  We investigated phonon behavior of hexagonal close packed titanium under
homogeneous shear deformation corresponding to the $\{10\bar{1}2\}$ twinning
mode using first-principles calculation and phonon calculation. By this
deformation, we found that a phonon mode located at a point on Brillouin zone
boundary is drastically soften increasing the shear and finally it triggers a
spontaneous structural transition by breaking the crystal symmetry toward twin
from parent.
