Superconductivity and antiferromagnetism in the three-dimensional Hubbard model

The interplay between antiferromagnetism and superconductivity is studied by using the three-dimensional nearly half-filled Hubbard model with anisotropic transfer matrices t(z) and t(perpendicular to). The phase diagrams are calculated for varying values of the ratio r(z) = t(z)/t(perpendicular to) using the spin fluctuation theory within the fluctuation-exchange approximation. The antiferromagnetic phase around the half-filled electron density expands while the neighboring phase of the anisotropic d(x2-y2)-wave superconductivity shrinks with increasing r(z). For small r(z) T-c decreases slowly with increasing r(z). For moderate values of r(z) we find a second order transition, with lowering temperature, from the d(x2-y2)-wave superconducting phase to a phase where an incommensurate spin density wave (SDW) coexists with d(x2-y2)-wave superconductivity. Resonance peaks discussed previously for two-dimensional (2D) superconductors are shown to survive in the d(x2-y2)-wave superconducting phase of 3D systems. Soft components of the incommensurate SDW spin fluctuation mode grow as the coexistent phase is approached.