  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).
