Gaussian fluctuation corrections to a mean-field theory of complex hidden order in ${\mathrm{URu}}_2{\mathrm{Si}}_2$

Hidden-order phase transition in the heavy-fermion superconductor ${\mathrm{URu}}_2{\mathrm{Si}}_2$ exhibits the mean-field-like anomaly in temperature dependence of heat capacity. Motivated by this observation, here we explore the impact of the complex order parameter fluctuations on the thermodynamic properties of the hidden-order phase. Specifically, we employ the mean-field theory for the hidden order which describes the hidden-order parameter by an average of the hexadecapole operator. We compute the Gaussian fluctuation corrections to the mean-field theory equations including both the fluctuations due to “hidden order” as well as antiferromagnetic order parameters. We find that the Gaussian fluctuations lead to the smearing of the second-order transition rendering it to become the first-order one. The strength of the first-order transition is weakly dependent on the strength of underlying antiferromagnetic exchange interactions.

Figure 1

Critical temperature $T_c$ of the hidden-order transition plotted in the units of the mean-field critical temperature $T_c^{\mathrm{mf}}$ for $N_b=6$. The reduction in the values of $T_c$ is due to Gaussian fluctuations which increase with an increase in the value of antiferromagnetic exchange coupling $U_y$.

Figure 2

Free energy dependence on the value of the order parameter calculated at various temperatures.

Figure 3

Temperature dependence of the order parameter ${\psi }_x$ in the presence of Gaussian fluctuations and at the mean-field level for $N_b=6$. Gaussian fluctuations lead to a sudden change of the order parameter at $T_c$: the second-order mean-field transition becomes the first-order transition.