A mean-field approach to Kondo-attractive-Hubbard model

With the purpose of investigating coexistence between magnetic order and superconductivity, we consider a model in which conduction electrons interact with each other, via an attractive Hubbard on-site coupling U, and with local moments on every site, via a Kondo-like coupling, J. The model is solved on a simple cubic lattice through a Hartree-Fock approximation, within a 'semi-classical' framework which allows spiral magnetic modes to be stabilized. For a fixed electronic density, nc, the small J region of the ground state (T = 0) phase diagram displays spiral antiferromagnetic (SAFM) states for small U. Upon increasing U, a state with coexistence between superconductivity (SC) and SAFM sets in; further increase in U turns the spiral mode into a Néel antiferromagnet. The large J region is a (singlet) Kondo phase. At finite temperatures, and in the region of coexistence, thermal fluctuations suppress the different ordered phases in succession: the SAFM phase at lower temperatures and SC at higher temperatures; also, reentrant behaviour is found to be induced by temperature. Our results provide a qualitative description of the competition between local moment magnetism and superconductivity in the borocarbides family.