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.
