Hybrid Improper Ferroelectricity in (Sr,Ca)3Sn2O7 and Beyond: Universal Relationship between Ferroelectric Transition Temperature and Tolerance Factor in n = 2 Ruddlesden-Popper Phases.

Hybrid improper ferroelectricity, which utilizes nonpolar but ubiquitous rotational/tilting distortions to create polarization, offers an attractive route to the discovery of new ferroelectric and multiferroic materials because its activity derives from geometric rather than electronic origins. Design approaches blending group theory and first principles can be utilized to explore the crystal symmetries of ferroelectric ground states, but in general, they do not make accurate predictions for some important parameters of ferroelectrics, such as Curie temperature ( TC). Here, we establish a predictive and quantitative relationship between TC and the Goldschmidt tolerance factor, t, by employing n = 2 Ruddlesden-Popper (RP) A3B2O7 as a prototypical example of hybrid improper ferroelectrics. The focus is placed on an RP system, (Sr1- xCa x)3Sn2O7 ( x = 0, 0.1, and 0.2), which allows for the investigation of the purely geometric (ionic size) effect on ferroelectric transitions, due to the absence of the second-order Jahn-Teller active (d0 and 6s2) cations that often lead to ferroelectric distortions through electronic mechanisms. We observe a ferroelectric-to-paraelectric transition with TC = 410 K for Sr3Sn2O7. We also find that the TC increases linearly up to 800 K upon increasing the Ca2+ content, i.e., upon decreasing the value of t. Remarkably, this linear relationship is applicable to the suite of all known A3B2O7 hybrid improper ferroelectrics, indicating that the  TC correlates with the simple crystal chemistry descriptor, t, based on the ionic size mismatch. This study provides a predictive guideline for estimating the TC of a given material, which would complement the convergent group-theoretical and first-principles design approach.