Strong influence of non-ideality of electrodes on stability of single domain state in ferroelectric-paraelectric superlattices

Abstract

We study the phase stabilities with respect to small perturbations in ferroelectric-paraelectric superlattices and show that nature of the electrodes characterized by a deviation from the ideal behavior strongly influences the possibility to obtain single-domain state in ferroelectric-paraelectric superlattices. To demonstrate this, we analyze the limit of stability of the paraelectric and the single domain state in ferroelectric-paraelectric superlattices in contact with top and bottom electrodes with finite screening lengths. The combined analytical and numerical analyses of one bilayer and two bilayer systems are carried out using the Landau-Ginzburg-Devonshire formalism and equations of electrostatics. The BaTiO3/SrTiO3 system was considered as an example. Unlike the case of ideal electrodes where the stability limits are independent of the system size, the stability analysis in a multilayer with real electrodes should take into account explicitly the number of the repeating units that makes the algebra very cumbersome, forcing us to consider systems with one and two bilayer stacks only. Extrapolating the difference between the two systems to the cases of many repeating units gives us the possibility to make qualitative but feasible predictions related to those with many repeating units. We observe that in systems with nearly equal thicknesses of the ferroelectric and paraelectric layers, the electrodes with realistic screening lengths lead to dramatic widening of the parametric region where the single-domain state is absolutely unstable expelling the single-domain state to unphysical layer thicknesses and temperatures. This region grows when one goes from a single bilayer to two bilayer system, implying that obtaining a single domain state becomes even less feasible in systems with many bilayers. When electrode properties approach that of ideal in addition to increasing the volume fraction of the ferroelectric component, the effect of growth of the region of absolute instability of the single domain state may remain very strong for relatively thin repeating units (a few nanometers). This tendency will continue with increasing the number of the repeating units.