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We report first principles calculations of the structural parameters andphonon dispersion of the tetragonal non-centrosymmetric heavy fermion compoundCeAuAl$_3$. Taking into account weak magnetoelastic interactions of therare-earth (RE) ions with the spectrum of phonons, we obtain an analyticalexpression for the hybridization of quadrupole excitations and phonons from thepoles of the one-phonon Green-function. In the paramagnetic phase, we predictthe formation of mixed modes that may be observed by inelastic neutronscattering. Our results show that magnetoelastic interactions, albeit beingmoderate, play an important role in CeAuAl$_3$. This suggests thatmagnetoelastic interactions may be equally important in a wide range of relatedcompounds.

Lattice dynamics and coupled quadrupole-phonon excitations in CeAuAl$_3$