This paper reports recent progress of ultrasonic measurements on URu$_2$Si$_2$, including ultrasonic measurements under hydrostatic pressure, in pulsed-magnetic fields, and the effect of Rh-substitution. The observed changes of the elastic responses
shed light on the orthorhombic-lattice instability with $Gamma_3$-symmetry existing within the hidden order and the hybridized 5$f$-electron states of URu$_2$Si$_2$.
We have performed ultrasonic measurements on single-crystalline URu2Si2 with pulsed magnetic fields, in order to check for possible lattice instabilities due to the hybridized state and the hidden-order state of this compound. The elastic constant (C
11-C12)/2, which is associated with a response to the {Gamma}3-type symmetry-breaking (orthorhombic) strain field, shows a three-step increase at H > 35 T for H || c at low temperatures, where successive meta-magnetic transitions are observed in the magnetization. We discovered a new fact that the absolute change of the softening of (C11-C12)/2 in the temperature dependence is quantitatively recovered at the suppression of hybridized-electronic state and the hidden order in high-magnetic field for H perp c associated with the successive transitions. The present results suggest that the {Gamma}3-type lattice instability, is related to both the emergence of the hybridized electronic state and the hidden-order parameter of URu2Si2. On the other hand, magnetic fields H || [100] and [110] enhance the softening of (C11-C12)/2 in the hidden order phase, while no step-like anomaly is observed up to 68.7 T. We discuss the limitation of the localized-electron picture for describing these features of URu2Si2 by examination of a crystalline electric field model in terms of mean-field theory.
Elastic properties of the filled skutterudite compound SmOs$_4$Sb$_{12}$ have been investigated by ultrasonic measurements. The elastic constant $C_{11}(omega)$ shows two ultrasonic dispersions at $sim$15 K and $sim$53 K for frequencies $omega$ betwe
en 33 and 316 MHz, which follow a Debye-type formula with Arrhenius-type temperature-dependent relaxation times, and remain unchanged even with applied magnetic fields up to 10 T. The corresponding activation energies were estimated to be $E_2$ = 105 K and $E_1$ = 409 K, respectively. The latter, $E_1$, is the highest value reported so far in the Sb-based filled skutterudites. The presence of magnetically robust ultrasonic dispersions in SmOs$_4$Sb$_{12}$ implies a possibility that an emergence of a magnetically insensitive heavy fermion state in this system is associated with a novel local charge degree of freedom which causes the ultrasonic dispersion.
