Low-energy phonon dispersion in LaFe$_4$Sb$_{12}$

We studied the vibrational dynamics of a single crystal of LaFe$_4$Sb$_{12}$ by three-axis inelastic neutron spectroscopy. The dispersion of phonons with wave vectors $q$ along $[xx0]$ and $[xxx]$ directions in the energy range of eigenmodes with high amplitudes of lanthanum vibrations, i.e., at $\hbar \omega < 12$\,meV is identified. Symmetry-avoided anticrossing dispersion of phonons is established in both monitored directions and distinct eigenstates at high-symmetry points and at the Brillouin-zone center are discriminated. The experimentally derived phonon dispersion and intensities are compared with and backed up by {\textit ab initio} lattice dynamics calculations. results of the computer model match well with the experimental data.