  The strain tuned magnetism of YTiO$_3$ film grown on the LaAlO$_3$ ($110$)
substrate is studied by the method of the first principles, and compared with
that of the ($001$)-oriented one. The obtained magnetism is totally different,
which is ferromagnetic for the film on the ($110$) substrate but A-type
antiferromagnetic on the ($001$) one. This orientation-dependent magnetism is
attributed to the subtle orbital ordering of YTiO$_3$ film. The
$d_{xz}$/$d_{yz}$-type orbital ordering is predominant for the ($001$) one, but
for the ($110$) case, the $d_{xy}$ orbital is mostly occupied plus a few
contribution from the $d_{xz}$/$d_{yz}$ orbital. Moreover, the lattice mismatch
is modest for the ($110$) case but more serious for the ($001$) one, which is
also responsible for this contrasting magnetism.
