  We performed inelastic neutron scattering (INS) experiments to measure spin
dynamics on a polycrystalline sample of a spin tube candidate CsCrF$_{4}$. The
compound exhibits a successive phase transition from a paramagnetic phase
through an intermediate temperature (IT) phase of a 120$^{\circ}$ structure to
a low temperature (LT) phase of another 120$^{\circ}$ structure. Elaborate
comparison between observed and calculated neutron spectra in LT phase reveals
that the spin Hamiltonian is identified as antiferromagnetic spin tubes
including perturbative terms of intertube interaction, Dzyaloshinskii-Moriya
interaction, and single ion anisotropy. A phase diagram for the ground state is
classically calculated. A set of parameters in the spin Hamiltonian obtained
from the INS spectra measured in LT phase is quite close to a boundary to the
phase of the 120$^{\circ}$ structure of IT phase. The INS spectra measured in
IT phase is, surprisingly, the same as those in LT phase in the level of powder
averaged spectra, even though the magnetic structures in IT and LT phases are
different. Identical dynamical structures compatible with two different static
structures are observed. No difference in the observed spectra indicates no
change of the spin Hamiltonian with the temperature, suggesting that the origin
of the successive phase transition being order-by-disorder mechanism.
