  Using density-functional theory calculations, we investigate the magnetic as
well as the dynamical properties of tetragonal SrRuO3 (SRO) under the influence
of epitaxial strain. It is found that both the tensile and compressive strain
in the xy-plane could induce the abrupt change in the magnetic moment of Ru
atom. In particular, under the in-plane ~4% compressive strain, a ferromagnetic
to nonmagnetic transition is induced. Whereas for the tensile strain larger
than 3%, the Ru magnetic moment drops gradually with the increase of the
strain, exhibiting a weak ferromagnetic state. We find that such magnetic
transitions could be qualitatively explained by the Stoner model. In addition,
frozen phonon calculations at {\Gamma} point reveal structural instabilities
could occur under both compressive and tensile strains. Such instabilities are
very similar to those of the ferroelectric perovskite oxides, even though SRO
remains to be metallic in the range we studied. These might have influence on
the physical properties of oxide supercells taking SRO as constituent.
