Phenomenological Theory of Superconductivity and Magnetism in Ho1−x_{1-x}Dyx_xNi2_2B2_2C

The coexistence of the superconductivity and magnetism in the Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C is studied by using Ginzburg-Landau theory. This alloy shows the coexistence and complex interplay of superconducting and magnetic order. We propose a phenomenological model which includes two magnetic and two superconducting order parameters accounting for the multi-band structure of this material. We describe phenomenologically the magnetic fluctuations and order and demonstrate that they lead to anomalous behavior of the upper critical field. The doping dependence of $T_c$ in Ho$_{1-x}$Dy$_x$Ni$_2$B$_2$C showing a reentrance behavior are analyzed yielding a very good agreement with experimental data.Comment: 4 pages, 3 figures, REVTeX, submitted to PR