Determination of the Anisotropy of Permittivity of Quantum Paraelectric Strontium Titanate

The dielectric properties of strontium titanate (SrTiO$_3$) have previously been reported from room temperature to low temperatures with conflicting results. In this work, precision measurement of the permittivity is undertaken by simultaneously measuring transverse electric and transverse magnetic resonant modes within a single crystal. It is unequivocally shown that the permittivity is isotropic at room temperature with a permittivity of order $316.3\pm2.2$ by measuring multiple modes of different electric field polarisations. As the crystal is cooled to 5 K and undergoes well known phase transitions, we show the material becomes uniaxial anisotropic with the ratio of the parallel to perpendicular permittivity to the cylinder z-axis of the sample as high as 2.4 below 6 K.