High-Field Ultrasonic Study of Quadrupole Ordering and Crystal Symmetry Breaking in CeRhIn5

We performed an ultrasonic measurement for the heavy-fermion compound CeRhIn${}_5$ to investigate the origin of the field-induced anisotropic phase in high magnetic fields. The transverse elastic constant $C_$\mathrm{T}$ = (C_{11} - C_{12})/2$andtheultrasonicattenuationcoefficient$\alpha_$\mathrm{T}$$ show clear anomaly at $B^{\star }=28.5$ T, which was discussed as the electronic nematic transition point. In addition, $C_{\mathrm{T}}$ exhibits acoustic de Haas-van Alphen oscillation below 28.5 T. These elastic anomalies around $B^{\star }$ indicate an electric quadrupole ordering of $O_{x^2-y^2}$ accompanied by $B_{1\mathrm{g}}$ crystal symmetry breaking and Fermi surface reconstruction due to the quadrupole-strain coupling, which results from itinerant $4f$ electrons and the $p$-$f$ hybridized state.