Effect of antiferromagnetic spin correlations on lattice distortion and charge ordering in Pr$_{0.5}$Ca$_{1.5}$MnO$_{4}$

We use neutron scattering to study the lattice and magnetic structure of the layered half-doped manganite Pr$_{0.5}$Ca$_{1.5}$MnO$_4$. On cooling from high temperature, the system first becomes charge- and orbital- ordered (CO/OO) near $T_{CO}=300$ K and then develops checkerboard-like antiferromagnetic (AF) order below $T_{N}=130$ K. At temperatures above $T_{N}$ but below $T_{CO}$ ($T_N<T<T_{CO}$), the appearance of short-range AF spin correlations suppresses the CO/OO induced orthorhombic strain, contrasting with other half-doped manganites, where AF order has no observable effect on the lattice distortion. These results suggest that a strong spin-lattice coupling and the competition between AF exchange and CO/OO ordering ultimately determines the low-temperature properties of the system.