  Ultrasonic measurements have been carried out to investigate the critical
dynamics of structural and superconducting transitions due to degenerate
orbital bands in iron pnictide compounds with the formula
Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$. The attenuation coefficient
$\alpha_{\mathrm{L}[110]}$ of the longitudinal ultrasonic wave for
$(C_{11}+C_{12}+2C_{66})/2$ for $x = 0.036$ reveals the critical slowing down
of the relaxation time around the structural transition at $T_\mathrm{s} = 65$
K, which is caused by ferro-type ordering of the quadrupole $O_{x'^2-y'^2}$
coupled to the strain $\varepsilon_{xy}$. The attenuation coefficient
$\alpha_{66}$ of the transverse ultrasonic wave for $C_{66}$ for $x = 0.071$
also exhibits the critical slowing down around the superconducting transition
at $T_\mathrm{SC} = 23$ K, which is caused by ferro-type ordering of the
hexadecapole $H_z^\alpha \bigl( \boldsymbol{r}_i, \boldsymbol{r}_j \bigr) =
O_{x'y'}\bigl( \boldsymbol{r}_i \bigr) O_{x'^2 - y'^2}\bigl( \boldsymbol{r}_j
\bigr)
  + O_{x'^2 - y'^2}\bigl( \boldsymbol{r}_i \bigr) O_{x'y'}\bigl(
\boldsymbol{r}_j \bigr)$ of the bound two-electron state coupled to the
rotation $\omega_{xy}$. It is proposed that the hexadecapole ordering
associated with the superconductivity brings about spontaneous rotation of the
macroscopic superconducting state with respect to the host tetragonal lattice.
