We calculate magnetization in magnetically doped semiconductors assuming a
local exchange model of carrier-mediated ferromagnetic mechanism and using a
number of complementary theoretical approaches. In general, we find that the
results of our mean-field calculations, particularly the dynamical mean field
theory results, give excellent qualitative agreement with the experimentally
observed magnetization in systems with itinerant charge carriers, such as
Ga_{1-x}Mn_xAs with 0.03 < x < 0.07, whereas our percolation-theory-based
calculations agree well with the existing data in strongly insulating
materials, such as Ge_{1-x}Mn_x. We comment on the issue of non-mean-field like
magnetization curves and on the observed incomplete saturation magnetization
values in diluted magnetic semiconductors from our theoretical perspective. In
agreement with experimental observations, we find the carrier density to be the
crucial parameter determining the magnetization behavior. Our calculated
dependence of magnetization on external magnetic field is also in excellent
agreement with the existing experimental data.Comment: 17 pages, 15 figure
