Critical slowing down of quadrupole and hexadecapole orderings in iron pnictide superconductor

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(Fe1_-xCo_x)₂As₂. The attenuation coefficient αL[110] of the longitudinal ultrasonic wave for (C₁₁ + C₁₂ + 2C₆₆)=2 for x = 0.036 reveals the critical slowing down of the relaxation time around the structural transition at Ts = 65K, which is caused by ferro-type ordering of the quadrupole O_x02-y02 coupled to the strain ϵxy. The attenuation coefficient α66 of the transverse ultrasonic wave for C₆₆ for x = 0.071 also exhibits the critical slowing down around the superconducting transition at TSC = 23K, which is caused by ferro-type ordering of the hexadecapole Hz (r_i; r_j) = O_x0_y0 (r_i)O_x2-y₂ (r_j) + O_x2-y₂ (r_i)O_x0y0(r_j) of the bound two-electron state coupled to the rotation ωxy. 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.