  Using density functional theory, we investigate the electronic and magnetic
properties of $3d$ transition-metal adatoms adsorbed on a monolayer of Mn on
W(110). Mn/W(110) has a noncollinear cycloidal spin-spiral ground state with an
angle of 173$^\circ$ between magnetic moments of adjacent Mn rows. It allows to
rotate the spin orientation of an adsorbed magnetic adatom quasi-continuously.
Therefore, this surface is ideally suited for manipulating the spin direction
of individual atoms and exploring their magnetic properties using scanning
tunneling microscopy (STM). The adsorbed V and Cr transition-metal adatoms
couple antiferromagnetically to the nearest neighbor Mn atom of Mn monolayer
while Mn, Fe, Co, and Ni couple ferromagnetically. The magnetic moments of the
$3d$ adatoms are large and show a Hund's rule type of trend with a peak in the
middle of the series. We find large spin splitting of the $3d$ transition-metal
adatoms, large spin polarization of the local vacuum density of states up to
73\% at the Fermi energy, and significant tunneling anisotropic
magnetoresistance enhancement up to 27\%. We conclude that such large values
stem from the strong hybridization between the adatoms and the Mn atoms of the
monolayer. Furthermore, identification of spin orientations of the adatom using
spin-polarized STM is only possible for Co and V adatoms.
