Colossal Hopping Magnetoresistance of GaAs/ErAs Nanocomposites
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ABSTRACT A theory of bound magnetic polaron (BMP) hopping, driven by thermodynamic fluctuations of the local magnetization, has been developed. It is based on a two-site model of BMP's. The BMP hopping probability rate was calculated in the framework of the "Golden Rule" approach by using the Ginzburg-Landau effective Hamiltonian method. The theory explains the main features of hopping resistivity observed in a variety of experiments in dilute magnetic semiconductors and magnetic nanocomposites, namely: (a) negative giant magnetoresistance, the scale of which is governed by a magnetic polaron localization volume, and (b) low magnetic field positive magnetoresistance, which usually preceeds negative magnetoresistance.
INTRODUCTION Spin-polarized electronic transport in solids has attracted much interest mainly due to the discovery of giant magnetoresistance (GMR) and the development of new device applications (high-speed magnetic sensors and memory elements) based on this phenomenon [1]. Several different mechanisms have been proposed for the spin-dependent GMR. Their common feature is the exchange interaction of charge carriers with the itinerant and/or localized magnetic moments of transition- or rare-earth-metal atoms. In this paper, we will restrict ourselves to hopping conductivity in magnetic semiconductors and nanostructures [2, 3]. In these systems, an electron or hole trapped by any kind of attractive potential of a defect, quantum dot, etc., can form a "cloud" of aligned spins of the surrounding magnetic atoms. Creation of such a complex (referred to as bound magnetic polaron (BMP) [4]) will further lower the free energy of the system by a quantity Wp called the polaron shift. The first consistent semiclassical analysis of BMP formation in dilute magnetic semiconductors was given by Dietl and Spalek [5], while its quantummechanical generalization was developed by Wolff et al (for references see [6]). This theory successfully described the spin-flip Raman scattering in magnetic semiconductors [7]. In order to describe BMP hopping conductivity, we need, first, to specify the mechanism of an elementary hopping event. Dietl et al [3, 7] considered a "static" picture in which the electron is transferred from an occupied site to an empty one with frozen equilibrium local magnetizations at both sites. For two identical sites this process is driven by absorption of an acoustic phonon and requires an activation energy 2Wp [3, 8]. Another mechanism, which was first suggested by loselevich [8], takes into account thermodynamic fluctuations of the local magnetizations that control the elementary hopping act. Indeed, since the electron energy levels at both sites follow the fluctuations of local magnetic order parameters, it is likely that the levels at the occupied and empty sites will move in opposite directions briefly establishing a resonance condition. For this to occur, the occupied site should spontaneously decrease its local magnetization while the empty one should increase it. The electron can then tunnel fro
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