A single electric relaxation time in $Ba_{1-x}Sr_{x}TiO_{3}$ nanoparticles at low temperatures

It is shown that the dielectric response of $Ba_{0.77}Sr_{0.23}TiO_{3}$ nanoparticles at temperatures below 200K has a frequency and temperature dependence in agreement with the Debye theory with a single relaxation time, which exhibits the Arrhenius law. By contrast, at temperature above 210K the dielectric response exhibits broad range of relaxation times characteristic of relaxor-ferroelectrics. We suggest that the single relaxation time at low temperature indicates frustrated ferroelectricity, analogous to frustrated antiferromagnetism.