Noncollinear order and gapless superconductivity in s -wave magnetic superconductors

Abstract

We study the behavior of magnetic superconductors which involve a local attractive interaction between electrons, and a coupling between local moments and the electrons. We solve this Hubbard-Kondo model through a variational minimization at zero temperature and validate the results via a Monte Carlo based on static auxiliary field decomposition of the Hubbard interaction. Over a magnetic coupling window that widens with increasing attractive interaction, the ground state supports simultaneous magnetic and superconducting order. The pairing amplitude remains $s$-wave like, without significant spatial modulation, while the magnetic phase evolves from a ferromagnet, through noncollinear ``spiral'' states, to a N\'eel state with increasing density and magnetic coupling. We find that at intermediate magnetic coupling, the antiferromagnetic-superconducting state is gapless, except for the regime of N\'eel order. We map out the phase diagram in terms of density, magnetic coupling, and attractive interaction, establish the electron dispersion and effective ``Fermi surface'' in the ground state, provide an estimate of the magnetic and superconducting temperature scales via Monte Carlo, and compare our results to available data on the borocarbides.