Experimental study of Raman-active two-level systems and the boson peak inLaF3-doped fluorite mixed crystals

Abstract

A broad spectral distribution of two-level systems (TLS) displaying only ${A}_{1g}$ symmetry, not ${E}_{g}$ or ${T}_{2g},$ is observed in the low-frequency, low-temperature Raman spectra of fluorite single crystal hosts doped with large amounts of ${\mathrm{LaF}}_{3}.$ The observed range of each TLS spectrum is found to be independent of the dopant concentration although each of the three crystalline hosts, ${\mathrm{CaF}}_{2},$ ${\mathrm{SrF}}_{2},$ and ${\mathrm{BaF}}_{2},$ displays a slightly different cutoff frequency. In a somewhat higher frequency range but still far below the Brillouin Zone TA phonon mode frequency, a boson peak, showing ${E}_{g}$ symmetry, is also observed and its strength is proportional to the defect-induced vibrational Raman activity for the three crystal lattices. A surprising property is that for all three host crystals the boson peak center frequency increases with increasing lattice disorder. The strengths of the TLS spectra show distinctively different ${\mathrm{La}}^{3+}$ concentration dependencies in each host, which is also different from that observed for the boson peaks. By comparing the density of state of TLS derived from the Raman scattering to the $\overline{P}$ density of states value determined from the earlier specific heat measurements, the number density of Raman-active TLS is separated from the coupling coefficient. When the total number density of Raman-active TLS is examined versus different physical properties it is found that lattice disorder, not the ${\mathrm{LaF}}_{3}$ concentration per se, is the important variable. The experimental results are consistent with a model where the TLS number density is controlled by the law of mass action with the ``effective'' temperature associated with the production of TLS determined by the frozen-in lattice disorder. Good agreement is found for the number density of TLS versus concentration as determined from the present Raman scattering data and the previous far infrared measurements when the far infrared dipole moment is used as a single fitting parameter. However, in contrast with the far infrared studies, no TLS excited state transitions are observed in Raman scattering. The overall findings from this study suggest that the Raman and infrared active TLS distributions, which extends up to about 2 meV, are associated with extended entities.