Magnetic Superstructure and Metal-Insulator Transition in Mn-Substituted Sr$_3$Ru$_2$O$_7$

We present a temperature-dependent resonant elastic soft x-ray scattering (REXS) study of the metal-insulator transition in Sr$_3$(Ru$_{1-x}$Mn$_x$)$_2$O$_7$, performed at both Ru and Mn $L$-edges. Resonant magnetic superstructure reflections together with ab-initio density functional theory calculations identify the ground state as a spin checkerboard with blocks of 4 spins up and 4 spins down. Based on modelling of the REXS intensity from randomly distributed Mn impurities, we establish the inhomogeneous nature of the metal-insulator transition, with an effective percolation threshold corresponding to an anomalously low $x\sim 0.05$ Mn substitution. Perhaps more important, our results suggest that the same checkerboard instability might be present already in the parent compound Sr$_3$Ru$_2$O$_7$. In collaboration with: A.G. Cruz Gonzalez, J.D. Denlinger (Berkeley) I. Zegkinoglou, M.W. Haverkort (MPI) J. Geck, D.G. Hawthorn (UBC) R. Mathieu, Y. Tokura, S. Satow, H. Takagi (Tokyo) H.-H. Wu and C. Schussler-Langeheine (Cologne).