Surface Melting of Electronic Order

We report temperature-dependent surface x-ray scattering studies of the orbital ordered surface in La$_{0.5}$Sr$_{1.5}$MnO$_4$. We find that the interfacial width of the electronic order grows as the bulk ordering temperature is approached from below, though the bulk correlation length remains unchanged. Close to the transition, the surface is so rough that there is no well-defined electronic surface, despite the presence of bulk electronic order, that is the electronic surface has melted. Above the bulk transition, finite-sized isotropic fluctuations of orbital order are observed, with a correlation length equal to that of the electronic surfaces' in-plane correlation length at the transition temperature.