Nonlinear Magnetization in Superconductors with s+d Ordering

The nonlinear magnetization is considered within the Ginzburg-Landau theoretical framework, in the Meissner regime. A calculational method in the case of conventional superconductors (one order parameter) is developed and is extended for the case of two order parameters (s+d mixing). It is confirmed that corrections tou the penetration depth, in the mean field analysis, are of the order of ${H_0}^2$ where $H_0$ is the applied field. We analyze carefully the possible solutions which lead to different scenarios in the physics of the symmetry of the order parameter. The anisotropy in the penetration depth is calculated and the temperature dependence of the magnetization is extracted. We discuss the relevant experimental results in the light of these calculations.