Scaling behavior of order parameters for the hybrid improper ferroelectric (Ca, Sr)3Ti2O7

We show that in contrast to the conventional view of a mean-field Landau-type behavior, the oxygen octahedral tilt (R) and polarization (P) in the A3B2O7 Ruddlesden-Popper hybrid improper ferroelectric (Ca, Sr)3Ti2O7 exhibits the scaling behavior of a 2D Ising class near the para-to-ferroelectric transition temperature (Tc). We also show that P exhibits an additional transition from a 2D Ising to a 3D mean-field critical behavior at a temperature Td < Tc, which is driven by enhanced interlayer dipolar correlations due to an increase in the ferroelectrically active B-site centered dipoles.