In summary, our ESR results have shown that the origin for the large $_{g}$-shift of the Yb 3+ KDGS, rela- tive to that in O$_{h}$ symmetry (y = 0), may be associ- ated to the B t $_{6}$( O 2 6 − O 6 $_{6}$) term in $_{H$_{CFZ}$}$. Coexisting narrow and broad Yb 3+ resonances were observed and associated, respectively, to a low occupation ($_{∼}$5$_{%}$) of on-center Yb 3+ rattling ions ($_{∼}$1 GHz) and to a highly occupied ($_{∼}$95$_{%}$) $_{T}$-dependent distribution of off-center rattling Yb 3+ ions ( ≳ 15 GHz). These assignments were based on: i) the much higher expected Yb 3+ rattling fre- quencies than the microwave frequency used in the ESR experiments 6–8 and; ii) on the observed reduction of the hyperfine constant for the on-center Yb 3+ ions and the absence of hyperfine structure in the spectra of the off- center Yb 3+ ions which were attributed to motional nar- rowing effects. 22,23 Although our findings relied on the Yb 3+ ESR results to witness the Yb 3+ rattling mode, they suggest that the R ions in other skutterudites and clathrate compounds may be also rattling in an analo- gous form as long as they are inside an oversized cage. However, it may not be always observable in an ESR ex- periment. We believe that the evidence for predominant off-center rattling Yb 3+ ions in these skuterudites is a result that could justify the existence of Einstein oscilla- tors and help to understand the low thermal conductiv- ity and the strongly correlated phenomena exhibited by these type of materials. mechanism 22 of on-center Yb 3+ ions rattling in the rigid oversized ($_{φ}$ ≃ 5 Å) (Fe 2 P 3 ) 4 -cages. 9 In the extreme mo- tional narrowing regime 23 a rattling frequency of ∼ 1 GHz will reduce in ∼ $_{20%}$the hyperfine constant. More- over, the hyperfine structure in the inhomogeneous broad line spectra was not observed, suggesting that a distribu- tion of Yb 3+ ions are rattling at higher frequencies and producing an even larger reduction of the hyperfine con- stant. Again, in the extreme motional narrowing regime, a rattling frequency ≳ 15 GHz will reduce in 90 to 95$_{%}$ the hyperfine splitting, and the ESR spectra would look like the observed single broad line of Δ H ≃ 30-40 Oe. We should mention that the reported rattling amplitudes are ≲ 0.1 Å. 24 Hence, the broad line $_{T}$-dependent shift and broadening is most likely the result of a$_{T}$ -dependent distribution of Yb 3+ ions rattling at higher frequencies inside the (Fe 2 P 3 ) 4 -cages. Thus, we associate the ho- mogeneous narrow line , corresponding to the low occu- pied sites, to on-center ($_{g}$ = 2.575) of $_{≃}$1 GHz rattling Yb 3+ ions at (x=0.523,y=0.082), whereas the inhomoge- neous broad line , corresponding to the highly occupied sites with lower $_{g}$-values, to a distribution of ≳ 15 GHz rattling Yb 3+ ions. Since this broad line is an inhomo- geneous resonance (distribution of $_{g}$-values) and the rat- tling frequency is of the order of or higher than the ESR frequency, the rattling Yb 3+ ions responsible for these spectra should be spending more time at off-center posi- tions in the over-size cage. Since no emerging second resonance was observed from the low-$_{T}$ ESR spectra of Er 3+ and Dy 3+ ions diluted in Ce 1 $_{$_{−}$x}$R$_{x}$ Fe 4 P 12 , 15 it is possible that for Yb 3+ , with smaller ionic radius than that of Er 3+ and Dy 3+ , larger voided excursion space may be available for the Yb 3+ ions inside the (Fe 2 P 3 ) 4 -cages which may further favor the Yb 3+ to rattle. A$_{T}$ -dependent distribution of CFPs, that in this T$_{h}$ symmetry allows for a continuous change on g$_{eff}$ 25 , or even a distribution of new 2 nd order CFPs in H$_{CFZ}$ associated to the off-center Yb 3+ sites may be also a plausible reason for the observed $_{T}$-dependence of the inhomogeneous broad line . We thank FAPESP-SP and CNPq for financial sup- port. PS is supported by DOE grant No. DE-FG02- 98ER45707. VI. ACKNOWLEDGMENTS V. CONCLUSIONS 4 2008. 13 Y. Nakanishi, T. Kumagai, M. Oikawa, T. Tanizawa, and M. Yoshizawa, H. Sugawara and H. Sato, Phys. Rev. B 75 , 134411 (2007); T. Yanagisawa et al., J. Magn. Magn. Mater., 310 , 223 (2007); W. M. Yuhasz, N. A. Frederick, P.-C. Ho, N. P. Butch, B. J. Taylor, T. A. Sayles, M. B. Maple, J. B. Betts, A. H. Lacerda, P. Rogl, and G. Giester, Phys. Rev. B 71 , 104402, (2005); C. R. Rotundu, K. In- 9 W. Jeitschko and D. Braun, Acta Crystallogr. B 33 , 3401 (1977). 10 T. Inui, Y. Tanabe and Y. Onodera, Group Theory and its Applications in Physics (Springer, Berlin, 1966). 11 K. Takegahara, H. Harima and A. Yanase, J. Phys. Soc. Japan, 70 , 1190 (2001). 12 A. Abragam and B. Bleaney, EPR of Transition Ions (Clarendon Press, Oxford, 1970). 8 M. M. Koza, M. R. Johnson, R. Viennois, H Mutka, L. Girard and D. Ravot, Nature Materials, Articles, Advance online Publication, doi: 10.1038/nmat 2260, 31 August 7 C. B. Vining, Nature Mat. 7 , 765 (2008). 6 C. H. Lee, I. Hase, H. Sugawara, H. Yoshizawa and H. Sato, J. Phys. Soc. Jpn. 75 123602 (2006). 5 T. Goto, Y. Nemoto, K. Sakai, T. Yamaguchi, M. Akatsu, T. Yanagisawa, H. Hazama, K. Onuki, H. Sugawara and H. Sato, Phys. Rev. B 69 , 180511(R) (2004). 4 T. Yanagisawa, P-C. Ho, W. M. Yuhasz, M. B. Maple, Y. Yasumoto, H. Watanabe, Y. Nemoto and T. Goto, J. Phys. Soc. Jpn. 77 074607 (2008).. 3 See, for example, the Skutterudite2007 conference proceed- ings at http://jpsj.ipap.jp/journal/JPSJS-77SA.html 2 G. Nolas and G.Slack, American Scientist 89 , 136 (2001). 1 G. J. Snyder and E. S. Toberer, Nature Mat. 7 , 105 (2008).