Lattice dynamics, crystal-field excitations and quadrupolar fluctuations of YbRu${}_2$Ge${}_2$

Abstract

We report Raman-scattering results of YbRu${}_2$Ge${}_2$ single crystals to explore the phononic and crystal-field (CF) excitations. This heavy-fermion metal is suggested to enter a ferroquadrupolar (FQ) phase below T${}_0$=10 K. The tetragonal CF potential splits the Yb${}^{3+}$ ${}^2{F}_{7/2}$ ground multiplet into two ${\Gamma }_6$ and two ${\Gamma }_7$ Kramers doublets. We establish the following CF level scheme of the ground multiplet: a ${\Gamma }_6$ ground state, with the two ${\Gamma }_7$ states at 2 cm${}^{-1}$, 95 cm${}^{-1}$ and the other ${\Gamma }_6$ state at 239 cm${}^{-1}$. The $\sim$2 cm${}^{-1}$ separation between the CF ground and first excited states is in agreement with the previously proposed quasi-quartet CF ground state. The intensity of the lowest-energy CF transition remarkably increases on cooling, indicating a coupling of this CF excitation to the quadrupolar fluctuations above T${}_0$. From symmetry analysis, we suggest that the FQ order has B${}_{1g}$ symmetry. Moreover, temperature-dependent study of four Raman-active phonon modes shows that the intensities of the A${}_{1g}$ and one E${}_g$ modes increase significantly on cooling, which is explained by a near-resonant coupling between these two phonon modes and CF transitions.

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