Scanning Tunneling Microscopy of Bilayer La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ Single Crystals

We employed a spin-polarized scanning tunneling microscope to image the (001) surface topography and spectroscopy in La$_{2-2x}$Sr$_{1+2x}$Mn$_{2}$O$_{7}$ (x$=$0.32, 0.40 {\&} 0.52) single crystals below the Curie temperature. As the doping is increased from x$=$0.3 to x$=$0.5 the spins arrange themselves in antiferromagnetic, ferromagnetic, in-plane and out-of-plane configurations. From local density of states (LDOS) maps, we observed a charge density wave with a wavelength of about 1.6 nm along the tetragonal a or b axes in the x$=$0.32 sample, which is known to be ferromagnetic with spins perpendicular to the surface. On the other hand, the x$=$0.52 crystal is expected to be type A antiferromagnetic with spins parallel to the surface, which is confirmed by our LDOS maps.