Curie Temperature Trends in (III,Mn)V Ferromagnetic Semiconductors

We present a theoretical survey of ferromagnetic transition temperatures in cubic (III,Mn)V semiconductors based on a model with $S=5/2$ local moments exchange coupled to itinerant holes in the host semiconductor valence band. Starting from the simplest mean-field theory of this model, we estimate the ${T}_{c}$ enhancement due to exchange and correlation in the itinerant-hole system and the ${T}_{c}$ suppression due to collective fluctuations of the ordered moments. We show that high critical temperatures in these ferromagnetic semiconductors require both the large magnetic susceptibility contribution from the valence-band heavy holes and the large spin stiffness resulting from a complex valence-band structure that includes the more dispersive light holes. Our calculations demonstrate that the model of carrier-induced ferromagnetism of these systems is consistent with high critical temperatures observed experimentally in (III,Mn)V semiconductors.