Generalized double-exchange model for magnetic semiconductors with angular momentum j

To facilitate the search for new magnetic semiconductors with high transition temperatures TC, we use dynamical mean-field theory to evaluate TC for a double-exchange system with general angular momentum j=1/2,3/2,5/2,… . For simplicity, we assume that there is one local moment per site and that the Hund's coupling Jc between the local moments and the charge carriers (with undoped bandwidth W) is large. The maximum Curie temperature TCmax(mj,j) for a given mj and j occurs when the mj sub-band is half-filled. For a fixed j, TCmax(mj,j) is the largest in the lowest or the highest sub-band with mj=±j, where the carriers are most optimally coupled to the local moments. When j⪢1, TCmax(±j,j) scales like W/2j+1, which is the bandwidth of each mj sub-band. For j=1/2, TCmax(±1/2,1/2) is suppressed by fluctuations of the carrier spin. Surprisingly, TCmax(±j,j) reaches a maximum for j=3/2, the same angular momentum as the charge carriers in p-band semiconductors like GaAs and Ge.