  Soft phonon behavior associated with a structural phase transition from the
low-temperature-orthorhombic (LTO) phase ($Bmab$ symmetry) to the
low-temperature-tetragonal (LTT) phase ($P4_{2}/ncm$ symmetry) was investigated
in La$_{1.875}$Ba$_{0.125}$CuO$_{4}$ using neutron scattering. As temperature
decreases, the TO-mode at $Z$-point softens and approaches to zero energy
around $T_{\rm d2}=62$ K, where the LTO -- LTT transition occurs. Below $T_{\rm
d2}$, the phonon hardens quite rapidly and it's energy almost saturates below
50 K. At $T_{\rm d2}$, the energy dispersion of the soft phonon along in-plane
direction significantly changes while the dispersion along out-of-plane
direction is almost temperature independent. Coexistence between the LTO phase
and the LTT phase, seen in both the soft phonon spectra and the peak profiles
of Bragg reflection, is discussed in context of the order of structural phase
transitions.
