Ferroelastic domain formation in epitaxial La$_{0.7}$Sr$_{0.3}$MnO$_{3}$ thin films

Epitaxial La$_{1-x}$Sr$_{x}$MnO$_{3}$ (LSMO) thin films are known to form domains to reduce substrate-induced strain. For instance, on cubic SrTiO$_{3}$ (100), LSMO thin films can have up to four rhombohedrally-strained variants. These individual strain states can distort the MnO$_{6}$ octahedra and lead to unique electrical and magnetic properties. We have used synchrotron x-ray diffuse scattering to probe the in- and out-of-plane domain structure of a 5 nm LSMO film grown on SrTiO$_{3}$ (100). Satellites are present near integer order and half-order peaks that result from octahedral tilting in the coherent LSMO film. By analyzing the amplitude, position, and anisotropy of the satellite peaks for multiple half-order peaks, we obtain a robust measure of the dimensions of the domains, the ordering of the variants, and the strain state of each variant. Implications of the domain structure on magnetic properties will be discussed.