Microwave-frequency loss and dispersion in ferroelectric Ba _0.3Sr _0.7 TiO ₃ thin films

We report on broadband microwave-frequency measurements of epitaxial ferroelectric Ba0.3 Sr0.7 TiO3 thin films that reveal systematic increases in the loss and dispersion as the frequency increases toward 40 GHz. Our analysis provides evidence that the origin of this increased loss and dispersion is the direct coupling of microwave energy into a broad distribution of damped soft-phonon modes. We believe that nanometer-sized polar regions in the thin films play a role in this process, resulting in lattice-dynamical loss mechanisms that extend several decades in frequency below the frequency of the soft mode in these thin-film materials.