Pauli paramagnetism and superconductivity in strongly anisotropic magnetic systems

A study is made of the influence of an external magnetic field $H_0$ on the thermodynamic properties of strongly anisotropic systems in the phase of coexistence of superconductivity and a spin density wave. The basic equations are obtained for the order parameters of these states, the difference between the free energies of the superconducting and normal phases is calculated and the behavior of the system in a number of limiting cases is investigated. The jump in the specific heat at the point $T=T_c$ is also calculated and its dependence on the magnetic field $H_0$ investigated. It is shown that the values of the thermodynamic characteristics of the system depend on the ratio of the densities $N_1$ and $N_2$ of the electron states corresponding to different regions of the anisotropic Fermi surface, and that the values are very different from the results of the BCS model.