Mixed state in antiferromagnetic superconductors

The free energy of the mixed state in antiferromagnetic superconductors was derived. The spin magnetic moment induced by the magnetic field of vortices changes drastically at the transition boundary between the antiferromagnetic state and the forced-ferromagnetic state. This effect causes a kink in the curves of the upper and lower critical fields versus temperature at the boundary. When the N\'eel temperature is very low compared with the superconducting transition temperature, the effect becomes strong enough to cause a dip in the curve of the upper critical field versus temperature. Even in this case the flux density at the upper critical field monotonically decreases with increasing temperature as in usual nonmagnetic superconductors. The present theory well explains the temperature dependence of the upper critical field observed in Dy${\mathrm{Mo}}_{6}$${\mathrm{S}}_{8}$. The magnetization curves were obtained for various cases of parameters.