Using electronic structure methods and statistical methods, we have studied theoretically the volume dependence of the exchange interactions and Curie temperatures in the diluted magnetic semiconductors. In both Mn-doped GaAs and Mn-doped InAs, the calculated Curie temperatures from numerical exact Monte Carlo simulations are more or less constant for a large volume interval. We have compared the exchange mechanisms in Mn-doped GaAs using both the local density approximation (LDA) and the LDA+U method. It is demonstrated that the magnetic properties are understood within Zener's p-d exchange model for the LDA+U, while in LDA they reflect a mixture between double and p-d exchange mechanisms.
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