Mobility of Charge Carriers in Dilute Magnetic Semiconductors
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Mobility of Charge Carriers in Dilute Magnetic Semiconductors Michael G. Foygel1, James Niggemann2,3, and A. G. Petukhov3 1 Physics, SDSM&T, 501 St Joseph St, Rapid City, SD, 57701 2 SDSMT, Rapid City, SD, 57701 3 SDSM&T, Rapid City, SD, 57701 ABSTRACT We studied electrical transport in dilute magnetic semiconductors (DMS), which is determined by scattering of free carriers by localized magnetic moments. In our calculations of the scattering time and the mobility of the majority and minority-spin carriers we took into account both the effects of the thermal spin fluctuations and of the built-in spatial disorder of the magnetic atoms. These effects are responsible for the magnetic-field dependence of the mobility of the charge carriers. The application of the external magnetic field suppresses the thermodynamic spin fluctuations thus changing the mobility. Simultaneously, scattering by built-in spatial fluctuations of the atomic spins usually increases with magnetic field. The latter effect is due to the increase in the magnitude of the random local Zeeman splitting with the magnetic field. The resultant outcome of the both effects is opposite for the majority and minority spin carriers. In DMS the mobility of the majority spin carriers, as a rule, increases with magnetic field thus leading to negative magnetoresistance. INTRODUCTION Dilute magnetic semiconductors (DMS) are materials of great promise in modern technology because they combine semiconductor transport and magnetic properties allowing reach and physically meaningful interplay between them [1,2]. In DMS alloys cations are substituted by randomly distributed magnetic atoms, such as Mn [1]. These magnetic impurities can effectively modify electronic transport and magnetism due to exchange coupling of the free carriers spins to the spins of magnetic atoms. As a result, scattering of the free carriers by the localized magnetic moments determines their mobility that is substantially spin and, therefore, magnetic-field dependent. It leads to giant magnetoresistance (MR), positive or negative. In this paper we will concentrate mainly on spin-dependent scattering which determines mobility of free carriers in DMS taking into account the spin-disorder effects that are intrinsic for these materials. There are two sources of the spin-disorder effects in question: (a) the thermodynamic fluctuations of atomic spins, which are present even in the ordered magnetic materials [3,4], and (b) the built-in spatial fluctuations of local concentrations of the magnetic impurities [5], which are substantial in disordered DMS even in the absence of magnetic field. The theory of spin-disorder scattering off the thermodynamic fluctuations of the local magnetization due to atomic moments of the magnetic atoms has been developed by P. G. de Gennes and J. Friedel [3] for magnetic metals and for ordered magnetic semiconductors by C. Haas [4]. In particular, they showed the application of an external magnetic field freezes out the above fluctuations thus leading to negative
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