response density functional theory. The position of the selenide layer is varied to model the transition between paramagnetic and antiferromagnetic phases. In the paramagnetic phase, close to the magnetic instability, we find a branch of long-lived collective spin excitations (paramagnons). An estimation of the paramagnon-mediated effective electron-electron interaction supports the scenario of Cooper pairing in FeSe induced by spin fluctuations.

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We present a first-principles approach to describe magnetic and superconducting systems and the phenomena of competition between these electronic effects. We develop a density functional theory: SpinSCDFT, by extending the Hohenberg-Kohn theorem and constructing the non-interacting KohnSham system. An exchange-correlation functional for SpinSCDFT is derived from the Sham Schlüter connection between the SpinSCDFT Kohn-Sham and a self-energy in Eliashberg approximation. The reference Eliashberg equations for superconductors in the presence of magnetism are also derived and discussed.