Signatures of asymmetric and inelastic tunneling on the spin torque bias dependence

The influence of structural asymmetries (barrier height and exchange splitting), as well as inelastic scattering (magnons and phonons) on the bias dependence of the spin transfer torque in a magnetic tunnel junction is studied theoretically using the free-electron model. We show that they modify the “conventional” bias dependence of the spin transfer torque, together with the bias dependence of the conductance. In particular, both structural asymmetries and bulk (inelastic) scattering add antisymmetric terms to the perpendicular torque ($\propto V$ and $\propto j_e\left|V\right|$) while the interfacial inelastic scattering conserves the junction symmetry and only produces symmetric terms ($\propto {\left|V\right|}^n$, $n∊\mathbb{N}$). The analysis of spin torque and conductance measurements displays a signature revealing the origin (asymmetry or inelastic scattering) of the discrepancy.

Figure 1

(Color online) Potential profile of an asymmetric magnetic tunnel junction. The right and left parabolae represent the dispersion of tunneling electrons.

Figure 2

(Color online) Bias dependence of the [(a) and (b)] in-plane torque, [(c) and (d)] perpendicular torque, and [(e) and (f)] parallel conductance in the case of [(a), (c), and (e)] barrier height and [(b),(d), and (f)] exchange splitting asymmetries. The solid lines correspond to numerical calculations based on the model presented in Ref. 9 and the squares are calculations using Eqs. (6, 7, 8). The parameters are $E_F=10\text{eV}$, $J=1\text{eV}$, $\varphi =5\text{eV}$, and $d=1\text{nm}$.