Effects of rare-earth ion size on the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites

We present a theoretical study on the relation between the size of the rare earth ion, often known as chemical pressure, and the stability of the coherent Jahn-Teller distortions in undoped perovskite manganites. Using a Keating model expressed in terms of atomic scale symmetry modes for a simplified two-dimensional model, we show that there exists a coupling between the uniform shear distortion and the staggered buckling distortion within the Jahn-Teller energy term. It is found that this coupling provides a mechanism by which the coherent Jahn-Teller distortion is more stabilized by a smaller rare earth ion. We analyze the appearance of the uniform shear distortion below the Jahn-Teller ordering temperature, estimate the Jahn-Teller ordering temperature and its variation among LaMnO ₃, PrMnO ₃, and NdMnO ₃, and obtain the relations between distortions. We find good agreement between theoretical results and experimental data.