Magnetic interaction in low density carrier ferromagnetic semiconductors

We developed a Monte Carlo method to study the magnetic and transport properties of low density carrier ferromagnetic semiconductors. The magnetization of local spins is calculated for the two- and the three-dimensional Ising spin systems interacting with the electrons. The AC conductivity is also calculated. When the temperature increases from T=0, the spontaneous magnetization of the local spins decreases appreciably even in the low temperature range, and rapidly at the Curie temperature. The intensity of AC conductivity transfers from ω∼0 range to the frequency range characterized by the excitation energy of the magnetic polaron state.