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Oscillation effect of the bias-dependent TMR  PDF
we present a spintronic tunnelling theory for ferromagnet/ insulator/ferromagnet (FM/I/FM) junctions. With the use of Airy functions, it can analytically account for both the low-bias and the high-bias TMRs. We find that the sign-change behaviour of TMR can only occur in the low-bias region,due to the quantum coherence in FM/I/FM junctions. In the high-bias region, the TMR will oscillate between positive and negative with increasing bias voltage. Physically, this oscillation arises from the interference between the incident and reflected electron waves in the barrier region. The effects of the barrier height, the barrier width and the electron effective mass in the barrier are studied systematically. The theoretical results obtained from the exact Airy functions agree well with TMR experiments on Ta2O5- and Al2O3-barrier junctions, within the wholemeasurable range of bias voltage.

Spin-filter effect in Ferromagnetic Junctions  PDF
Within the framework of the single electron spintronic model, we systematically studied the bias-dependent spin-filter effect and TMR in ferromagnetic metal/ferromagnetic insulator/ferromagnetic metal (FM/FI/FM) tunnel junctions. We find that it is the extended quantum-coherence factor of Slonczewski kappa_{L up}^2-k_{L up}*k_{L down} that physically controls the sign of the zero-bias TMR. This factor is a linear function of the mean barrier height. The zero-bias TMR is positive when the mean barrier is high, and negative when the mean barrier gets low, which agrees well with the experimental results observed in GdOx-barrier junctions. As a cooperation result of the mean barrier and spin-filter effect, a positively or negatively large TMR can be maintained in rather a wide range near the zero bias if the mean barrier of the FI spacer is much higher or much lower. This property is believed to be of practical use in designing spintronic devices. Besides, the TMR can oscillate positively, or negatively, or alternately with the applied voltage within the high bias region, different from the conventional FM/I/FM tunnel junctions.

Impurity resonance and TMR for nanojunctions PDF
We present a microscopic study of impurity resonance and TMR for nanojunctions. We employ the Green's function method to derive the tunneling wave functions and TMR from the spintronic model with nonmagnetic impurities and at a finite bias voltage. The analytical expressions for both direct and impurity-resonance tunnelings are obtained, where the lateral effect has been included. Within this framework, the TMR can be determined directly by the basic quantities of the junction, e.g., the position and the energy level of the impurity, the height and width of the barrier, the Fermi level and polarization of the electrodes, as well as the applied voltage. If the cross sectional area of the junction gets very small, we find that it is the impurity resonance and the quantum-coherence effect that control the bias dependence of TMR: the impurity resonance makes the TMR change from positive to negative, and the quantum-coherence e®ect decreases the TMR as the bias voltage increases. The experimental results of TMR for the junctions with the area smaller than 0:01 micro squared can then be explained naturally. We also find that the direct and impurity-resonance tunnelings will compete with each other when the area of the junction is enlarged. Taking into account both the contributions of direct tunneling and impurity-resonance tunneling, the total TMR agrees quite well with the more recent experiments on the larger-area nanojunctions.