Suppression of impurity magnetization by the saddle points

We study the localized magnetic states of an impurity in the semi-Dirac-like system where the saddle point (SP) is present. It is found that with increasing the saddle point energy (SPE), the impurity magnetization region diminishes greatly, and reaches a minimum at the SPE equal to the impurity energy. When continuing to increase the SPE, the impurity magnetization region rapidly becomes large. Correspondingly, an explicit decrease with the SPE close to the impurity energy is also observed in the magnetic moment of the impurity. This suppression behavior for the magnetization of the impurity can be understood from the SP induced mitigation of asymmetry on the density of state at impurity energy. In contrast, when the SP vanishes, due to the opening of the gap, the magnetic region exhibits a monotonous decay when the conduction band edge goes up through the impurity energy. The combined effect of the SP and the Coulomb interaction at the impurity on the local magnetization is also investigated.