  Recent theoretical studies have predicted magnetic states for Ru and Os in
the body centered tetragonal structure (bct) with c/a < 1. In this study, we
present first principles calculations of the phonon dispersion for
ferromagnetic Ru- and Os-bct along the epitaxial and uniaxial Bain paths, to
evaluate their dynamical stability. The phonon dispersions were computed using
the density function perturbation theory, including the gradient corrections to
the exchange-correlation functional within the plane-waves
ultrasoft-pseudopotential approximation. The phonon dispersion for the local
minimum in the Bain path with c/a < 1 as well as the uniaxial and epitaxial
strained structures are analyzed. We find imaginary frequencies along different
directions of the Brillouin zone, which indicates that both systems are
dynamically unstable. Consequently, ferromagnetic Ru and Os in the body
centered tetragonal structure with c/a < 1 are not truly metastable phases.
