  Using the full potential linearized augmented plane wave (FLAPW) method, we
have explored the magnetic properties of one dimensional (1D) Ti atomic chain.
Astonishingly, we for the first time observed that the 1D Ti atomic chain has
ferromagnetic ground state even on NiAl(110) surface although the Ti has no
magnetic moment in bulk or macroscopic state. It was found that the physical
property of direct exchange interaction among Ti atoms occurred in free
standing state is well preserved on NiAl(110) surface and this feature has an
essential role in ferromagnetism of 1D Ti atomic chain. It was shown that the
m=$|2|$ state has the largest contribution to the magnetic moment of Ti atom
grown on NiAl(110) surface. In addition, we found that the magnetic dipole
interaction is a key factor in the study of magnetic anisotropy, not the
magnetocrystalline anisotropy arising from spin-orbit interaction.
