Electronic theory of magnetic interactions in diluted magnetic semiconductors

A common theoretical framework describing the electronic structure and magnetic interactions of Mn-alloyed II-VI diluted magnetic semiconductors (DMS) is developed, with emphasis on Cd{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Te. The derived electronic structure is based on a combination of first principles spin-polarized band calculations, and a semi-empirical tight binding model incorporating the relevant experimental information. To calculate magnetic interactions the important features of the electronic structure are incorporated in a multi-site Anderson model Hamiltonian describing the effects of magnetic Mn 3d states hybridized with semiconducting II-VI host sp bands (II = Cd,Zn; VI = S,Se,Te). Mn-(sp band) exchange and both isotropic and anisotropic Mn-Mn exchange interactions for {dollar}(II)sb{lcub}1-x{rcub}Mnsb{lcub}x{rcub}(VI){dollar}, calculated through second and fourth order perturbation theory, respectively, agree with experiment at least as well as previous calculations for other materials. The calculations establish the importance of (anion-p)-Mn-d hybridization by demonstrating that the dominant isotropic and anisotropic magnetic interactions arise from superexchange. A simplified three level model for superexchange in DMS provides physical insight and accounts for chemical trends in both types of superexchange in agreement with experiment. We use the derived exchange constants to calculate two measured experimental magnetic properties, magnetization and spin resonance linewidths. We explain the shift and broadening observed in magnetization step measurements on dilute ({dollar}x <{dollar} 0.05) DMS samples by developing a new model for treating the effects of second and more distant neighbor exchange interactions. Reanalysis of existing magnetization data leads to an accurate determination of the first neighbor exchange constant and to the first values yet obtained for second and third neighbor exchange constants in Cd{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Te and Cd{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Se. We also give the first quantitative calculation of the exchange narrowed electron paramagnetic resonance linewidths in DMS. Anisotropic superexchange is found to account for the majority of the broadening, and is responsible for the observed anion-dependent trend in the linewidths. A fit of parameterized expressions obtained from this theory to the experimental data for Cd{dollar}sb{lcub}1-x{rcub}{dollar}Mn{dollar}sb{lcub}x{rcub}{dollar}Te yields a definitive value of the anisotropic superexchange constant, in excellent agreement with the value calculated theoretically.