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The low-temperature homogeneous broadening of the electronic transitions of Eu 3ϩ and Pr 3ϩ rare-earth impurity ions in Y 2 O 3 and LaF 3 nanocrystals embedded into amorphous materials ͑polymer and oxyfluoride glass ceramics͒ was studied with hole-burning and fluorescence line narrowing techniques. It is shown that the homogeneous linewidth is determined by the interaction of the impurity ions contained in the nanocrystals with the two-level systems ͑TLS's͒ of the surrounding glass matrix. A comparison of the experiments with a calculation provides direct evidence for the long-range nature of the interaction with the TLS's. DOI: 10.1103/PhysRevB.64.100201 PACS number͑s͒: 78.67.Ϫn, 78.67.Bf It is well known that when rare-earth ͑RE͒ ions are doped into glasses, their dynamics are governed by interactions with the two-level systems ͑TLS's͒ of the glass. Experiments in many systems provide evidence that at low temperatures the homogeneous linewidths, ␥ h , in these systems obey a power law in temperature, ␥ h ϳT ␣ with 1Ͻ␣Ͻ2. Theoretical calculations show that this behavior is predicted for interactions with the TLS's of the glass. [1][2][3][4][5] With the recent availability of nanocrystals containing RE ions, it is of great interest to determine whether RE ions separated from the glassy TLS's by the crystalline nanoparticle in which they are contained also exhibit interactions with TLS's when the nanoparticles are embedded in an amorphous matrix such as a glass. This can provide an independent test of the TLS model and can determine the length scale of the interactions.It has been recently determined that materials consisting of insulating nanocrystals doped with RE ions embedded into amorphous ͑glassy͒ matrices possess nearly identical spectra to those of RE ions in single crystals of the same crystalline composition and structure.6 This is not unexpected, as the optical spectra of RE ions are determined by the short-range local environment of the RE site, which ͑with the exception of the ions at the nanocrystal-glass interface͒ remains unperturbed in crystallites of a few nanometers size. The sharp line spectra allow one to spectrally isolate ions in the nanoparticles from those in the amorphous matrix. Here we apply the technique of spectral hole burning to examine their dynamical properties. This work is motivated, in part, by the interest in these materials for applications such as hole-burning memories 7 and optical processors. 8,9The mechanisms responsible for changes in the dynamical properties of the excited states of RE ions in insulating nanocrystals embedded in amorphous matrix, compared to single crystals, can be grouped into two categories: ͑i͒ those connected with size restriction effects and ͑ii͒ those caused by the interaction of RE ions with the amorphous environment surrounding the crystallites. The effects of the first kind are due mainly to the modification of the phonon spectrum of the nanocrystals at low frequencies due to their sizerestricted nature as reported for ''free-standing'' na...