Magnetoelastic Spin Flip in La$_{1.4}$Sr$_{1.6}$Mn$_2$O$_7$

The magnetoelastic coupling in a bilayer manganite was investigated by using x-ray absorption spectroscopy (XAS) and resonant soft x-ray scattering (RSXS) at Mn $L_{2,3}$-edge. Huge occupation reversal of $e_g$ level from $d_{3z^2-r^2}$ to $d_{x^2-y^2}$ was observed at the temperature and magnetic field induced phase transition in La$_{1.4}$Sr$_{1.6}$Mn$_2$O$_7$. The CI model calculation indicated that the direction of magnetocrystalline anisotropy is affected by the configuration of $e_g$ level, and the sharp spin flip transition was expected. The field dependent RSXS measurements demonstrated a strong magnetoelastic coupling in La$_{1.4}$Sr$_{1.6}$Mn$_2$O$_7$, where the AFM spin axis was changed from out-of-plane to in-plane as a result of the field induced change of $e_g$ orbital occupation. Finally, we discuss the spin-orbital-lattice coupling in bilayer manganites.