Anisotropic superexchange and spin-resonance linewidth in diluted magnetic semiconductors

The Dzyaloshinski-Moriya (DM) anisotropic superexchange constant and the resulting electron-paramagnetic-resonance (EPR) linewidth in Mn-based II-VI-compound diluted magnetic semiconductors (DMS) such as ${\mathrm{Cd}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Mn}}_{\mathrm{x}}$Te are calculated quantitatively. An Anderson Hamiltonian, developed in a previous study of isotropic superexchange, describing correlated Mn 3d states hybridized with semiconducting s- and p-derived levels, is generalized to include the anion spin-orbit coupling responsible for anisotropic superexchange. DM exchange is shown to be the dominant anisotropic interaction, with magnitude ∼5% of isotropic superexchange. The EPR line shape is calculated with use of a moment expansion of the magnetic response function to first order in inverse temperature together with a maximum-entropy ansatz. The calculated infinite-temperature linewidths are in good agreement with extrapolated experimental values. A novel fit of the theoretical temperature dependence to existing experimental linewidth data provides the first empirical value for the anisotropic exchange constant, in excellent agreement with the theoretical value. Calculated chemical trends for the exchange constants yield the experimentally expected linewidth trends.