Superconductors of mixed order parameter symmetry in a Zeeman magnetic field

We study the effect of Zeeman magnetic field in the superconducting phase with two component order parameter scenario, such as, $d_{x^2-y^2} + e^{i\theta}{\alpha}$, where $\alpha = d_{xy}, s$. This scenario is equivalent to applying magnetic field parrllel to Cu-O planes. In a weak magnetic field, which does not cause much change to the predominant d-wave, supresses the minor $\alpha$ component leading to pure d-wave phase. This observation is in contrary to the effect of magnetic field applied in the c-direction to the Cu-O planes which is believed to induce a minor component $\alpha$ to d-wave superconductors. We also show that the response of such superconductors to a weak Zeeman magnetic field can be quite different depending on the phase $\theta$ of the minor component ($\alpha$).