Spontaneous strain due to ferroquadrupolar ordering in UCu${}_2$Sn

The ternary uranium compound UCu${}_2$Sn with a hexagonal ZrPt${}_2$Al-type structure shows a phase transition at 16 K. We reported previously that huge lattice-softening is accompanied by the phase transition, which originates from ferroquadrupolar ordering of the ground state non-Kramers doublet ${\mathrm{\Gamma }}_5$. A macroscopic strain, which is expected to emerge spontaneously, was not detected by powder X-ray diffraction in the temperature range between 4.2 and 300 K. To search the spontaneous strain, we have carried out thermal expansion measurements on a single-crystalline sample along the $a$, $b$ and $c$ axes using a capacitance technique with the resolution of ${10}^{-8}$. In the present experiment, we found the spontaneous $e_{xx}-e_{yy}$ strain which couples to the ground state doublet ${\mathrm{\Gamma }}_5$. The effect of uniaxial pressure along the $a$, $b$ and $c$ axes on the transition temperature is also discussed.