Fig. 2: Crystal structure and permittivity of LN and BTO.

a,b, Crystal structures of LN (a) and BTO (b) and how they are oriented as thin films. In each unit cell, the spontaneous polarization P is marked with the black arrow. The ‘empty’ atoms with the dashed outline represent the hypothetical positions of the Li (orange) or Ti (red) ions if the polarization was flipped. In the depiction of thin films, the black arrows are also used to represent the spontaneous polarization. Both have an in-plane c axis. LN has a single domain, with only one polarization direction (indicated by the single black arrow). BTO has a multidomain structure in which the c axes of the neighbouring domains are oriented at 90° to each other (indicated by the multiple black arrows and differently shaded regions). For BTO, the black arrows are double-sided to represent the fact that the raw film might have P in either direction. c, LN permittivity data along the a axis (light blue) and c axis (dark blue) collected from the literature^{17,18,19,20,21,22,23,24,25,26,27}. The blue solid lines represent a linear fit to the literature data. The black lines represent the values produced from the model in this work. d, BTO permittivity data (light green) collected from the literature^{28,29,30,31,32,33,34,35,36,37}. The green solid and dashed lines are the real and imaginary parts, respectively, of the Debye model from equation (2) fitted to the literature data. The permittivity values extracted from the measurements of the RF-sputtered BTO of this work are plotted in black. The inset shows the loss tangent tanδ = ε″/ε′ for the literature fit and the data from this work.