Coexistence of superconductivity and magnetic order

The microscopic theory of simple antiferromagnetic superconductors is extended to structures where the magnetic order is described by a spin-density wave. For the case where the magnetic system is inherently ferromagnetic, the free energy of the combined system is minimized with respect to the amplitude and the wave vector of the spin-density wave. It is found that the wave vector depends very weakly on temperature. We apply the theory to the coexistence region in ErRh₄B₄, finding a first-order re-entry transition.