The tunnelling anisotropic magnetoresistance (TAMR) effect describes the sensitivity of spin-polarized electron transport to the orientation of the magnetization with respect to the crystallographic axes. As the TAMR effect requires only a single magnetic electrode, in contrast to the tunnelling magnetoresistance effect, it offers an attractive route towards alternative spintronics applications. In this work we consider the TAMR effect at the single-atom limit by investigating the anisotropy of the local density of states in the vacuum above transition-metal adatoms adsorbed on a noncollinear magnetic surface, the monolayer of Mn on W(110). This surface presents a cycloidal spin spiral ground state with an angle of 173$^circ$ between neighbouring spins and thus allows a quasi-continuous exploration of the angular dependence of the TAMR of adsorbed adatoms using scanning tunnelling microscopy. Using first-principles calculations, we investigate the TAMR of Co, Rh and Ir adatoms on Mn/W(110) and relate our results to magnetization direction dependent changes in the local density of states. The anisotropic effect is found to be enhanced dramatically on the adsorption of heavy transition-metal atoms, with values of up to 50% predicted from our calculations. This effect will be measurable even with a non-magnetic STM tip.
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