On the origin of CE-type orbital fluctuations in the ferromagnetic metallic La_(1.2)Sr_(1.8)Mn₂O₇

We investigate the orbital fluctuations in the ferromagnetic-metallic phase of La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$ by considering a two orbital model within a tight-binding description which reproduces the ARPES Fermi surface. We find strong antisymmetric transverse orbital fluctuations at wavevector ($ 0.5 \pi, 0.5 \pi$) resulting from the Fermi-surface nesting between the portions of bonding and antibonding bands instead of the widely believed nesting between the portions of bonding band despite their flat segments, which provide an insight into the origin of so called CE-type orbital fluctuations in the ferromagnetic-metallic phase. Subsequent renormalization of the phonons near wavevector ($0.5 \pi,0.5 \pi$) and the behavior of the phonon linewidth as a function of momentum are in agreement with the inelastic neutron scattering experiments.