Properties of a magnetic superconductor with weak magnetization - application to $ErN{i}_2{B}_{2}C$

Using a Ginsburg-Landau free energy functional, we study the $H-T$ phase diagram of a weak magnetic superconductor, where the magnetization from the magnetic component is marginal in supporting a spontaneous vortex phase in absence of external magnetic field. In particular, the competition between the spiral state and spontaneous vortex phase is analysed. Our theory is applied to understand the magnetic properties of $ErN{i}_2{B}_{2}C$.