Softening of Spin-Wave Stiffness near the Ferromagnetic Phase Transition in Diluted Magnetic Semiconductors

Employing the self-consistent Green's function approach, we studied the temperature dependence of the spin-wave stiffness in diluted magnetic semiconductors. Note that the Green's function approach includes the spatial and temperature fluctuations simultaneously which was not possible within conventional Weiss mean-field theory. It is rather interesting that we found the stiffness becomes dramatically softened as the critical temperature is approached, which seems to explain the mysterious sharp drop of magnetization curves in samples within diffusive regime.