THz spectroscopy is used to identify a broad distribution of two-level systems, characteristic of glasses, in the substitutional monatomic mixed crystal systems, ${\mathrm{Ba}}_{1-x}{\mathrm{Ca}}_x{\mathrm{F}}_2$ and ${\mathrm{Pb}}_{1-x}{\mathrm{Ca}}_x{\mathrm{F}}_2$. In these minimally disordered systems, two-level behavior, which was not previously known to occur, begins at a specific ${\mathrm{CaF}}_2$ concentration. The concentration dependence, successfully modeled using the statistics of the impurity distribution in the lattice, points to a collective dopant tunneling mechanism.

• Received 18 November 2005

DOI:https://doi.org/10.1103/PhysRevLett.96.235503