  We present a theoretical study on the relation between the size of the rare
earth ions, 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, 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 smaller rare earth ions. We analyze the appearance of the uniform
shear distortion below the Jahn-Teller ordering temperature, estimate the
Jahn-Teller ordering temperature and its variation between NdMnO3 and LaMnO3,
and obtain the relations between distortions. We find good agreement between
theoretical results and experimental data.
