Spin Transfer Torque as a Non-Conservative Pseudo-Field

Abstract

In this paper we show that the spin transfer torque can be described by a pseudo magnetic field, proportional to the magnetic moment of the itinerant electrons that enters the Landau-Lifshitz-Gilbert equation in the same way as other external or internal magnetic fields. However, unlike an ordinary magnetic field, which is always conservative in nature, the spin torque induced pseudo field may have both conservative and non-conservative components. We further show that the magnetic moment of itinerant electrons develops an out-of-plane component only at non-equilibrium and this component is responsible for the Slonczewski type switching that acts against the damping and is always non-conservative. On the other hand, the in-plane components of the pseudo field exist both at equilibrium and out-of-equilibrium, and are responsible for the field like term. For tunnel based devices, this term results in lower switching current for anti-parallel (AP) to parallel (P) switching compared to P to AP, even when the torque magnitudes are completely symmetric with voltage.