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Enhancement of the spin transfer torque efficiency in magnetic STM junctions

We introduce a method for a combined calculation of charge and vector spin transport of elastically tunneling electrons in magnetic scanning tunneling microscopy (STM). The method is based on the three-dimensional Wentzel-Kramers-Brillouin (3D-WKB) approach combined with electronic structure calculations using first principles density functional theory. As an application, we analyze the STM contrast inversion of the charge current above the Fe/W(110) surface depending on the bias voltage, tip-sample distance and relative magnetization orientation between the sample and an iron tip. For the spin transfer torque (STT) vector we find that its in-plane component is generally larger than the out-of-plane component, and we identify a longitudinal spin current component, which, however, does not contribute to the torque. Our results suggest that the torque-current relationship in magnetic STM junctions follows the power law rather than a linear function. Consequently, we show that the ratio between the STT and the spin-polarized charge current is not constant, and more importantly, it can be tuned by the bias voltage, tip-sample distance and magnetization rotation. We find that the STT efficiency can be enhanced by about a factor of seven by selecting a proper bias voltage. Thus, we demonstrate the possible enhancement of the STT efficiency in magnetic STM junctions, which can be exploited in technological applications. We discuss our results in view of the indirect measurement of the STT above the Fe/W(110) surface reported by Krause et al. in Phys. Rev. Lett. 107, 186601 (2011).