Surface melting of electronic order in La_0.5Sr _1.5MnO₄

We report temperature-dependent surface x-ray scattering studies of the orbital ordered surface in La_0.5Sr_1.5MnO₄. We find that as the bulk ordering temperature is approached from below the thickness of the interface between the electronically ordered and electronically disordered regions at the surface grows, 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 ordering at the surface has melted. Above the bulk transition, long-range ordering in the bulk is destroyed but finite-sized isotropic fluctuations persist, with a correlation length roughly equal to that of the low-temperature in-plane surface correlation length.