Superconductivity and Ferromagnetism in Nonadiabatic Systems with Magnetic Impurity: A Step Beyond the Migdal Theorem

The possibility of the ferromagnetic ordering of a paramagnetic impurity in nonadiabatic superconducting systems is investigated. The effect of the relative shift of the Fermi surface by the internal magnetic field, the exchange interaction of the impurity ions through the conductivity electrons, and the spin-orbit interaction of the nonmagnetic impurity are taken into account. The problem is solved in the linear approximation with respect to the nonadiabaticity by taking the vertex and crossing diagrams corresponding to the electron-phonon and the electron-impurity interactions into account. We obtain basic equations of the superconductivity theory for nonadiabatic systems with the ferromagnetic ordering of the impurity spins and show that the nonadiabaticity alters the superconducting transition temperature $T_{\mathrm c}$ and the critical impurity concentration. The behavior of the magnetic-ordering temperature $T_{\mathrm K}$ as a function of the impurity concentration $c$ in the superconductive state of the nonadiabatic system is also investigated. We obtain the phase diagram $(T,c)$ and show that the nonadiabaticity effects lead to the enlargement of the domain where the superconductivity and the ferromagnetism exist simultaneously.