Hybridization-driven orthorhombic lattice instability in URu${}_2$Si${}_2$

We have measured the elastic constant ($C_{11}$-$C_{12}$)/2 in URu${}_2$Si${}_2$ by means of high-frequency ultrasonic measurements in pulsed magnetic fields $H\parallel$ [001] up to 61.8 T in a wide temperature range from 1.5 to 116 K. We found a reduction of ($C_{11}$-$C_{12}$)/2 that appears only in the temperature and magnetic field region in which URu${}_2$Si${}_2$ exhibits a heavy-electron state and hidden order. This change in ($C_{11}$-$C_{12}$)/2 appears to be a response of the 5$f$ electrons to an orthorhombic and volume conservative strain field ${\epsilon }_{xx}$-${\epsilon }_{yy}$ with ${\Gamma }_3$ symmetry. This lattice instability is likely related to a symmetry-breaking band instability that arises due to the hybridization of the localized $f$ electrons with the conduction electrons and is probably linked to the hidden-order parameter of this compound.

Figure 1

(a) Magnetic field (right axis) and output voltage of in-phase ($I$) and quadrature ($Q$) signals of the gated integrators at 4.14 K and 159.5 MHz (left axis) as a function of the elapsed time. Inset (b) shows the Lissajous curve of the $I$ and $Q$ signals.

Figure 2

Upper panel: Elastic constant ($C_{11}$-$C_{12}$)/2 normalized by the values at 0 T vs. the magnetic field $H\parallel$ [001] of URu${}_2$Si${}_2$ at various fixed temperatures between 1.56 and 116 K. Lower panel: Sound-attenuation change $\Delta \alpha$ vs. $H$ for 1.56 to 13.2 K. All the data were taken with both up- and down-sweeps of the magnetic field, as indicated by arrows.

Figure 3

Normalized elastic constant ($C_{11}$-$C_{12}$)/2 vs. temperature at various magnetic fields $H\parallel$ [001] from 0 to 61.85 T. The curves indicated by a magnetic field with an asterisk, 0 and 17.8 T, have been measured with the conventional method as a basis for the conversion from isotherms to curves at constant fields. Upward and downward facing triangles indicate the HO transition and local minimum, respectively.

Figure 4

Three-dimensional plots of the elastic constant ($C_{11}$-$C_{12}$)/2 vs. temperature and magnetic field along the $c$ axis of URu${}_2$Si${}_2$. The white and black circles indicate the hidden-order transition and local minima found in the temperature dependence of ($C_{11}$-$C_{12}$)/2, respectively. The bottom of the box shows the magnetic field-temperature phase diagram of URu${}_2$Si${}_2$ (See text for details).