Quantum transport with spin dephasing: A nonequlibrium Green’s function approach

A quantum transport model incorporating spin scattering processes is presented using the nonequilibrium Green’s function formalism within the self-consistent Born approximation. This model offers a unified approach by capturing the spin-flip scattering and the quantum effects simultaneously. A numerical implementation of the model is illustrated for magnetic tunnel junction devices with embedded magnetic impurity layers. This model seems to explain three experimentally observed features regarding the dependence of the junction magnetoresistances (JMRs) on the barrier thickness, barrier height, and number of magnetic impurities. It is shown that small variations in magnetic impurity spin states and concentrations could cause large deviations in JMRs.

Figure 1

A schematic illustration of device partitioning in NEGF formalism. Magnetization direction of the drain is defined relative to the source $(\Delta \theta ={\theta }_{\mathrm{R}}-{\theta }_{\mathrm{L}})$.

Figure 2

Energy band diagram for the model MTJs considered here.

Figure 3

(Color online) For impurity free MTJs, (a) thickness dependence of JMRs for different barrier heights are shown in comparison with experimental measurements (Refs. 15, 16, 17, 18, 19, 20, 21, 22, 23, 24) while an (b) energy resolved analysis of $\mathrm{JMR}\left(E_z\right)$ (left axis) and normalized $w\left(E_z\right)$ (right axis) distributions is also presented for a device with a tunneling barrier height of $1.6\mathrm{eV}$. For MTJs with impurity layers, (c) variation of JMRs for varying barrier thicknesses and interactions strengths $({⟨J^2⟩}_{2\mathrm{D}}{n}_I=0∕3∕6{\mathrm{eV}}^2\mathrm{nm})$ are shown together with (d) an energy resolved analysis. Normalized JMRs are proven to be thickness independent as displayed in the inset.

Figure 4

(Color online) (a) Normalized JMRs deteriorates with increasing spin-dephasing strenghts independently from the tunneling barrier heights. (b) Using a barrier height dependent scaling parameter $c\left(U_{\mathrm{barr}}\right)$, (c) this general trend can be scaled to a single universal curve. Experimental data taken at $77\mathrm{K}$ (solid) and $300\mathrm{K}$ (dashed) is compared with theoretical analysis in the presence of (d) Pd, (e) Ni and (f) Co magnetic impurities with increasing impurity concentrations for a scaling constant $c\left(U_{\mathrm{barr}}\right)=1$.