Lattice dynamics and anomalous softening in the YbFe${}_4$Sb${}_{12}$ skutterudite

The lattice dynamics of the filled skutterudite YbFe${}_4$Sb${}_{12}$ was studied by resonant ultrasound spectroscopy and an anomalous softening in the temperature dependence of the elastic constants at $\sim$50 K was observed. This anomaly can not be explained by the dynamics of the filler, in contrast to other filled skutterudites. We have further investigated the origin of this anomaly using macroscopic and microscopic measurements. A rearrangement of the spectral weight of the Yb phonon states was observed in the temperature dependence of the density of phonon states, obtained by inelastic neutron scattering. We suggest that the anomaly is due to a change of the Yb valence state and that the anomaly and the phonon spectral weight rearrangement have the same origin.

Figure 1

(a) The temperature dependence of the elastic constants $c_{11}$, left axis, and $c_{44}$, right axis, of YbFe${}_4$Sb${}_{12}$ measured by resonant ultrasound spectroscopy. The dashed-dotted line indicates a Varshni behavior for $c_{11}$, which would indicate a normal temperature dependence and the dashed line indicates the fit to the data of a two-level system model with a variation of the level spacing with temperature. (b) The temperature dependence of the filler mode energy, i.e., the level spacing of the two-level system, used for the fit. (c) The temperature dependence of the inverse of the quality factor, $1/q$, as described in the text.

Figure 2

The crystal structure of YbFe${}_4$Sb${}_{12}$. Blue, red, and yellow spheres indicate Sb, Fe, and Yb, respectively. Yb is located in a Sb dodecahedron (blue shaded) and Fe is located in a Sb octahedron (red shaded).

Figure 3

The temperature dependence of the lattice parameter, $a$, and the thermal expansion, $\alpha$, of YbFe${}_4$Sb${}_{12}$. For comparison, the thermal expansion of FeSb${}_3$ is also shown.[23] The dotted black line indicates the model for the temperature dependence of the lattice parameter $a$ and the dashed lines are extrapolated guides for the eye. The yellow points indicate the lattice parameter determined from the diffraction patterns obtained by integrating over the elastic line in the INS data, see Sec. 3d.

Figure 4

The temperature dependence of the mean-square displacements of Yb and Sb obtained by x-ray diffraction and the fits between 100 and 300 K for extraction of the Debye and Einstein temperatures, see text. The red line indicates the Fe mean-square displacement obtained from the NIS measurement, see Sec. 3e.

Figure 5

Magnetic susceptibility of YbFe${}_4$Sb${}_{12}$ measured with an applied magnetic field of 0.1 and 3 T. The inset shows the inverse susceptibility, and the dashed line represents a linear fit between 100 and 300 K.

Figure 6

The quadrupole splitting, $\Delta E_Q$, obtained from the ${}^{57}$Fe Mössbauer spectra. For comparison, the data from Ref. 40 are given as red triangles and blue points. The inset shows the Mössbauer spectra at 4.2 K. The blue line indicates the contribution from the FeSb${}_2$ impurity.

Figure 7

(a) The temperature dependence of the neutron cross section weighted DPS in YbFe${}_4$Sb${}_{12}$. The upper panels show the change of the peak area with temperature (b) for the peak at 5.5 meV and (c) for the peak at 11 meV. (d) The inelastic structure factor $S(Q,E)$ of YbFe${}_4$Sb${}_{12}$ measured at 10 K. The color box indicates the $S(Q,E)$ intensity.

Figure 8

The neutron diffraction pattern of YbFe${}_4$Sb${}_{12}$ and from the Al sample holder obtained from the elastic line in the INS measurements. The data were integrated between 2 and $-2$ meV energy transfer. The simulated neutron diffraction pattern calculated with fullprof with the lattice parameter at 10 K, obtained from x-ray diffraction, is shown as the pink line at the bottom of the figure. The Al diffraction pattern of the background measurement at 10 K is indicated by the black line and was not subtracted from the YbFe${}_4$Sb${}_{12}$ pattern shown here.

Figure 9

The NIS and nuclear forward scattering, NFS, measured at the ${}^{57}$Fe, top, and ${}^{121}$Sb, bottom, resonances on YbFe${}_4$Sb${}_{12}$. The black lines indicate the nuclear forward scattering.

Figure 10

The partial DPS of YbFe${}_4$Sb${}_{12}$ of ${}^{57}$Fe, top, and ${}^{121}$Sb, bottom, in comparison to the partial DPS of FeSb${}_3$ from Ref. 23. The insets show the reduced DPS, $g\left(E\right)/E^2$, and the Debye levels, black lines in the same line style, obtained at low energies.

Figure 11

Comparison between the DPS of YbFe${}_4$Sb${}_{12}$ obtained by INS at 65 K, black line, and the DPS obtained by NIS with the ${}^{121}$Sb resonance, blue, and with the ${}^{57}$Fe resonance, red. The NIS data are normalized to the neutron scattering cross section and the stoichiometry of the sample. The orange area indicates the Yb DPS obtained by subtraction of the Sb and Fe DPS from the total DPS obtained by INS. The brown area indicates the added normalized DPS from Sb and Fe obtained by NIS. The inset shows the temperature dependence of the Sb DPS obtained by NIS.

Figure 12

Temperature-dependent EPR measurements on YbFe${}_4$Sb${}_{12}$ with an applied frequency of 9.5 GHz. The signal arising below 50 K is most likely due to Yb${}^{3+}$ ions.