Critical Slowing Down of Quadrupole and Hexadecapole Orderings in Iron Pnictide Superconductor

Abstract

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.