Spin-dependent Trap-assisted Tunneling in Ferromagnet-Oxide-Semiconductor Structures
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چکیده
Silicon is an ideal material for spintronic applications due to its weak spin-orbit interaction and long spin lifetime [1,2]. Spin injection from a ferromagnetic electrode into n-type silicon was claimed at room [3] and elevated [4] temperatures. However, the amplitude of the spin-accumulation signal extracted from a three-terminal injection method [2,3] is orders of magnitude higher than predicted [1]. The reasons for this discrepancy are currently heavily debated [1,5-8]. Recently an alternative interpretation of the three-terminal signal based on spin-dependent magnetoresistance due to trap-assisted resonant tunneling was proposed [5]. However, the effects due to finite spin lifetime [6] were not taken into consideration. Here we investigate in detail the role of spin relaxation and decoherence on a trap in determining the trap-assisted tunneling magnetoresistance. To elucidate the role of spin relaxation and decoherence we introduce the corresponding relaxation terms into a Lindblad equation for the density matrix evolution of spin on a trap. This results in coupled master equations for the density matrix elements in the presence of the spin lifetime T1 and decoherence time T2 (T2≤T1) and the tunneling rates ΓN from silicon and Γ± = ΓF (1-p) to the ferromagnet (Fig.1). The current I due to tunneling via a trap is different from I0 = ΓF ΓN /(ΓF + ΓN) and depends on the angle Θ between the spin quantization axis and the magnetization orientation.
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تاریخ انتشار 2015