3 tive intensities the broad and narrow lines correspond, respectively, to ∼ 95% ∼ 5% of the Yb 3+ ions fill- ing cages. Figure 3b presents the $_{T}$-dependence of the relative population for the low occupied sites ( narrow line ). The large observed drop strongly suggests that, as $_{T}$-increases, the low populated Yb 3+ sites migrate, in a reversible way, to the highly populated Yb 3+ ones. The inset of Fig. 3b shows for the broad , narrow and hy- perfine lines the $_{T}$-dependence of their intensities ($_{×}$$_{T}$ ) normalized at T ≃ 4.2 K. This data reveals that the broad line practically follows a Curie-Weiss (C-W) law, while the narrow line surprisingly drops faster than a C- W behavior, given further support to the sites migration idea. The C-W behavior is another indication that the 170 Yb 3+ ions carry localized magnetic moment and that the resonances arise from a CF KDGS. In order to analyze our ESR data in Ref. 15 we used the expanded Hamiltonian, $_{H$_{CFZ}$}$: where a magnetic moment J with a Landé g -factor$_{g}$$_{J}$ is considered. The CF includes the usual cubic O$_{h}$ 21 terms parametrized by the x variable that measures the relative weight of the 4th and 6th order terms and also takes into consideration the new term O t $_{6}$. The relative weight y linearly interpolates between the O$_{h}$ cubic terms for y$_{= 0}$ and the O t 6 term for y$_{= 1}$. This (x,y) parametrization allows the entire range of the CFP’s to be accounted for within the finite intervals − 1 $_{≤}$x$_{≤}$ 1 and |y|$_{<}$ 1 and the results do not depend on the sign of y. By diagonalizing H$_{CFZ}$ one obtains, as a function of x and y, the CF wave functions and energies for each of the R in units of W. From the ground state wave function the low field$_{g}$-value can be calculated 15 . A combined analysis of the ESR data for Er 3+ , Dy 3+ and Yb 3+ impurities in Ce 1 $_{$_{−}$x}$R$_{x}$ Fe 4 P 12 allowed us to pinpoint the exact (x=0.523,y=0.082) values correspond- ing to the Yb 3+ narrow line observed at T ≃ 4.2 K and g ≃ 2 . $_{575}$. 15 However, as T increases, a second Yb 3+ broad line emerges from the low-$_{T}$ narrow line (Fig. 1) and its $_{g}$-value decreases, reaching g = 2.54(1) at our highest-$_{T}$ ($_{≃}$ 45 K). Therefore, these two resonances should be associated to two coexisting Yb 3+ sites with different peculiarities. In these compounds the R-ions are known to rattle at frequencies of ∼ 10 3 GHz 6–8 which are low compared to the cage ion vibrations, but still much higher than the ESR frequencies ($_{∼}$10-30 GHz). Thus, we argue that the reduced hyperfine constant for the homogeneous narrow line spectra results from a motional narrowing scales at all-$_{T}$ with the relative change of its $_{g}$-value, δg/g ($_{δ}$$_{(Δ}$$_{H}$$_{)}$$_{/H}$ ≃ 1.3(3) $_{δg/g}$, see inset of Fig. 2a); f ) saturation ESR intensity measurements show that at 4.2 K and ∼ 10 mW the broad and narrow lines present, re- spectively, a ∼ 30% and ∼ 50% saturation (see inset of Fig. 2b). All the experimental features given in Figs. 1 and 2 were confirmed in crystals from different batches with comparable Yb concentrations. They lead us to con- clude that: i) the narrow and the broad lines are, re- spectively, homogeneous and inhomogeneous resonances; ii) the origin of the inhomogeneity is a distribution of $_{g}$- values of the order of the change in the$_{g}$-value; iii) the$_{T}$ - independent Δ H for the narrow line indicates that there is no Yb 3+ spin-lattice relaxation via exchange interac- tion with the conduction-electrons; 19,20 iv) the saturation of the spectra at low-$_{T}$ suggests slow spin-lattice relax- ation involving lattice phonons via spin-orbit coupling; 12 and v) at low-$_{T}$ the Yb 3+ ions behave as an adiabatic spin system allowing the formation of Einstein oscilla- tors inside the (Fe 2 P 3 ) 4 -cages. Figure 3a displays the $_{T}$-dependence of the unsatu- rated ($_{∼}$2 mW) ESR intensity for the broad and narrow lines of the 170 Yb 3+ (I=0) isotope of Fig. 1a. The inten- sity of one of the 171 Yb 3+ (I=1/2) isotope hyperfine lines, normalized by its natural abundance, is also shown. The inset shows the data in a log scale. From their rela- IV. ANALYSIS AND DISCUSSION H$_{CFZ}$ = W { (1 − | y | ) [ x O c 4 F 0 4 + (1 − | x | ) O c 6 F 0 $_{6}$] + y O t 6 F 2 $_{6}$} + g$_{J}$µ$_{B}$ H · J , (1) Figure 3: a) T -dependence of the ESR intensity for the two resonances of the $^{170}$Yb$^{3+}$(I=0) isotope. The intensity of one of the $^{171}$Yb$^{3+}$(I=1/2) hyperfine line, normalized by the nat- ural abundance, is also shown. The inset presents the same data in log scale. b) T -dependence of the relative intensity for the narrow line . The inset displays the data of Fig. 3a ( × T ) normalized at 4.2 K. 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