Surface magnetism is analyzed by spin-dependent He+-ion neutralization (the Auger neutralization) in the vicinity of a surface using an electron spin-polarized low-energy He+-ion beam [spin-polarized ion scattering spectroscopy (SP-ISS)]. Recently, spin-orbit coupling (SOC) has been found to act as another mechanism of spin-dependent low-energy He+-ion scattering. Thus, it is crucial for surface magnetism analyses by SP-ISS to separate those two mechanisms. In the present study, we investigated the spin-induced asymmetry in scattering of low-energy He+ ions on ultrathinAu and Sn films as well as the oxygen adsorbate on amagnetized-Fe(100) surface where these two mechanisms may coexist. We found that the Fe surface magnetism immediately disappeared with the growth of those overlayers. On the other hand, we observed no induced spin polarization in the Au and Sn thin films even in the very initial stage of the growth. We also observed that the spin asymmetry of the O adsorbate was induced by the magnetism of the underlying Fe substrate. The present study demonstrates that the two mechanisms of the spin-asymmetric He+-ion scattering (the ion neutralization and SOC) can be separated by an azimuthal-angle-resolved SP-ISS measurement.