ity: blue, Minority: red) vacuum LDOS including SOC above the Bi adatom on Mn/W(110) for out-of-plane ($\perp$, solid lines) and in-plane (parallel to the $[1\overline{1}0]$ direction) magnetizations ($\parallel$, dashed lines). (b) TAMR obtained from the spin-averaged vacuum LDOS according to Eq. (\[eq:TAMR\]). (c) Orbital decomposition of the LDOS of the Bi adatom in terms of the majority (up) and minority (down) states. Solid (dashed) lines correspond to the magnetization direction perpendicular (parallel) to the surface plane. The orange up and down arrow indicates majority and minority spin channels, respectively.[]{data-label="fig:BiAdatom"}](figure5.pdf)

In this section we will focus on the description of the electronic structure of $6p$ adatoms adsorbed on the Mn monolayer of W(110). Especially the anisotropy of the LDOS due to SOC and the subsequent TAMR effect will be discussed in detail.

Fig. \[fig:PbAdatom\](a) shows both the total (spin-averaged) and spin-resolved vacuum LDOS above the Pb adatom – in an energy range around $E_F$ typically accessible to STM – calculated for the two magnetization directions including SOC: (i) perpendicular to the surface (out-of-plane) denoted as $n_\perp(z, \epsilon)$ and parallel to the $[1\overline{1}0]$ direction (in-plane) denoted as $n_\parallel(z, \epsilon)$. Differences between both magnetization components are clearly discernible in the energy range below the Fermi level ([[$E_{\text{F}}$]{}]{}). The most significant feature is located at $-0.37$ eV in $n_\parallel(z, \epsilon)$ and corresponds to a peak of majority $p_z$ states being split and shifted towards lower energies as the magnetization rotates from the film plane ($\parallel$) to the perpendicular ($\perp$) direction of the surface. The same effect, although much less prominent, is also visible for the minority states. This behavior leads to a maximum value in the TAMR of $-49$% (see Fig. \[fig:PbAdatom\](b)). Around [[$E_{\text{F}}$]{}]{} this effect is considerably smaller and of opposite