Analytical description of ballistic spin currents and torques in magnetic tunnel junctions

Abstract

In this work we demonstrate explicit analytical expressions for both charge and spin currents which constitute the 2x2 spinor in magnetic tunnel junctions with noncollinear magnetizations under applied voltage. The calculations have been performed within the free electron model in the framework of the Keldysh formalism and WKB approximation. We demonstrate that spin/charge currents and spin transfer torques are all explicitly expressed through only three irreducible quantities, without further approximations. The conditions and mechanisms of deviation from the conventional sine angular dependence of both spin currents and torques are shown and discussed. It is shown in the thick barrier approximation that all tunneling transport quantities can be expressed in an extremely simplified form via Slonczewski spin polarizations and our effective spin averaged interfacial transmission probabilities and effective out-of-plane polarizations at both interfaces. It is proven that the latter plays a key role in the emergence of perpendicular spin torque as well as in the angular dependence character of all spin and charge transport considered. It is demonstrated directly also that for any applied voltage, the parallel component of spin current at the FM/I interface is expressed via collinear longitudinal spin current components. Finally, spin transfer torque behavior is analyzed in a view of transverse characteristic length scales for spin transport.

10 pages, 6 figures

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Cited by in corpus (6)

• Magnetization reversal driven by spin-transfer-torque in perpendicular shape anisotropy magnetic tunnel junctions
• Impact of intergrain spin transfer torques due to huge thermal gradients on the performance of heat assisted magnetic recording
• Stabilizing current-driven steady flows of 180${}^{\circ }$ domain walls in spin valves by interfacial Dzyaloshinskii-Moriya interaction
• Spin current and second harmonic generation in non-collinear magnetic systems: the hydrodynamic model
• Efficient solution strategy to couple micromagnetic simulations with ballistic transport in magnetic tunnel junctions
• Slonczewski-spin-current driven dynamics of 180${}^{\circ }$ domain walls in spin valves with interfacial Dzyaloshinskii-Moriya interaction