Limitation of Mean Field Approximation for Carrier States and Ferromagnetism in Diluted Magnetic Semiconductors

Abstract

In spite of a great deal of recent experimental and theoretical activities, there has not yet been a consensus on the fundamental mechanism leading to the ferromagnetism of Ga1 xMnxAs. 1) In diluted magnetic semiconductors (DMSs), there are two types of disorder: substitutional disorder and the thermal fluctuation of localized spins. Neglecting disorder effects, the mean-field Zener model (the phenomenological model) predicts the possibility of a high Curie temperature for some materials. Properly taking the disorder effects into consideration, however, is indispensable in the calculation of the Curie temperature TC of DMSs, as clarified in this study. To show the importance of the disorder effects, we calculate TC by applying three approximations to a simple model: the coherent potential approximation (CPA), the virtual crystal approximation (VCA), and the mean-field approximation (MFA). In the present model, Ga1 xMnxAs is regarded as a semiconducting alloy in which a mole fraction x of Ga ions (symbol: A) in GaAs are replaced at random by Mn ions (symbol:M). A single carrier (a p hole) moving in Ga1 xMnxAs is affected by the local potential EA or EM I Sm, depending on whether it is on a Ga site or a Mn site. Here, EA and EM denote the spinindependent potentials on the Ga ion and Mn ion, respectively; I Sm represents the p–d exchange interaction between the carrier (p hole) and the localized spin Sm (d spin) of Mn located on the m site. Setting EA 1⁄4 0, we employ the model density of states (DOS) of semicircular form: