Local Structure and Its Effect on The Ferromagnetic Properties of La$_{0.5}$Sr$_{0.5}$CoO$_3$ thin films}

We have used high-resolution Extended X-ray Absorption Fine-Structure and diffraction techniques to measure the local structure of strained La$_{0.5}$Sr$_{0.5}$CoO$_3$ films under compression and tension. The lattice mismatch strain in these compounds affects both the bond lengths and the bond angles, though the larger effect on the bandwidth is due to the bond length changes. The popular double exchange model for ferromagnetism in these compounds provides a correct qualitative description of the changes in Curie temperature $T_C$, but quantitatively underestimates the changes. A microscopic model for ferromagnetism that provides a much stronger dependence on the structural distortions is needed.